List of integer sequences with links to LODA programs.

  • A150500 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)}
  • A151019 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (-1, 0, 0), (1, 1, 0), (1, 1, 1)}
  • A151090 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 0), (0, 0, 1), (0, 1, 0), (1, 1, 1)}.
  • A151093 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 0, -1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
  • A151162 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
  • A151241 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}
  • A151251 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (0, 0, 1), (0, 1, 0), (1, 1, 0), (1, 1, 1)}
  • A151253 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, 0, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0)}.
  • A151254 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (1, 0, 0), (1, 0, 1), (1, 1, 0), (1, 1, 1)}.
  • A151281 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (1, 0), (1, 1)}.
  • A151282 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, 1), (1, 1)}.
  • A151292 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (0, 1), (1, 1)}
  • A151312 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 1), (-1, 0), (1, -1), (1, 0), (1, 1)}.
  • A151318 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 1), (-1, 0), (0, 1), (1, 0), (1, 1)}
  • A151323 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (0, -1), (0, 1), (1, 0), (1, 1)}.
  • A151332 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 4 n steps taken from {(-1, -1), (-1, 1), (1, 0)}
  • A151341 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 0)}.
  • A151345 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 1)}.
  • A151362 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of 2*n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 0), (1, 1)}.
  • A151374 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0, 0), ending on the vertical axis and consisting of 2n steps taken from {(-1, -1), (-1, 0), (1, 1)}.
  • A151379 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (1, -1), (1, 1)}.
  • A151383 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, 1)}
  • A151403 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (-1, 1), (1, 0), (1, 1)}.
  • A151410 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, 0), (1, -1), (1, 0), (1, 1)}.
  • A151471 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of 2 n steps taken from {(-1, -1), (-1, 0), (-1, 1), (1, -1), (1, 0), (1, 1)}.
  • A151478 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 1)}.
  • A151483 (program): Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0)}.
  • A151502 (program): a(n) = A006720(n)^4 (fourth powers of Somos-4 sequence).
  • A151542 (program): Generalized pentagonal numbers: a(n) = 12*n + 3*n*(n-1)/2.
  • A151548 (program): When A160552 is regarded as a triangle with rows of lengths 1, 1, 2, 4, 8, 16, …, this is what the rows converge to.
  • A151549 (program): a(n) = (A151548(n)-1)/2.
  • A151550 (program): Expansion of g.f. Product_{n >= 1} (1 + x^(2^n-1) + 2*x^(2^n)).
  • A151551 (program): G.f.: (1 + 3x) * Product_{n>=1} (1 + x^(2^n-1) + 2*x^(2^n)).
  • A151552 (program): G.f.: Product_{k>=1} (1 + x^(2^k-1) + x^(2^k)).
  • A151553 (program): G.f.: (1 + x) * Product_{n>=1} (1 + x^(2^n-1) + x^(2^n)).
  • A151554 (program): G.f.: (1 + 2x) * Product_{n>=1} (1 + x^(2^n-1) + x^(2^n)).
  • A151555 (program): G.f.: (1 + 2x) * Product_{n>=1} (1 + x^(2^n-1) + 2*x^(2^n)).
  • A151566 (program): Leftist toothpicks (see Comments for definition).
  • A151568 (program): a(0)=1, a(1)=1; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.
  • A151569 (program): a(0)=1, a(1)=2; a(2^i+j)=2*a(j)+a(j+1) for 0 <= j < 2^i.
  • A151575 (program): G.f.: (1+x)/(1+x-2*x^2).
  • A151576 (program): Number of permutations of 1..n arranged in a circle with exactly 3 adjacent element pairs in decreasing order.
  • A151577 (program): Number of permutations of 1..n arranged in a circle with exactly 4 adjacent element pairs in decreasing order.
  • A151583 (program): Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
  • A151590 (program): Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
  • A151597 (program): Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
  • A151603 (program): Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
  • A151607 (program): Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
  • A151610 (program): Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 2 adjacent element pairs in decreasing order.
  • A151665 (program): G.f.: Product_{k>=0} (1 + 3*x^(4^k)).
  • A151666 (program): Number of partitions of n into distinct powers of 4.
  • A151667 (program): Number of partitions of n into distinct powers of 5.
  • A151668 (program): G.f.: Product_{k>=0} (1 + 2*x^(3^k)).
  • A151669 (program): G.f.: Product_{k>=0} (1 + 2*x^(4^k)).
  • A151670 (program): G.f.: Product_{k>=0} (1 + 2*x^(5^k)).
  • A151671 (program): G.f.: Product_{k >= 0} (1 + 3*x^(5^k)).
  • A151672 (program): G.f.: Product_{k>=0} (1 + 4*x^(3^k)).
  • A151673 (program): G.f.: Product_{k>=0} (1 + 4*x^(4^k)).
  • A151674 (program): G.f.: Product_{k >= 0} (1 + 4*x^(5^k)).
  • A151675 (program): Row sums of A154685.
  • A151677 (program): a(n) = sum_{k >= 0} binomial(3*wt(n+k),k), where wt() = A000120().
  • A151678 (program): a(n) = sum_{k >= 0} binomial(wt(n+k),2*k), where wt() = A000120().
  • A151679 (program): a(n) = sum_{k >= 0} binomial(2*wt(n+k),k), where wt() = A000120().
  • A151680 (program): a(n) = sum_{k >= 0} binomial(wt(n+k),k+1), where wt() = A000120().
  • A151681 (program): a(n) = sum_{k >= 0, k even} binomial(wt(n+k),k+1), where wt() = A000120().
  • A151682 (program): a(n) = sum_{k >= 0, k odd} binomial(wt(n+k),k+1), where wt() = A000120().
  • A151685 (program): a(n) = Sum_{k >= 0} bin2(wt(n+k),k+1), where bin2(i,j) = A013609(i,j), wt(i) = A000120(i).
  • A151687 (program): G.f.: x + x^2 * Product_{n>=0} (1 + x^(2^n-1) + x^(2^n)).
  • A151688 (program): G.f.: Product_{n>=0} (1 + x^(2^n-1) + 2*x^(2^n)).
  • A151689 (program): a(n) = sum_{k >= 1} 2^wt(k) * binomial(wt(n+k),k).
  • A151690 (program): A151689/2.
  • A151692 (program): G.f.: Product_{k>=2} (1 + x^(2^k-1) + x^(2^k)).
  • A151702 (program): a(0)=1, a(1)=0; a(2^i + j) = a(j) + a(j+1) for 0 <= j < 2^i.
  • A151704 (program): a(0)=1, a(1)=0; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.
  • A151712 (program): a(n) = A048883(n) + 1.
  • A151714 (program): When A151552 is written as a triangle the rows converge to this.
  • A151740 (program): Composites that are the sum of two consecutive composite numbers.
  • A151741 (program): Composite which are the sum of three consecutive composite numbers.
  • A151746 (program): G.f.: (1-2*x-5*x^2+4*x^3)/((1-4*x)*(1-x)^2).
  • A151749 (program): a(0) = 1, a(1) = 3; a(n+2) = (a(n+1) + a(n))/2 if 2 divides (a(n+1) + a(n)), a(n+2) = a(n+1) + a(n) otherwise.
  • A151754 (program): Number of n-digit numbers that are divisible by 5^n.
  • A151757 (program): Positive integers n, excluding 1 and 2^i+1 for all i, having wt <= 3.
  • A151758 (program): G.f.: Theta^2-Theta, where Theta = Sum_{k>=0} x^(2^k).
  • A151763 (program): If n is a prime == 1 mod 4 then a(n) = 1, if n is a prime == 3 mod 4 then a(n) = -1, otherwise a(n) = 0.
  • A151774 (program): Characteristic function of numbers with binary weight 2 (A018900).
  • A151779 (program): a(1)=1; for n > 1, a(n)=6*5^{wt(n-1)-1}.
  • A151780 (program): a(n) = 5^(wt(n) - 1) where wt(n) = A000120(n).
  • A151781 (program): Partial sums of A151779.
  • A151782 (program): a(1)=1; for n > 1, a(n)=8*7^{wt(n-1)-1}.
  • A151783 (program): a(n) = 4^(wt(n) - 1) where wt(n) = A000120(n).
  • A151784 (program): a(n) = 6^(wt(n) - 1) where wt(n) = A000120(n).
  • A151785 (program): a(n) = 7^(wt(n) - 1) where wt(n) is the binary weight of n (A000120).
  • A151786 (program): a(n) = 8^(wt(n)-1) where wt(n) is the binary weight of n (A000120).
  • A151787 (program): a(1)=1; for n > 1, a(n)=3*2^{wt(n-1)-1}.
  • A151788 (program): Partial sums of A151787.
  • A151789 (program): a(1)=1; for n > 1, a(n)=5*4^{wt(n-1)-1}.
  • A151790 (program): Partial sums of A151789.
  • A151791 (program): a(1)=1; for n > 1, a(n) = 7*6^(wt(n-1)-1).
  • A151792 (program): Partial sums of A151791.
  • A151793 (program): Partial sums of A151782.
  • A151794 (program): a(1)=2, a(2)=4, a(3)=6; a(n+3) = a(n+2)+ 2*a(n), n>=1.
  • A151798 (program): a(0)=1, a(1)=2, a(n)=4 for n>=2.
  • A151799 (program): Version 2 of the “previous prime” function: largest prime < n.
  • A151800 (program): Least prime > n (version 2 of the “next prime” function).
  • A151816 (program): a(n) = n! - A001147(n)^2.
  • A151817 (program): a(n) = 2*(2*n)!/n!.
  • A151819 (program): First component x of pairs (x,y) where x!+y! is a square, sorted on x.
  • A151821 (program): Powers of 2, omitting 2 itself.
  • A151842 (program): a(3n)=n, a(3n+1)=2n+1, a(3n+2)=n+1.
  • A151859 (program): a(0)=0; a(1)=0; a(2)=0; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=2*a(j) + a(j + 1) except we add 1 if j=2^i-1.
  • A151860 (program): If A151859 is regarded as a triangle then the rows converge to this sequence.
  • A151861 (program): a(0)=0; a(1)=1; a(2)=1; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=2*a(j) + a(j + 1) except we add 1 if j=2^i-1.
  • A151862 (program): If A151861 is regarded as a triangle then the rows converge to this sequence.
  • A151863 (program): a(0)=1; a(1)=0; a(2)=2; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=2*a(j) + a(j + 1) except we add 1 if j=2^i-1.
  • A151864 (program): If A151863 is regarded as a triangle then the rows converge to this sequence.
  • A151881 (program): Sum (number of cycles)^2 over all n! permutations of [1..n].
  • A151885 (program): Similar to the original toothpick sequence A139250, except that the rule is now: a toothpick changes state if its midpoint is adjacent to exactly one ON toothpick.
  • A151888 (program): Net increase in number of ON toothpicks at generation n in A151885.
  • A151889 (program): a(1)=2, a(2)=3; a(2k-1)=2a(2k-2)+a(2k-3), a(2k)=3a(2k-2)+2a(2k-3), k >= 2.
  • A151890 (program): Triangle read by rows: T(l,c) = 2*l*c + l + c (0 <= c <= l).
  • A151898 (program): First differences of Frobenius numbers for 7 successive numbers A138987.
  • A151899 (program): Period 6: repeat [0, 0, 1, 1, 1, 2].
  • A151902 (program): a(n) = wt(k) + f(j) if n = 6k+j, 0 <= j < 6, where wt() = A000120(), f() = A151899().
  • A151904 (program): a(n) = (3^(wt(k)+f(j))-1)/2 if n = 6k+j, 0 <= j < 6, where wt = A000120, f = A151899.
  • A151905 (program): a(0) = a(2) = 0, a(1) = 1; for n >= 3, n = 3*2^k+j, 0 <= j < 3*2^k, a(n) = A151904(j).
  • A151906 (program): a(0) = 0, a(1) = 1; for n>1, a(n) = 8*A151905(n) + 4.
  • A151907 (program): Partial sums of A151906.
  • A151910 (program): First differences of A001682.
  • A151912 (program): Expansion of (1-8x-8x^3)/(1-2x+4x^2)^2.
  • A151914 (program): a(0)=0, a(1)=4; for n>=2, a(n) = (8/3)*(Sum_{i=1..n-1} 3^wt(i)) + 4, where wt() = A000120().
  • A151915 (program): Wythoff AAAA numbers.
  • A151916 (program): Numbers n such that A108197(n) = 0.
  • A151917 (program): a(0)=0, a(1)=1; for n>=2, a(n) = (2/3)*(Sum_{i=1..n-1} 3^wt(i)) + 1, where wt() = A000120().
  • A151919 (program): a(n) = (-2)^n*A_{n,3}(1/2) where A_{n,k}(x) are the generalized Eulerian polynomials.
  • A151920 (program): a(n) = (Sum_{i=1..n+1} 3^wt(i))/3, where wt() = A000120().
  • A151921 (program): Net gain in number of ON cells at stage n of the cellular automaton described in A079317.
  • A151922 (program): Number of first-quadrant cells (including the two boundaries) that are “ON” after n-th stage of the Holladay-Ulam cellular automaton.
  • A151923 (program): A079316(2n+1).
  • A151927 (program): Decimal expansion of 4*Pi^4/3.
  • A151928 (program): Decimal expansion of 8*Pi^6/27.
  • A151929 (program): First differences of A070952.
  • A151930 (program): First differences of A001316.
  • A151931 (program): First differences of A071049.
  • A151948 (program): a(n) = tau(sigma(phi(n))).
  • A151949 (program): a(n) = image of n under the Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).
  • A151953 (program): Primes of the form 6*n^2+17.
  • A151954 (program): Expansion of Product_{k>0} (1-k^2*x^k)^(-1/k).
  • A151961 (program): Semiperimeter of the n-th Heronian triangle.
  • A151969 (program): a(n) = smallest integer >= n which has only prime factors 2 and 5.
  • A151970 (program): a(n) = smallest integer >= n which has only prime factors 3 and 5.
  • A151971 (program): Numbers n such that n^2 - n is divisible by 21.
  • A151972 (program): Numbers that are congruent to {0, 1, 6, 10} mod 15.
  • A151973 (program): Numbers n such that n^2 - n is divisible by 24.
  • A151974 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)/8.
  • A151975 (program): The number of ways one can flip seven consecutive tails (or heads) when flipping a coin n times.
  • A151976 (program): Minimal recursive sequence beginning with 5 similar to N with respect to property of integer to be or not to be in A079523.
  • A151977 (program): Numbers that are congruent to {0, 1} mod 16.
  • A151978 (program): Numbers that are congruent to {0, 1} mod 17.
  • A151979 (program): Numbers congruent to {0, 1} (mod 19).
  • A151980 (program): Numbers n such that n^2 - n is divisible by 20.
  • A151981 (program): Numbers n such that n^2 - n is divisible by 48.
  • A151982 (program): Arrangement of Fibonacci-numbers in a centered triangular fashion, such that every number is the difference and/or sum of adjacent numbers.
  • A151983 (program): Numbers congruent to {0, 1} mod 32.
  • A151984 (program): Numbers that are congruent to {0, 1} mod 64.
  • A151988 (program): G.f.: (x*(x^4+1)*(x^2-x+1)*(x^2+x+1))/((x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)*(x-1)^2).
  • A151989 (program): a(n) = A001512(n)/24 = (5*n+1)*(5*n+2)*(5*n+3)*(5*n+4)/24.
  • A151990 (program): If p and q are (odd) twin primes and q > p then p*q^2 + (p + q) + 1 is divisible by 6; a(n) = (p*q^2 + (p + q) + 1)/6.
  • A151997 (program): a(n) = (n 1’s followed by a 3)^2.
  • A151998 (program): Directed genus of the binary de Bruijn graph D_n.
  • A152009 (program): (L)-sieve transform of {1,4,7,10,…,3n-2,…} (A016777)
  • A152010 (program): Sum of digits of A127335(n).
  • A152011 (program): a(0) = 1 and a(n) = (3^n - (-1)^n)/2 for n >= 1.
  • A152015 (program): a(n) = n^3 - n^2 - n.
  • A152016 (program): a(n) = n^4 - n^3 - n^2 - n.
  • A152017 (program): a(n) = n^5-n^4-n^3-n^2-n.
  • A152018 (program): Denominator of 1/n^2-1/(3n)^2 or of 8/(9n^2).
  • A152020 (program): Denominator of 8/(9n^2) divided by 9.
  • A152029 (program): a(n) = 2^n*(2*n)!/((n+1)!).
  • A152030 (program): a(n)=n^6-n^5-n^4-n^3-n^2-n.
  • A152031 (program): a(n) = n^5 + n^4 + n^3 + n^2 + n.
  • A152032 (program): a(n) = 3/8+(3/8)*(-1)^n+((n+1)/4)*(-1)^(n+1)+((n+2)*(n+1)/4)*(-1)^(n+2).
  • A152035 (program): G.f.: (1-2*x^2)/(1-2*x-2*x^2).
  • A152036 (program): Triangular product sequence based 2^n times the Fibonacci version and 4 replaced with m: t(m,n)=2^n*Product[(1 + m*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}].
  • A152041 (program): A008893/2.
  • A152046 (program): a(n) = Product_{k=1..floor((n-1)/2)} (1 + 8*cos(k*Pi/n)^2) for n >= 0.
  • A152053 (program): a(n) = A144433(3n+1) + A144433(3n+2) + A144433(3n+3).
  • A152055 (program): a(n) = ((8+sqrt3)^n + (8-sqrt3)^n/2.
  • A152056 (program): a(n) = ((9+sqrt(3))^n + (9-sqrt(3))^n)/2.
  • A152059 (program): a(n) is the number of ways 2n-1 seats can be occupied by at most n people for n>=1, with a(0)=1.
  • A152061 (program): Counts of unique periodic binary strings of length n.
  • A152064 (program): a(n) = 2*n^3 - 3*n^2 + 5.
  • A152065 (program): A triangular sequence of polynomial coefficients: p(x,n)=If[n == 0, x^n - x^Floor[(n - 1)/2]*Sum[x^m, {m, 0, n - Floor[(n - 1)/2] - 1}] + 1/x, x^n - x^Floor[(n - 1)/2]*Sum[x^m, {m, 0, n - Floor[(n - 1)/2] - 1}] + 1].
  • A152078 (program): Numbers a(n) for which A000695(a(n)) = A077718(n).
  • A152083 (program): Number of occurrences of “I” in all Roman numerals of numbers from 1 to n
  • A152086 (program): a(n) = Sum_{k=1..n-1} k*A110971(n,k).
  • A152087 (program): Primes p such that q - p is not squarefree, where q is the next prime immediately following p.
  • A152090 (program): a(n) = 2^n*Product_{k=1..floor((n-1)/2)} (1 + 2*cos(k*Pi/n)^2 + 4*cos(k*Pi/n)^4).
  • A152094 (program): Quartic product sequence: a(n) = Product_{k=1..floor((n-1)/2)} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4 ), with m = 2*4, q=2*4^3.
  • A152098 (program): Quartic product sequence: m = 4; p = 4^3; a(n) = Product_{k=1..(n-1)/2} ( 1 + m*cos(k*Pi/n)^2 + p*cos(k*Pi/n)^4 ).
  • A152099 (program): Semiprimes based on powers of two and primes: a(n)=(2^Prime[n] - 1)*(2^Prime[n] + 1)=2^(2*Prime[n])-1.
  • A152100 (program): G.f.: 1 - 2*x*(-7 - 10*x + x^2)/(x - 1)^4.
  • A152101 (program): a(n)=16^n - 3*2^(2*n - 1) - 1.
  • A152103 (program): a(n) = 2^n*Product_{k=1..floor((n-1)/2)} (1 + 2*cos(k*Pi/n)^2 + 4*cos(k*Pi/n)^4).
  • A152104 (program): Quartic product sequence: a(n) = 2^n*Product_{k=1..(n-1)/2} (1 + m*cos(k*Pi/n)^2 + q*cos(k*Pi/n)^4), with m=6, q=4.
  • A152105 (program): a(n) = ((8 + sqrt4)^n + (8 - sqrt4)^n)/2.
  • A152106 (program): a(n) = (11^n + 7^n)/2.
  • A152107 (program): a(n) = ((6+sqrt(5))^n+(6-sqrt(5))^n)/2.
  • A152108 (program): a(n) = ((7+sqrt(5))^n + (7-sqrt(5))^n)/2.
  • A152109 (program): a(n) = ((8+sqrt(5))^n + (8-sqrt(5))^n)/2.
  • A152110 (program): G.f.: -2*(-2 - 11*x - 4*x^2 + x^3)/(x - 1)^4.
  • A152113 (program): A001333 with terms repeated.
  • A152114 (program): Numbers a(n) are obtained by the application of an algorithm which is similar to sieve of Eratosthenes for A000045: retaining A000045(3)=2, we delete all multiples of 2, which are more than 2; retaining A000045(4)=3, we delete all multiples of 3, which are more than 3, etc.
  • A152117 (program): a(n) = n*(n-th prime) + (n+1)*((n+1)-th prime).
  • A152118 (program): a(n) = product( 4 +4*cos(k*Pi/n)^2, k=1..(n-1)/2 ).
  • A152119 (program): a(n) = Product_{k=1..(n-1)/2} (5 + 4*cos(k*Pi/n)^2).
  • A152120 (program): a(n) = 2^n * Product_{k=1..(n-1)/2} (2 + 3*cos(k*Pi/n)^2).
  • A152125 (program): Consider a square grid with side n consisting of n^2 cells (or points); a(n) is the minimal number of points that can be painted black so that, out of any four points forming a square with sides parallel to the sides of the grid, at least one of the four is black.
  • A152126 (program): If f(x) = x^3+x^5+x^11+x^17+x^29+x^41+…, where the exponents are the smaller twin of twin prime pairs, consider {f(x)}^2 and write the exponents of that expansion down : x^6+2x^8+x^10+2x^12+…. The proposed sequence is that sequence of exponents
  • A152132 (program): Maximal length of rook tour on an n X n+1 board.
  • A152133 (program): Maximal length of rook tour on an n X n+2 board.
  • A152134 (program): Maximal length of rook tour on an n X n+3 board.
  • A152135 (program): Maximal length of rook tour on an n X n+4 board.
  • A152148 (program): Riordan array [exp(-x/2)(1-2x)^(-1/4),x].
  • A152151 (program): Riordan array [(1-x)exp(x/(1-x)),x]
  • A152152 (program): A sequence related to sine products and the Fibonacci numbers A000045: a(n) = Product_{k=1..n} (1 + 4*sin(2*Pi*k/n)^2).
  • A152158 (program): A sequence set up on the first 1000 base ten Pi digits: a(n)=a(n-1)+a(n-2)*Floor[Mod[N[Pi*10^(n - 2), 1000], 10]].
  • A152161 (program): a(n) = 100*n^2 + 100*n + 21.
  • A152163 (program): a(n) = a(n-1)+a(n-2), n>1 ; a(0)=1, a(1)=-1.
  • A152166 (program): a(2*n) = 2^n; a(2*n+1) = -(2^(n+1)).
  • A152167 (program): a(n)=-a(n-1)+3*a(n-2), n>1 ; a(0)=1, a(1)=-3 .
  • A152170 (program): a(n) is the total size of all the image sets of all functions from [n] to [n]. I.e., a(n) is the sum of the cardinalities of every image set of every function whose domain and co-domain is {1,2,…,n}.
  • A152171 (program): G.f. := (1-sqrt(1-4*x+4*x^2-4*x^3))/(2(1-x+x^2)x)
  • A152174 (program): a(n) = -2*a(n-1)+4*a(n-2), n>1 ; a(0) = 1, a(1) = -4.
  • A152179 (program): (n^2-2=A008865) mod 9. Period 9:repeat 8,2,7,5,5,7,2,8,7.
  • A152185 (program): a(n) = -3*a(n-1) + 5*a(n-2), n > 1; a(0)=1, a(1)=-5.
  • A152187 (program): a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=5.
  • A152189 (program): Product_{k=1..floor((n-1)/2)} (1 + 4*cos(k*Pi/n)^2)*(1 + 4*sin(k*Pi/n)^2).
  • A152192 (program): a(n) = Product_{k=1..floor((n-1)/2)} (1 + 4*cos(2*Pi*k/n)^2).
  • A152195 (program): Triangle read by rows, A000012 * A152194
  • A152198 (program): Triangle read by rows, A007318 rows repeated.
  • A152199 (program): Trajectory of 7 under the map m -> A082010(m).
  • A152201 (program): Triangle read by rows, A000012 * A152198
  • A152203 (program): Triangle T(n,k) = (2n+1-2k)*fibonacci(k), read by rows.
  • A152204 (program): Triangle read by rows: T(n,k) = 2*n-4*k+5 (n >= 0, 1 <= k <= 1+floor(n/2)).
  • A152205 (program): Triangle read by rows, A000012 * A152204.
  • A152206 (program): a(n) = sum of base-2 digits of A037308(n) = sum of base-10 digits of A037308(n).
  • A152211 (program): a(n) = n * sigma_0(n) + sigma_1(n).
  • A152223 (program): a(n) = -4*a(n-1) + 6*a(n-2) for n > 1 with a(0) = 1 and a(1) = -6.
  • A152224 (program): a(n)=4*a(n-1)+6*a(n-2), n>1 ; a(0)=1, a(1)=6 .
  • A152225 (program): Number of Dyck paths of semilength n with no peaks at height 0 (mod 3) and no valleys at height 2 (mod 3).
  • A152226 (program): Binomial transform of A027826.
  • A152231 (program): Similar to A072921 but starting with 2.
  • A152232 (program): Similar to A072921 but starting with 3.
  • A152233 (program): Similar to A072921 but starting with 4.
  • A152234 (program): Similar to A072921 but starting with 5.
  • A152235 (program): Largest squarefree number dividing the number of divisors n.
  • A152236 (program): A modulo two parity function as a triangle sequence: t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, Binomial[n, m], If[Mod[Binomial[ n, m], 2] == 1 && Binomial[n, m] > 1, 1 + Binomial[n, m], 0]].
  • A152237 (program): A modulo two parity function as a triangle sequence:k=1; t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]].
  • A152238 (program): A modulo two parity function as a triangle sequence:k=2; t(n,m)=Binomial[n,m]+p(n,m); Always even parity function: p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]].
  • A152239 (program): a(n) = -5*a(n-1) + 7*a(n-2) for n > 1 with a(0) = 1 and a(1) = -7.
  • A152240 (program): a(n)=5*a(n-1)+7*a(n-2), n>1 ; a(0)=1, a(1)=7 .
  • A152241 (program): Products of cubes of 2 successive primes.
  • A152251 (program): Eigentriangle, row sums = A001519, odd-indexed Fibonacci numbers.
  • A152252 (program): Triangle read by rows, M*Q, where M = an infinite lower triangular matrix with powers of 3 prefaced by a 1 in every row: (1, 1, 3, 9, 27, …) and Q = a matrix with A006012 prefaced by a 1 as the main diagonal and the rest zeros.
  • A152254 (program): Twice A084773.
  • A152256 (program): a(n) = (3^n - 1)*(3^n + 1)*(3^n + 1)/32.
  • A152257 (program): a(n) = (3^n - 1)^2*(3^n + 1)/16.
  • A152258 (program): a(n) = ((3^n - 1)*(3^n + 1))^2/2^(7 - (n mod 2)).
  • A152261 (program): a(n) = ((9 + sqrt(5))^n + (9 - sqrt(5))^n)/2.
  • A152262 (program): a(n) = 14*a(n-1) - 43*a(n-2), n > 1; a(0)=1, a(1)=7.
  • A152263 (program): a(n) = ((8 + sqrt(6))^n + (8 - sqrt(6))^n)/2.
  • A152264 (program): a(n) = ((9+sqrt(6))^n + (9-sqrt(6))^n)/2.
  • A152265 (program): a(n) = ((8+sqrt(7))^n + (8-sqrt(7))^n)/2.
  • A152266 (program): a(n) = ((9 + sqrt(7))^n + (9 - sqrt(7))^n)/2.
  • A152267 (program): a(n) = ((9 + sqrt(8))^n + (9 - sqrt(8))^n)/2.
  • A152268 (program): A hidden Markov recursion involving the matrices: M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}}; as Mh=M0.M.(M0+I); v[(n)=Mh.v(n-1): first element of v.
  • A152269 (program): A switched hidden Markov recursion involving the matrices: M0 = {{0, 1}, {1, 1/2}}; M = {{0, 2}, {2, 1}}; as Mh=M0.M.(M0+I*mod[n.2]); v[(n)=Mh.v(n-1): first element of v.
  • A152271 (program): a(n)=1 for even n and (n+1)/2 for odd n.
  • A152291 (program): a(n) = (n+1)^floor((n-1)/2).
  • A152297 (program): Alternate binomial partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
  • A152298 (program): a(n) = (3^n-1)/2 if n odd, (3^n-1)/8 if n even.
  • A152299 (program): A threes sequence that gets more even factors out: a(n)=(3^n - 1)*(3^n + 1)/2^(4 - Mod[n, 2]).
  • A152302 (program): Marsaglia-Zaman type recursive sequence: f(x)=f(x - 1) + f(x - 2) + Floor[f(x - 1)/10]; a(n)=Mod[f(n),10].
  • A152303 (program): Marsaglia-Zaman type recursive sequence as a vector Markov: M = {{0, 1}, {1, 1}}; M1 = {{0, 0}, {1/10, 0}}; v(n)=M.v(n-1)+Floor[M1.v(n-1),10] a(n)=Mod[v(n)[[1]],10].
  • A152305 (program): Marsaglia-Zaman type recursive sequence: f(x)=f(x - 2) + f(x - 3) + Floor[f(x - 1)/10]; a(n)=Mod[f(n),10].
  • A152390 (program): Arises in enumerating non-degenerate colorings in Brook’s Theorem.
  • A152416 (program): Decimal expansion of 2 - Pi^2/6.
  • A152417 (program): a(n) = (5^n - 1)/(2^(3 - (n mod 2))).
  • A152418 (program): A sevens sequence: a(n)=(7^n - 1)/(2^(4 - 3*Mod[n, 2])).
  • A152420 (program): Irregular triangle read by rows: T(n,k) = n*(n-2) - (k-n)*(k-n-2), with 0 <= k <= 2*n.
  • A152421 (program): a(n) = binomial(A000290(n), A006218(n)).
  • A152422 (program): Decimal expansion of (sqrt(3)-1)/2.
  • A152423 (program): A variation of the Josephus problem, removing every other person, starting with person 1; a(n) is the last person remaining.
  • A152424 (program): a[n_]:=IntegerPart[Prime[n^n]^(1/n)];
  • A152429 (program): a(n) = (11^n + 5^n)/2.
  • A152435 (program): a(n)=(11^n - 1)/(5*2^(3 - 2*Mod[n, 2])).
  • A152436 (program): a(n)=(13^n - 1)/(3*2^(3 - Mod[n, 2])).
  • A152437 (program): (17^n - 1)/(2^(5 - (n % 2))).
  • A152438 (program): a(n)=(19^n - 1)/(9*2^(3 - 2*Mod[n, 2])).
  • A152440 (program): Riordan matrix (1/(1-x-x^2),x/(1-x-x^2)^2).
  • A152442 (program): n is included if the largest divisor of n that is coprime to d(n) is a composite, where d(n) is the number of divisors of n.
  • A152448 (program): a(0)=a(1)=1, a(2)=6, a(3)=11; a(n+4) = 10*a(n+2) - a(n).
  • A152450 (program): a(0)=a(1)=1, a(2)=4, a(3)=7, a(n+4) = 10*a(n+2) - a(n).
  • A152455 (program): a(n) = minimal integer m such that there exists an m X m integer matrix of order n.
  • A152456 (program): a(n)=1*(n+2)!-2*(n+1)!-3*n!.
  • A152457 (program): Partial sums of A027444.
  • A152465 (program): Degrees of irreducible representations of SL(2,9).
  • A152467 (program): a(n) = floor(n/6).
  • A152470 (program): Largest of three consecutive primes whose sum is a prime.
  • A152476 (program): Inverse binomial transform of A005329.
  • A152481 (program): Degrees of irreducible representations of SL(2,11).
  • A152482 (program): Even numbers which are not the sum of 2 even semiprimes.
  • A152485 (program): Degrees of irreducible representations of SL(2,13).
  • A152494 (program): 1/3 of the number of permutations of 2 indistinguishable copies of 1..n with exactly 2 local maxima.
  • A152499 (program): 1/12 of the number of permutations of 3 indistinguishable copies of 1..n with exactly 2 local maxima.
  • A152521 (program): Juxtaposition of prime(2n-1) and prime(2n) is a prime.
  • A152524 (program): a(n) is the number of L-bit words in which, if up to k bits are perturbed, the resulting change in unsigned L-bit value is n, for L=8 and k=7.
  • A152527 (program): a(n) = (p(n)*p(n+1)-p(n+2))/2, where p(n) is the n-th odd prime.
  • A152528 (program): a(n) = p(n)*p(n+2) - 3*p(n+1), where p(n) is the n-th prime.
  • A152529 (program): a(n) = (p(n)*p(n+2) - 3*p(n+1))/2, where p(n) is the n-th odd prime.
  • A152530 (program): a(n) = p(n)*p(n+2)-p(n+1), where p(n) is the n-th prime.
  • A152531 (program): a(n) = (p(n)*p(n+2) - p(n+1))/2, where p(n) is the n-th odd prime.
  • A152532 (program): a(n) = prime(n) * prime(n+2) - 2 * prime(n+1).
  • A152535 (program): a(n) = n*prime(n) - Sum_{i=1..n} prime(i).
  • A152537 (program): Convolution sequence: convolved with A000041 = powers of 2, (A000079).
  • A152539 (program): Partial sum of A146538.
  • A152540 (program): Primes p of the form A152539(n) + 1.
  • A152548 (program): Sum of squared terms in rows of triangle A152547: a(n) = Sum_{k=0..C(n,[n/2])-1} A152547(n,k)^2.
  • A152551 (program): a(n) = (2*n+1)^floor((n-1)/2).
  • A152556 (program): a(n) = 2*(2*n+2)^floor((n-1)/2).
  • A152568 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 2^(n - 1), T(n,k) = -2^(n - k - 1), 1 <= k <= n - 1.
  • A152570 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 3^(n - 1), T(n,k) = -3^(n - k - 1), 1 <= k <= n - 1.
  • A152571 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 4^(n - 1), T(n,k) = -4^(n - k - 1), 1 <= k <= n - 1.
  • A152572 (program): Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 5^(n - 1), T(n,k) = -5^(n - k - 1), 1 <= k <= n - 1
  • A152574 (program): Numbers n such that entering (N*0.3/N*0.1) on a Rumor LG Sprint cell phone produced the value 2 instead of 3, where N = n * (2**k) for k = 0, 1, 2, ….
  • A152577 (program): a(n) = 10^(2*n - 1) + 1.
  • A152579 (program): a(n) = (10*n+3)*(10*n+17).
  • A152584 (program): Decimal expansion of (Pi^3)/24.
  • A152594 (program): a(n) = -5*a(n-1)-2*a(n-2), n>1 ; a(0)=1, a(1)=-1 .
  • A152596 (program): a(n) = 7*a(n-1) - 6*a(n-2), n>1; a(0)=1, a(1)=3.
  • A152599 (program): a(n)=10*a(n-1)-12*a(n-2), n>1 ; a(0)=1, a(1)=4 .
  • A152600 (program): a(n)=0^n+sum{k=0..n-1, C(n+k-1,2k)*A000108(k)*3^k*2^(n-k)}
  • A152601 (program): a(n) = Sum_{k=0..n} C(n+k,2k)*A000108(k)*3^k*2^(n-k).
  • A152618 (program): a(n) = (n-1)^2*(n+1).
  • A152619 (program): n*(n+2)^2
  • A152620 (program): a(n)=-8*a(n-1)-6*a(n-2), n>1 ; a(0)=1, a(1)=-2 .
  • A152621 (program): a(n)=8*a(n-1)-6*a(n-2), n>1 ; a(0)=1, a(1)=2.
  • A152622 (program): Tetrahedral numbers n*(n+1)*(n+2)/6 with n, n+1 and n+2 nonprime.
  • A152623 (program): Decimal expansion of 3/2.
  • A152624 (program): Decimal expansion of 7/2.
  • A152627 (program): Decimal expansion of 3/4.
  • A152648 (program): Decimal expansion of 2*zeta(3).
  • A152649 (program): Decimal expansion of Pi^4/72.
  • A152653 (program): a(n) = (n-1)! * Product_{k=1..n-2} (n-k)!.
  • A152659 (program): Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) with steps E=(1,0) and N=(0,1) and having k turns (NE or EN) (1<=k<=2n-1).
  • A152661 (program): Number of permutations of [n] for which the first two entries have the same parity (n>=2).
  • A152663 (program): Number of leading odd entries in all permutations of {1,2,…,n} (see example).
  • A152665 (program): Number of leading even entries in all permutations of {1,2,…,n}.
  • A152668 (program): Number of runs of even entries in all permutations of {1,2,…,n} (the permutation 274831659 has 3 runs of even entries: 2, 48 and 6).
  • A152669 (program): Last digit of Catalan number A000108(n).
  • A152670 (program): Even Catalan numbers.
  • A152671 (program): Even Catalan numbers divided by 2.
  • A152672 (program): a(n) is the number of distinct tuples of up to k bit locations in L-bit words, in which, if bits are perturbed, the resulting change in unsigned L-bit value is n, for L=8 and k=7.
  • A152674 (program): Number of divisors of the numbers that are not squares.
  • A152677 (program): Subsequence of odd terms in A000203 (sum-of-divisors function sigma), in the order in which they occur and with repetitions.
  • A152678 (program): Even members of A000203.
  • A152679 (program): Even members of A000203, divided by 2.
  • A152680 (program): a(n) = 4*A005098(n) = A002144(n) - 1.
  • A152681 (program): [x^(n+1)]Reversion[x*(1-x)/(1-3*x)].
  • A152684 (program): a(n) is the number of top-down sequences (F_1, F_2, …, F_n) whereas each F_i is a labeled forest on n nodes, containing i directed rooted trees. F_(i+1) is proper subset of F_i.
  • A152686 (program): Partial products of the partial products of the nonzero Fibonacci numbers.
  • A152687 (program): Partial products operator applied thrice to nonzero Fibonacci numbers.
  • A152689 (program): Apply partial sum operator thrice to factorials.
  • A152690 (program): Partial sums of superfactorials (A000178).
  • A152691 (program): Multiples of 64.
  • A152692 (program): a(n) = n*3^n - n*2^n - n*1^n.
  • A152714 (program): Triangle read by rows: T(n,k) = 3^min(k, n-k).
  • A152716 (program): Triangle T(n,k) read by rows: T(n,k) = 4^min(k, n-k) = 4^A004197(n,k).
  • A152717 (program): Triangle T(n,k) read by rows: T(n,k) = 5^min(k, n-k) = 5^A004197(n,k).
  • A152718 (program): a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) - a(n-4) + a(n-5), n > 5.
  • A152719 (program): Triangle read by rows: T(n,k) = A000129( 1 + min(k,n-k) ), n>=0, 0<=k<=n.
  • A152723 (program): In binary, count of least frequent bit of n.
  • A152724 (program): In binary, count of most frequent bit of n.
  • A152725 (program): a(n) = n*(n+1)*(n^4 + 2*n^3 - 2*n^2 - 3*n + 3)/2.
  • A152726 (program): a(n) = n^7 - (n-1)^7 + (n-2)^7 - … + ((-1)^n)*0^7.
  • A152727 (program): Smallest positive non-divisor of the n-th Fibonacci number (A000045).
  • A152728 (program): a(n) + a(n+1) + a(n+2) = n^3.
  • A152729 (program): a(n) = (n-2)^4 - a(n-1) - a(n-2), with a(1) = a(2) = 0.
  • A152730 (program): a(n) + a(n+1) + a(n+2) = n^5, with a(1) = a(2) = 0.
  • A152731 (program): a(n) + a(n+1) + a(n+2) = n^6, a(1)=a(2)=0.
  • A152732 (program): a(n) + a(n+1) + a(n+2) = 2^n.
  • A152733 (program): a(n) + a(n+1) + a(n+2) = 3^n.
  • A152734 (program): 5 times pentagonal numbers: 5*n*(3*n-1)/2.
  • A152738 (program): a(n) = floor((n^2)/phi).
  • A152740 (program): 11 times triangular numbers.
  • A152741 (program): 13 times triangular numbers.
  • A152742 (program): 13 times the squares: a(n) = 13*n^2.
  • A152743 (program): 6 times pentagonal numbers: a(n) = 3*n*(3*n-1).
  • A152744 (program): 7 times pentagonal numbers: a(n) = 7*n*(3*n-1)/2.
  • A152745 (program): 5 times hexagonal numbers: 5*n*(2*n-1).
  • A152746 (program): Six times hexagonal numbers: 6*n*(2*n-1).
  • A152749 (program): a(n) = (n+1)*(3*n+1)/4 for n odd, a(n) = n*(3*n+2)/4 for n even.
  • A152750 (program): Eight times hexagonal numbers: 8*n*(2*n-1).
  • A152751 (program): 3 times octagonal numbers: 3*n*(3*n-2).
  • A152752 (program): Terms of A118962 that are == 9 (mod 10).
  • A152753 (program): Last digit of even Catalan number A152670(n).
  • A152756 (program): Bisection of A000533.
  • A152757 (program): Numbers k such that the deficiency of k plus the number of proper divisors of k is a prime number (see A152864).
  • A152758 (program): Numbers k such that the deficiency of k plus the number of proper divisors of k is not a prime number (see A152864).
  • A152759 (program): 3 times 9-gonal (or nonagonal) numbers: 3n(7n-5)/2.
  • A152760 (program): 4 times 9-gonal numbers: a(n) = 2*n*(7*n-5).
  • A152761 (program): Sum of divisors of Catalan number A000108(n).
  • A152762 (program): Sum of proper divisors of Catalan number A000108(n).
  • A152763 (program): Number of divisors of Catalan number A000108(n).
  • A152764 (program): Bisection of A138144.
  • A152765 (program): Smallest prime divisor of Catalan number A000108(n), with a(0) = a(1) = 1.
  • A152766 (program): Largest proper divisor of the Catalan number A000108(n).
  • A152767 (program): 3 times 10-gonal (or decagonal) numbers: 3n(4n-3).
  • A152769 (program): Numbers n such that pi(n) is nonprime.
  • A152770 (program): Sum of proper divisors minus the number of proper divisors of n: a(n) = sigma(n) - n - d(n) + 1.
  • A152771 (program): a(n) = sigma(n) - 2*d(n) + 1.
  • A152772 (program): a(n) = sigma(n) - 3*d(n) + 3.
  • A152773 (program): 3 times heptagonal numbers: a(n) = 3n(5n-3)/2.
  • A152775 (program): Numbers with 3n binary digits where every run length is 3, written in binary.
  • A152776 (program): Numbers such that every run length in base 2 is 3.
  • A152777 (program): 7 times heptagonal numbers: 7*n*(5*n-3)/2.
  • A152785 (program): a(n)=Floor[(n^2)/Catalan].
  • A152786 (program): Integers k such that (k^2)/2 is the arithmetic mean of a pair of twin primes.
  • A152810 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives odd n such that e(n) > o(n) and e(n)-o(n) == 1 or 2 (mod 6).
  • A152811 (program): a(n) = 2*(n^2 + 2*n - 2).
  • A152813 (program): a(n) = 2*n^2 + 10*n + 3.
  • A152815 (program): Triangle T(n,k), read by rows given by [1,0,-1,0,0,0,0,0,0,…] DELTA [0,1,-1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A152818 (program): Array read by antidiagonals: T(n,k) = (k+1)^n*(n+k)!/n!.
  • A152822 (program): Periodic sequence [1,1,0,1] of length 4.
  • A152823 (program): Largest divisor < n of n^2 + 1, a(1) = 1.
  • A152827 (program): Partial products of PartitionsQ numbers (A000009).
  • A152828 (program): Triangle read by rows, A007318 rows repeated three times .
  • A152829 (program): Numbers k whose squares can be written in exactly one way as a sum of three squares: k^2 = a^2 + b^2 + c^2 with 1 <= a <= b <= c.
  • A152830 (program): Triangle read by rows, A007318 rows repeated four times .
  • A152831 (program): Triangle read by rows, A007318 repeated five times .
  • A152832 (program): a(0) = -2; a(n) = n - a(n-1) for n > 0.
  • A152833 (program): a(0) = -3; a(n) = n-a(n-1).
  • A152834 (program): Numbers of form 6k+1 that use only digits 2 and 3.
  • A152835 (program): a(0) = -22; a(n) = n-a(n-1).
  • A152842 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,…] DELTA [3,-2,-1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A152843 (program): Numbers n such that both 2n+3 and 4n+7 are prime.
  • A152847 (program): Triangle read by rows, A007318 rows repeated nine times .
  • A152848 (program): Triangle read by rows, A007318 rows repeated ten times .
  • A152849 (program): Triangle read by rows, A007318 rows repeated eleven times .
  • A152854 (program): Numbers n such that either 2n+3 is not prime or 4n+7 is not prime.
  • A152855 (program): Periodic sequence [1,2,0,2,0] of period 5
  • A152856 (program): Periodic sequence [4,0,4,3,4] of period 5
  • A152857 (program): Period 5: repeat [0, 2, 3, 0, 0].
  • A152864 (program): Deficiency of n, plus the number of proper divisors of n: a(n) = 2n - sigma(n) + d(n) - 1.
  • A152873 (program): Number of permutations of {1,2,…,n} (n>=2) having a single run of even entries. For example, the permutation 513284679 has a single run of even entries: 2846.
  • A152875 (program): Number of permutations of {1,2,…,n} (n >= 2) with all odd entries preceding all even entries or all even entries preceding all odd entries.
  • A152881 (program): Positions of those 1’s that are followed by a 0, summed over all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
  • A152883 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} in which k is an excedance (n >= 2, 1 <= k <= n-1). An excedance of a permutation p is a value j such that p(j) > j.
  • A152885 (program): Number of descents beginning and ending with an odd number in all permutations of {1,2,…,n}.
  • A152886 (program): Number of descents beginning and ending with an even number in all permutations of {1,2,…,n}.
  • A152887 (program): Number of descents beginning with an even number and ending with an odd number in all permutations of {1,2,…,n}.
  • A152888 (program): Partial sums of length of terms in A081368 where A081368(1) is set to 0.
  • A152889 (program): Periodic sequence [1,0,4,0,0] of period 5
  • A152890 (program): Periodic sequence [4,1,4,0,1] of period 5
  • A152891 (program): a(1) = b(1) = 0; for n > 1, b(n) = b(n-1) + n-1 + a(n-1) and a(n) = a(n-1) + n-1 + b(n).
  • A152892 (program): Period 5: repeat [0, 3, 1, 0, 1].
  • A152893 (program): Periodic sequence [3, 3, 0, 0, 4] of period 5
  • A152894 (program): Periodic sequence [0,0,1,4,0] of period 5.
  • A152895 (program): Partial sums of A152891.
  • A152896 (program): a=b=c=0;c(n)=c+n+a;b(n)=b+n+c;a(n)=a+n+b.
  • A152897 (program): Partial sums of A152896.
  • A152898 (program): Periodic sequence [1,4,0,0,0] of period 5
  • A152902 (program): Convolution sequence, A000027 / A008683
  • A152904 (program): Triangle read by rows: T(n,k) = A008683(n-k+1); 1<=k<=n; mu(n) “decrescendo”.
  • A152906 (program): Irregular triangle read by rows, numbers in A007318 repeated three times .
  • A152907 (program): Irregular triangle read by rows, numbers in A007318 repeated four times .
  • A152912 (program): Primes p such that 2*p^2-1 is not prime.
  • A152915 (program): Exponacci (or exponential Fibonacci) numbers.
  • A152917 (program): A000169 prefixed by an initial 0.
  • A152919 (program): a(1)=1, for n>1, a(n) = n^2/4 + n/2 for even n, a(n) = n^2/4 + n - 5/4 for odd n.
  • A152920 (program): Triangle read by rows: triangle A062111 reversed.
  • A152927 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 1 as k varies.
  • A152928 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two m-gonal polygonal components chained with string components of length 1 as m varies.
  • A152929 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two 4-gonal polygonal components chained with string components of length l as l varies.
  • A152930 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 4-gonal polygonal components chained with string components of length 2 as k varies.
  • A152933 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of k 6-gonal polygonal components chained with string components of length 2 as k varies.
  • A152934 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defining a polygonal configuration consisting of two m-gonal polygonal components chained with string components of length 3 as m varies.
  • A152947 (program): a(n) = 1 + (n-2)*(n-1)/2.
  • A152948 (program): a(n) = (n^2 - 3*n + 6)/2.
  • A152949 (program): a(n) = 3 + binomial(n-1,2).
  • A152950 (program): a(n) = 3 + n*(n-1)/2.
  • A152958 (program): Alladi’s third-order function phi_3(n).
  • A152965 (program): Twice 12-gonal numbers: a(n) = 2*n*(5*n-4).
  • A152966 (program): Twice repdigit numbers.
  • A152967 (program): Partial sums of A152770.
  • A152968 (program): a(n) = A139251(n+1)/2.
  • A152978 (program): a(n) = A139251(n+2)/4 = A152968(n+1)/2.
  • A152980 (program): First differences of toothpick corner sequence A153006.
  • A152984 (program): Absolute values of A152864.
  • A152985 (program): Sum of proper divisors minus the number of proper divisors of the square A000290(n).
  • A152986 (program): Sum of proper divisors minus the number of proper divisors of pentagonal number A000326(n).
  • A152987 (program): Sum of proper divisors minus the number of proper divisors of the number of partitions of n, A000041(n).
  • A152989 (program): Sum of proper divisors minus the number of proper divisors of triangular number A000217(n).
  • A152991 (program): a(n) = sigma(n) - pi(n).
  • A152992 (program): a(n) = sigma(n) - d(n) - pi(n).
  • A152993 (program): a(n) = n - d(n) - pi(n) + 1.
  • A152994 (program): Nine times hexagonal numbers: a(n) = 9*n*(2*n-1).
  • A152995 (program): Twice 11-gonal numbers: a(n) = n*(9*n-7).
  • A152996 (program): 9 times pentagonal numbers: 9*n*(3*n-1)/2.
  • A152997 (program): Twice 13-gonal numbers: a(n) = n*(11*n - 9).
  • A152998 (program): Toothpick sequence on the semi-infinite square grid.
  • A153000 (program): Toothpick sequence in the first quadrant.
  • A153001 (program): Rows of A152980 when written as a triangle converge to this sequence.
  • A153003 (program): Toothpick sequence in the first three quadrants.
  • A153004 (program): First differences of toothpick numbers A153003.
  • A153006 (program): Toothpick sequence starting at the outside corner of an infinite square from which protrudes a half toothpick.
  • A153007 (program): Triangular number A000217(n) minus toothpick number A153006(n).
  • A153008 (program): Catalan number A000108(n) minus Motzkin number A001006(n).
  • A153010 (program): Indices of A153007 where the entry equals zero.
  • A153011 (program): Sum of proper divisors, minus the number of proper divisors, minus cototient of n, plus 1.
  • A153012 (program): Differences between adjacent digits of square root of 2.
  • A153026 (program): a(1)=0, a(n) = n^3 - a(n-1).
  • A153028 (program): Special values of the hypergeometric function of the type 4F0.
  • A153030 (program): Positions of even digits of Pi.
  • A153031 (program): Positions of prime digits of Pi.
  • A153032 (program): Positions of digits of Pi that are divisible by 3.
  • A153033 (program): Numbers with adjacent 1’s and no adjacent 0’s in binary expansion.
  • A153034 (program): Numbers with adjacent 0’s and no adjacent 1’s in binary expansion.
  • A153036 (program): Integer parts of the full Stern-Brocot tree.
  • A153037 (program): a(n) = 2*n^2 + 16*n + 23.
  • A153038 (program): Denominators of the fixed point a=(a_1,a_2,…) of the transformation x’= fix(x) where fix(x)_n = Sum_{d|n} d x_d, i.e., fix(a)=a.
  • A153039 (program): Numbers n such that 2*n-7 is composite.
  • A153040 (program): Numbers n>3 such that 2*n-5 is not a prime.
  • A153041 (program): Numbers n >=10 such that 2*n-19 is not a prime.
  • A153043 (program): Numbers n > 1 such that 2*n-3 is not a prime.
  • A153044 (program): Numbers n such that 2*n-9 is not a prime.
  • A153045 (program): Numbers k such that 2*k-11 is not a prime.
  • A153047 (program): Numbers n such that 2*n-15 is not a prime.
  • A153049 (program): Numbers n such that 2*n - 13 is not a prime.
  • A153051 (program): Numbers n>=9 such that 2*n-17 is not a prime.
  • A153052 (program): Numbers n such that 2*n + 5 is not a prime.
  • A153053 (program): Numbers n such that 2*n + 7 is not a prime.
  • A153056 (program): a(0)=2, a(n) = n^2+a(n-1).
  • A153057 (program): a(0)=3; a(n) = n^2 + a(n-1) for n>0.
  • A153058 (program): a(0)=4; a(n)=n^2+a(n-1) for n>0.
  • A153059 (program): a(0) = 0, a(n) = a(n-1)^2 - n.
  • A153062 (program): a(0)=1, a(n)=a(n-1)^2-n^2.
  • A153071 (program): Decimal expansion of L(3, chi4), where L(s, chi4) is the Dirichlet L-function for the non-principal character modulo 4.
  • A153079 (program): a(n) = 13^n + 2.
  • A153080 (program): a(n) = 13*n + 2.
  • A153081 (program): Nonnegative numbers n such that 2n + 13 is prime.
  • A153082 (program): Numbers k such that 2*k + 13 is not prime.
  • A153083 (program): Numbers such that 2*n + 11 is not prime.
  • A153085 (program): Numbers k such that 4*k + 5 is not prime.
  • A153086 (program): Numbers n such that 4*n+7 is not prime
  • A153088 (program): Numbers k such that 5*k - 1 is not prime.
  • A153110 (program): Period 6: repeat [1, 5, 7, 2, 4, 8].
  • A153111 (program): Solutions of the Pell-like equation 1 + 6*A*A = 7*B*B, with A, B integers.
  • A153122 (program): G.f.: 1/p(x) where p(x)=x^5 + 2x^4 - 2x^3 - x^2 + 2x - 1.
  • A153125 (program): Triangle read by rows: T(n,k) = maximal number of squares that can be covered by a queen on an n X k chessboard, 1<=k<=n.
  • A153126 (program): Sums of rows of the triangle in A153125.
  • A153127 (program): a(n) = (2*n + 1)*(5*n + 6).
  • A153129 (program): Numbers n such that 8*n + 5 is not prime.
  • A153130 (program): Period 6: repeat [1, 2, 4, 8, 7, 5].
  • A153134 (program): Numbers n such that 6n - 7 is prime.
  • A153135 (program): Primes p such that 6*p - 7 is also prime.
  • A153141 (program): Permutation of nonnegative integers: A059893-conjugate of A153151.
  • A153142 (program): Permutation of nonnegative integers: A059893-conjugate of A153152.
  • A153143 (program): Nonnegative numbers n such that 2n + 19 is prime.
  • A153144 (program): Numbers n such that 2*n+19 is not a prime.
  • A153145 (program): Primes p such that 2*p + 19 is also prime.
  • A153146 (program): Numbers n such that 2*n + 19 and 2*n - 19 are prime.
  • A153147 (program): a(n) = A007916(n)^3.
  • A153150 (program): Self-inverse permutation of natural numbers: A059893-conjugate of A056539.
  • A153151 (program): Rotated binary decrementing: For n<2 a(n) = n, if n=2^k, a(n) = 2*n-1, otherwise a(n) = n-1.
  • A153152 (program): Rotated binary incrementing: For n<2 a(n)=n, if n=(2^k)-1, a(n)=(n+1)/2, otherwise a(n)=n+1.
  • A153153 (program): Permutation of natural numbers: A059893-conjugate of A003188.
  • A153154 (program): Permutation of natural numbers: A059893-conjugate of A006068.
  • A153157 (program): A007916(n)^4.
  • A153158 (program): a(n) = A007916(n)^2.
  • A153159 (program): A007916(n)^5.
  • A153160 (program): A007916(n)^6.
  • A153161 (program): Numerators of Stern-Brocot tree hanging between 1/3 and 2/3; denominators=A153162.
  • A153162 (program): Denominators of Stern-Brocot tree hanging between 1/3 and 2/3; numerators=A153161.
  • A153165 (program): Primes of form 6k+1 that use only digits 2 and 3.
  • A153169 (program): a(n) = 4*n^2 + 12*n + 3.
  • A153170 (program): Numbers k such that 3*k + 2 is not prime.
  • A153171 (program): First differences of A046163.
  • A153173 (program): a(n) = L(5*n)/L(n) where L(n) = Lucas number A000204(n).
  • A153183 (program): Numbers k such that 3k-2 is prime.
  • A153184 (program): Numbers n such that 3*n-2 is not prime.
  • A153186 (program): Period 9: repeat 1,7,4,7,4,7,1,1,1.
  • A153187 (program): Triangle sequence: T(n, k) = -Product_{j=0..k+1} ((n+1)*j - 1).
  • A153188 (program): Triangle sequence: t(n,m)=Product[m*k, {k, 1, n}].
  • A153189 (program): Triangle T(n,k) = Product_{j=0..k} n*j+1.
  • A153190 (program): Triangle read by rows: t(n,m)=If[m == 0, 1, Product[m*k + 2, {k, 0, n}]].
  • A153191 (program): a(n) = 9*a(n-1) + 6*a(n-2); a(0)=0, a(1)=1.
  • A153192 (program): Numbers such that the numerator of floor(sqrt(n))/n, when reduced to its lowest terms, is equal to 2.
  • A153193 (program): a(n) is the number of integers of the form n*(n+1)*k / (k - n*(n+1)) where k is an integer >= 1.
  • A153194 (program): Numbers such that the numerator of floor(sqrt(n))/n, when reduced to its lowest terms, is equal to 3.
  • A153196 (program): Numbers n such that 6*n+5 and 6*n+7 are twin primes.
  • A153211 (program): Sum of digits of n, times digital reversal of sum of digits of n.
  • A153217 (program): a(n)=n^(n+3)-(n+3)^n.
  • A153218 (program): Numbers n such that 6n + 7 is prime.
  • A153219 (program): Numbers n such that 6*n + 7 is not prime.
  • A153229 (program): a(0) = 0, a(1) = 1, and for n>=2, a(n) = (n-1) * a(n-2) + (n-2) * a(n-1).
  • A153231 (program): a(n) = 2^n * binomial(3n,n)/(2n+1).
  • A153232 (program): a(n) = Sum((-1)^(n-i)*binomial(3i,i)*binomial(n+2i,3i)*2^i/(2i+1),i=0..n).
  • A153234 (program): a(n) = floor(2^n/9).
  • A153235 (program): Numbers n such that 8*n+7 is not prime.
  • A153236 (program): Numbers n such that 8*n + 3 is not prime.
  • A153237 (program): a(n) = A000079(n) - A153130(n).
  • A153238 (program): Numbers k such that 2*k + 3 is composite.
  • A153245 (program): Numbers n>1 such that 6*n-7 is not prime.
  • A153246 (program): Number of fleeing trees computed for Catalan bijection A057164.
  • A153257 (program): a(n) = n^3-(n+1)^2.
  • A153258 (program): n^3 - (n+2)^2.
  • A153259 (program): a(n)=n^3-(3*(n+3))^2.
  • A153260 (program): a(n) = n^3 - 3*(n+3)^2.
  • A153261 (program): Primes p such that 3*p-2 is not prime.
  • A153263 (program): a(n) = A014217(n+3) - A014217(n).
  • A153264 (program): Numbers n such that 16*n+15 is not prime.
  • A153270 (program): Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 2, read by rows.
  • A153271 (program): Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 3, read by rows.
  • A153272 (program): Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 4, read by rows.
  • A153273 (program): Triangle read by rows: T(n,k) = Product_{i=0..k-2} (i*n + n - 1).
  • A153274 (program): Triangle, read by rows, T(n,k) = k^(n+1) * Pochhammer(1/k, n+1).
  • A153275 (program): Numbers n such that 10*n+1 is not prime.
  • A153276 (program): Numbers n >= 0 such that 5*n+6 is not prime.
  • A153279 (program): Eigentriangle by rows, T(n,k) = A000079(n-k) * (diagonalized matrix of (1,1,3,9,27,81,…)).
  • A153280 (program): Eigensequence of triangle A153279
  • A153281 (program): Triangle read by rows, A130321 * A127647. Also, number of subsets of [n+2] with consecutive integers that start at k.
  • A153282 (program): Numbers k such that 3*k + 4 is not prime.
  • A153284 (program): a(n) = n + Sum_{j=1..n-1} (-1)^j * a(j) for n >= 2, a(1) = 1.
  • A153285 (program): a(1)=1; for n > 1, a(n) = n^2 + Sum_{j=1..n-1} (-1)^j*a(j).
  • A153286 (program): a(n) = n^3 + sum((-1)^j*a(j)); for j=1 to n-1; a(1)=1.
  • A153287 (program): First differences of A152738.
  • A153291 (program): G.f.: A(x) = F(x*F(x)) where F(x) = 1 + x*F(x)^3 is the g.f. of A001764.
  • A153299 (program): G.f.: A(x) = F(x*G(x)) where F(x) = G(x*F(x)) = 1 + x*F(x)^3 is the g.f. of A001764 and G(x) = F(x/G(x)) = 1 + x*G(x)^2 is the g.f. of A000108 (Catalan).
  • A153307 (program): Numbers n such that 14*n+3 is not prime.
  • A153308 (program): Numbers n such that 10*n+7 is not prime.
  • A153309 (program): Numbers k such that 3*k + 1 is not prime.
  • A153315 (program): Denominators of continued fraction convergents to sqrt(5/4).
  • A153316 (program): Numerators of continued fraction convergents to sqrt(5/4).
  • A153317 (program): Denominators of continued fraction convergents to sqrt(6/5).
  • A153318 (program): Numerators of continued fraction convergents to sqrt(6/5).
  • A153319 (program): Primes p such that 6*p-7 is not prime.
  • A153327 (program): Numbers n such that 16*n+5 is not prime.
  • A153329 (program): Numbers k such that 5*k + 1 is not prime.
  • A153330 (program): Differences in adjacent elements of the sequence quantifying the steps needed for n to converge to 1 in the Collatz Conjecture.
  • A153334 (program): Number of zig-zag paths from top to bottom of an n X n square whose color is that of the top right corner.
  • A153335 (program): Number of zig-zag paths from top to bottom of an n X n square whose color is not that of the top right corner.
  • A153336 (program): Number of zig-zag paths from top to bottom of a 2n by 2n square whose color is that of the top right corner
  • A153337 (program): Number of zig-zag paths from top to bottom of a 2n-1 by 2n-1 square whose color is that of the top right corner
  • A153338 (program): Number of zig-zag paths from top to bottom of a 2n-1 by 2n-1 square whose color is not that of the top right corner.
  • A153339 (program): Number of zig-zag paths from top to bottom of a rectangle of width 5 with n rows whose color is that of the top right corner
  • A153340 (program): Number of zig-zag paths from top to bottom of a rectangle of width 8 with n rows.
  • A153342 (program): Binomial transform of triangle A046854 (shifted).
  • A153343 (program): Numbers k such that 5*k + 4 is not prime.
  • A153347 (program): Numbers n>0 such that 7*n-4 is not prime.
  • A153348 (program): Numbers n such that 16*n+3 is not prime.
  • A153349 (program): Period 6: repeat [1, 7, 4, 4, 7, 1].
  • A153350 (program): Numbers n such that 7n+11 is not prime.
  • A153351 (program): Numbers n such that 7*n+2 is not prime.
  • A153355 (program): Numbers k such that 5k-1 is a prime.
  • A153360 (program): Number of zig-zag paths from top to bottom of a rectangle of width 10 with n rows.
  • A153362 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows.
  • A153363 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows whose color is that of the top right corner
  • A153364 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows whose color is not that of the top right corner
  • A153365 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n rows whose color is that of the top right corner.
  • A153366 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n-1 rows whose color is that of the top right corner.
  • A153367 (program): Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n-1 rows whose color is not that of the top right corner.
  • A153368 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows.
  • A153369 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is that of the top right corner.
  • A153370 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with n rows whose color is not that of the top right corner.
  • A153371 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n rows whose color is that of the top right corner.
  • A153372 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n-1 rows whose color is that of the top right corner.
  • A153373 (program): Number of zig-zag paths from top to bottom of a rectangle of width 11 with 2n-1 rows whose color is not that of the top right corner.
  • A153380 (program): Numbers n such that 10*n+9 is not prime.
  • A153381 (program): Numbers n such that 11*n+5 is not prime.
  • A153382 (program): a(n)=a(n-1)+2a(n-2)-a(n-3)-a(n-4), a(0)=0,a(1)=8,a(2)=10,a(3)=18.
  • A153383 (program): Numbers n such that 12*n+1 is not prime.
  • A153384 (program): Numbers n such that 24*n+1 is not prime.
  • A153388 (program): Second bisection of A153382.
  • A153400 (program): Numbers n such that 18*n+1 is not prime.
  • A153403 (program): Numbers n such that 10*n+3 is not prime.
  • A153417 (program): Primes p such that p+14 is also prime.
  • A153418 (program): Primes p such that p+18 is also prime.
  • A153419 (program): Primes p such that p+20 is also prime.
  • A153422 (program): Primes of the form n^2+15n+13
  • A153423 (program): Primes of the form n^2+9n+241.
  • A153424 (program): Primes of the form n^2+3n+223
  • A153426 (program): a(n) = (n+1)! mod prime(n).
  • A153435 (program): Numbers with 2n binary digits where every run length is 2, written in binary.
  • A153448 (program): 3 times 12-gonal (or dodecagonal) numbers: 3*n*(5*n-4).
  • A153449 (program): 11 times pentagonal numbers: 11*n*(3n-1)/2.
  • A153464 (program): Numbers n such that 4*n+9 is not prime.
  • A153465 (program): 9*4^n - 2.
  • A153466 (program): a(n) = A027941(n) + A027941(n+6).
  • A153478 (program): Sum of first n isolated (or single) primes A007510.
  • A153480 (program): a(n) = 2*prime(n)^2 - 4.
  • A153481 (program): a(n) = prime(n)^3 - 2.
  • A153482 (program): a(n) = prime(n)^4 - 8.
  • A153483 (program): a(n) = prime(n)^4 - 32.
  • A153484 (program): a(n) = prime(n)^5 - 128.
  • A153485 (program): Sum of all aliquot divisors of all positive integers <= n.
  • A153486 (program): a(n) = prime(n)^6 - 512.
  • A153490 (program): Sierpinski carpet, read by antidiagonals.
  • A153491 (program): Triangle T(n,m)= 11*binomial(n,k) - 8 read by rows, 0<=k<=n.
  • A153497 (program): a(n) is the number whose binary expansion is A153498(n).
  • A153498 (program): Palindromes formed from concatenation of A147759(n) and the same string A147759(n) but without its initial digit.
  • A153499 (program): a(n) is the number whose binary expansion is A153500(n).
  • A153500 (program): First 3 terms coincide with A152756. For n>3, a(n) is the palindromic number formed from concatenation of 1, 0, A147759(n-3), 0, A147759(n-3), 0 and 1.
  • A153502 (program): Primes of the form 3*n^2 - 3*n + 11.
  • A153509 (program): Period 9: repeat [6, 6, 6, 3, 3, 3, 0, 0, 0].
  • A153511 (program): a(n) = 4 * A051189(n).
  • A153587 (program): a(n) = n mod (A062383(n) - n).
  • A153590 (program): Primes p such that p^2 + 3p + 1 is also prime.
  • A153591 (program): Primes p such that 6p^2+6p+1 is also prime.
  • A153593 (program): a(n) = ((9 + sqrt(2))^n - (9 - sqrt(2))^n)/(2*sqrt(2)).
  • A153594 (program): a(n) = ((4 + sqrt(3))^n - (4 - sqrt(3))^n)/(2*sqrt(3)).
  • A153596 (program): a(n) = ((5 + sqrt(3))^n - (5 - sqrt(3))^n)/(2*sqrt(3)).
  • A153597 (program): a(n) = ((6 + sqrt(3))^n - (6 - sqrt(3))^n)/(2*sqrt(3)).
  • A153598 (program): a(n) = ((7 + sqrt(3))^n - (7 - sqrt(3))^n)/(2*sqrt(3)).
  • A153599 (program): a(n) = ((8 + sqrt(3))^n - (8 - sqrt(3))^n)/(2*sqrt(3)).
  • A153600 (program): a(n) = ((9 + sqrt(3))^n - (9 - sqrt(3))^n)/(2*sqrt(3)).
  • A153638 (program): Odiousness of triangular numbers.
  • A153639 (program): Evilness of triangular numbers.
  • A153642 (program): a(n) = 4*n^2 + 24*n + 8.
  • A153643 (program): Jacobsthal numbers A001045 incremented by 2.
  • A153644 (program): a(n) = 4*n^2 + 28*n + 10.
  • A153647 (program): a(n) = 3^n*(n + 2)!.
  • A153659 (program): Triangle read by rows. A074206 interleaved with k-1 zeros in the k-th column.
  • A153703 (program): Partial sums of A069996.
  • A153709 (program): Expansion of (1 + 7*x)/(1 - 11*x - 26*x^2).
  • A153726 (program): Initial digit of Catalan number A000108(n).
  • A153727 (program): Period 3: repeat [1, 4, 2] ; Trajectory of 3x+1 sequence starting at 1.
  • A153728 (program): Expansion of q^(-1/3) * (eta(q)^8 + 8 * eta(q^4)^8) in powers of q^2.
  • A153729 (program): Expansion of q^(-1/3) * (eta(q)^8 + 32 * eta(q^4)^8) in powers of q.
  • A153732 (program): Binomial transform of A109747.
  • A153733 (program): Remove all trailing 1’s in the binary representation of n.
  • A153757 (program): a(n) = Sum_{k=1..n} A003266(k).
  • A153758 (program): a(n) = Sum_{k=1..n} A153757(k).
  • A153760 (program): Number of degree-n permutations of order exactly 7.
  • A153762 (program): Numbers n such that 8n + 9 is prime.
  • A153763 (program): Numbers k >= 0 such that 8*k+9 is not prime.
  • A153764 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,-1,0,0,0,0,0,0,0,0,…] DELTA [0,1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A153766 (program): Numbers n such that 8n-9 is prime.
  • A153767 (program): Primes p such that 8*p - 9 is also prime.
  • A153769 (program): Numbers n such that 8n-9 is not prime.
  • A153772 (program): a(n) = (2^n + 2*(-1)^n - 6)/3.
  • A153773 (program): a(2*n) = 3*a(2*n-1) - 1, a(2*n+1) = 3*a(2*n), with a(1)=1.
  • A153774 (program): a(2*n) = 3*a(2*n-1), a(2*n+1) = 3*a(2*n) - 1, with a(1) = 1.
  • A153775 (program): Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x are in S.
  • A153776 (program): Sequence S such that 1 is in S and if x is in S, then 5x-3 and 5x-1 are in S.
  • A153777 (program): Sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S.
  • A153778 (program): Binary sequence constructed like a Stern-Brocot tree between 0 and 1, where XOR is applied instead of the mediant operation.
  • A153780 (program): 10 times pentagonal numbers: a(n) = 5*n*(3*n-1).
  • A153781 (program): Numbers n such that n^2+13n+23 is prime.
  • A153783 (program): 3 times 11-gonal (or hendecagonal) numbers: 3*n*(9*n-7)/2.
  • A153784 (program): 4 times heptagonal numbers: 2n(5n-3).
  • A153785 (program): 5 times heptagonal numbers: a(n) = 5*n*(5*n-3)/2.
  • A153786 (program): 6 times heptagonal numbers: a(n) = 3*n*(5*n-3).
  • A153788 (program): Number of proper divisors of the Catalan number A000108(n).
  • A153792 (program): 12 times pentagonal numbers: a(n) = 6*n*(3*n-1).
  • A153793 (program): 13 times pentagonal numbers: a(n) = 13*n*(3*n-1)/2.
  • A153794 (program): 4 times octagonal numbers: a(n) = 4*n*(3*n-2).
  • A153795 (program): 5 times octagonal numbers: a(n) = 5*n*(3*n-2).
  • A153796 (program): 6 times octagonal numbers: a(n) = 6*n*(3*n-2).
  • A153797 (program): 7 times octagonal numbers: a(n) = 7*n*(3*n-2).
  • A153799 (program): Decimal expansion of 4 - Pi.
  • A153805 (program): Decimal expansion of 3-e.
  • A153808 (program): 8 times octagonal numbers: 8*n*(3*n-2).
  • A153809 (program): Complement of A134928.
  • A153814 (program): a(n) = 1001*n.
  • A153817 (program): a(n)=Sum_{k=1..n} floor((n*k)/(n+k)).
  • A153818 (program): a(n) = Sum_{k=1..n} floor(n^2/k^2).
  • A153819 (program): Linear recurrence with a(n) = 3a(n-1) - a(n-2) + 2 = 4a(n-1) - 4a(n-2) + a(n-3). Full sequence for A153466.
  • A153823 (program): Number of proper divisors of n!.
  • A153824 (program): Sum of proper divisors of n!: a(n) = sigma(n!) - n!.
  • A153836 (program): a(n) = 2^(n^2) - 2^(n^2 - n + 1) for n >= 1; a(0) = 0.
  • A153839 (program): First Sunday in n-th month of 365-day year starting on Sunday
  • A153840 (program): First Sunday in the n-th month of a 365-day year starting on Monday.
  • A153841 (program): First Sunday in n-th month of 365-day year starting on Tuesday
  • A153842 (program): First Sunday in n-th month of 365-day year starting on Wednesday
  • A153843 (program): First Sunday in n-th month of 365-day year starting on Thursday
  • A153844 (program): First Sunday in n-th month of 365-day year starting on Friday
  • A153845 (program): First Sunday in n-th month of 365-day year starting on Saturday
  • A153848 (program): Repeat 21.
  • A153859 (program): Triangle read by rows, A007318 * (A007476 * 0 ^(n-k))
  • A153860 (program): Triangle by columns: leftmost column = (1, 0, 1, -1, 1, -1, 1, …); columns >1 = (1, 1, 0, 0, 0, …).
  • A153861 (program): Triangle read by rows, binomial transform of triangle A153860.
  • A153869 (program): Triangle read by rows, A129186 * A128064(unsigned).
  • A153873 (program): a(n) = 9*Fibonacci(2n+1) - 1.
  • A153875 (program): 3 times 13-gonal (or tridecagonal) numbers: 3*n*(11*n - 9)/2.
  • A153877 (program): Numbers n such that 5n-1 and 5n+1 are both prime.
  • A153880 (program): Shift factorial base representation left by one digit.
  • A153881 (program): 1 followed by -1, -1, -1, … .
  • A153882 (program): a(n) = ((6 + sqrt(5))^n - (6 - sqrt(5))^n)/(2*sqrt(5)).
  • A153883 (program): A153880(n)/2
  • A153884 (program): a(n) = ((7 + sqrt(5))^n - (7 - sqrt(5))^n)/(2*sqrt(5)).
  • A153885 (program): a(n) = ((8 + sqrt(5))^n - (8 - sqrt(5))^n)/(2*sqrt(5)).
  • A153886 (program): a(n) = ((9 + sqrt(5))^n - (9 - sqrt(5))^n)/(2*sqrt(5)).
  • A153893 (program): a(n) = 3*2^n - 1.
  • A153894 (program): a(n) = 5*2^n - 1.
  • A153972 (program): a(n) = 2^n + 6.
  • A153973 (program): a(n) = 3*a(n-1) - 2*a(n-2), with a(1) = 9, a(2) = 12.
  • A153974 (program): Numbers n such that n^3 - 3 is prime.
  • A153976 (program): a(n) = n^3 + (n+2)^3.
  • A153977 (program): One-fourth of partial sums of A153976.
  • A153978 (program): a(n) = n*(n-1)*(n+1)*(3*n-2)/12.
  • A153979 (program): Prime sums of prime factors of composite(k)=A002808(k).
  • A153981 (program): a(n) = 36*Fibonacci(2*n+1) - 4.
  • A153990 (program): Period 6: repeat [1, 2, 5, 4, 7, 8].
  • A154021 (program): a(n+2) = 16*a(n+1) - a(n), with a(1)=0, a(2)=4.
  • A154022 (program): a(n) = 5*A097780(n-2).
  • A154023 (program): a(n+2) = 36*a(n+1) - a(n), a(1)=0, a(2)=6.
  • A154024 (program): a(n+2) = 49*a(n+1) - a(n), a(1)=0, a(2)=7.
  • A154025 (program): a(n+2) = 64*a(n+1) - a(n), a(1)=0, a(2)=8.
  • A154026 (program): a(n+2) = 81*a(n+1) - a(n), a(1)=0, a(2)=9.
  • A154027 (program): a(n+2) = 100*a(n+1) - a(n), a(1)=0, a(2)=10.
  • A154028 (program): a(2n) = n*(n+1)/2, a(2n+1) = n!.
  • A154029 (program): List of pairs of numbers: {n^2-1, (2*n-1)!!} such that F((2*n-1)!!) = n^2 - 1.
  • A154030 (program): Sequence defined by a(2*n) = 2*(n^2 + 2*n) and a(2*n-1) = (2*n)!/n!.
  • A154032 (program): Number of planar triangular n X n X n nonnegative integer grids symmetric under 120 degree rotation with every similarly oriented 2 X 2 X 2 subtriangle summing to 3.
  • A154105 (program): a(n) = 12*n^2 + 18*n + 7.
  • A154106 (program): a(n) = 12*n^2 + 22*n + 11.
  • A154108 (program): A000110 / (1,2,3,…): (convolved with (1,2,3,…) = Bell numbers.
  • A154112 (program): Numbers n such that (n+1)^3 - n^2 is prime.
  • A154113 (program): Primes of the form (n+1)^3 - n^2.
  • A154115 (program): Numbers n such that n + 3 is prime.
  • A154117 (program): Expansion of (1 - x + 3*x^2)/((1-x)*(1-2*x)).
  • A154118 (program): Expansion of (1 - x + 5x^2)/((1-x)*(1-2x)).
  • A154120 (program): Array read by antidiagonals: T(n,k) = (k+1)^n*(n+k)!.
  • A154127 (program): Period 6: repeat [1, 2, 5, 8, 7, 4].
  • A154128 (program): a(n) = 5^n*(n+4)!/n!.
  • A154129 (program): a(n) = (A132207(n)-1)/3.
  • A154138 (program): Indices k such that 3 plus the k-th triangular number is a perfect square.
  • A154139 (program): Indices k such that 4 plus the k-th triangular number is a perfect square.
  • A154140 (program): Indices k such that 6 plus the k-th triangular number is a perfect square.
  • A154141 (program): Indices k such that 8 plus the k-th triangular number is a perfect square.
  • A154142 (program): Indices k such that 9 plus the k-th triangular number is a perfect square.
  • A154143 (program): Indices k such that 10 plus the k-th triangular number is a perfect square.
  • A154144 (program): Indices k such that 13 plus the k-th triangular number is a perfect square.
  • A154146 (program): Numbers k such that 16 plus the k-th triangular number is a perfect square.
  • A154147 (program): Indices k such that 19 plus the k-th triangular number is a perfect square.
  • A154148 (program): Numbers k such that 21 plus the k-th triangular number is a perfect square.
  • A154149 (program): Indices k such that 22 plus the k-th triangular number is a perfect square.
  • A154150 (program): Numbers k such that 24 plus the k-th triangular number is a perfect square.
  • A154151 (program): Indices k such that 25 plus the k-th triangular number is a perfect square.
  • A154152 (program): Indices k such that 26 plus the k-th triangular number is a perfect square.
  • A154153 (program): Numbers k such that 28 plus the k-th triangular number is a perfect square.
  • A154154 (program): Numbers k such that 30 plus the k-th triangular number is a perfect square.
  • A154221 (program): A simple Pascal-like triangle.
  • A154222 (program): Row sums of number triangle A154221.
  • A154223 (program): Diagonal sums of number triangle A154221.
  • A154225 (program): List of pairs: {n*(n + 1)*(2*n + 1)/6, (n!)^2}.
  • A154226 (program): List of pairs: {(n*(n+1)/2)^2, (n!)^3}.
  • A154232 (program): a(2n) = (n^2-n-1) + a(2n-2), a(2n+1) = (n^2-n-1)*a(2n-1), with a(0)=0 and a(1)=1.
  • A154234 (program): Triangle read by rows: T(n,k) = (n mod d(k)), where d(i) is the number of divisors of i.
  • A154235 (program): a(n) = ( (4 + sqrt(6))^n - (4 - sqrt(6))^n )/(2*sqrt(6)).
  • A154236 (program): a(n) = ( (5 + sqrt(6))^n - (5 - sqrt(6))^n )/(2*sqrt(6)).
  • A154237 (program): a(n) = ( (6 + sqrt(6))^n - (6 - sqrt(6))^n )/(2*sqrt(6)).
  • A154239 (program): a(n) = ( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)).
  • A154240 (program): a(n) = ( (8 + sqrt(6))^n - (8 - sqrt(6))^n )/(2*sqrt(6)).
  • A154241 (program): a(n) = ( (9 + sqrt(6))^n - (9 - sqrt(6))^n )/(2*sqrt(6)).
  • A154244 (program): a(n) = 6*a(n-1) - 2*a(n-2) for n>1; a(1)=1, a(2)=6.
  • A154245 (program): a(n) = ( (4 + sqrt(7))^n - (4 - sqrt(7))^n )/(2*sqrt(7)).
  • A154246 (program): a(n) = ( (5 + sqrt(7))^n - (5 - sqrt(7))^n )/(2*sqrt(7)).
  • A154247 (program): a(n) = ( (6 + sqrt(7))^n - (6 - sqrt(7))^n )/(2*sqrt(7)).
  • A154248 (program): a(n) = ( (7 + sqrt(7))^n - (7 - sqrt(7))^n )/(2*sqrt(7)).
  • A154249 (program): a(n) = ( (8 + sqrt(7))^n - (8 - sqrt(7))^n )/(2*sqrt(7)).
  • A154250 (program): a(n) = ( (9 + sqrt(7))^n - (9 - sqrt(7))^n )/(2*sqrt(7)).
  • A154251 (program): Expansion of (1-x+7x^2)/((1-x)(1-2x)).
  • A154252 (program): Expansion of (1-x+8x^2)/((1-x)(1-2x)) .
  • A154253 (program): Primes of the form 9n^2-8n+2.
  • A154254 (program): a(n) = 9n^2 - 8n + 2.
  • A154260 (program): Numbers of the form m*(4*m +- 1)/2.
  • A154261 (program): Primes of the form 9n^2-10n+3.
  • A154262 (program): a(n) = 9*n^2 - 10*n + 3.
  • A154264 (program): Nonnegative numbers n such that 9*n^2 - 10*n + 3 is prime.
  • A154266 (program): a(n) = 27*n + 12.
  • A154267 (program): a(n) = 27*n + 15.
  • A154269 (program): Dirichlet inverse of A019590; Fully multiplicative with a(2^e) = (-1)^e, a(p^e) = 0 for odd primes p.
  • A154271 (program): Dirichlet inverse of A154272; Fully multiplicative with a(3^e) = (-1)^e, a(p^e) = 0 for primes p <> 3.
  • A154272 (program): 1,0,1 followed by 0,0,0,…
  • A154276 (program): Primes of the form 81*n^2 - 72*n + 17.
  • A154277 (program): a(n) = 81*n^2 - 72*n + 17.
  • A154281 (program): 1,0,0,1 followed by 0,0,0…
  • A154282 (program): Dirichlet inverse of A154281.
  • A154286 (program): a(n) = E(k)*C(n+k,k) = Euler(k)*binomial(n+k,k) for k=4.
  • A154287 (program): (L)-sieve transform of {1,4,9,16,…,n^2,…}=A000290.
  • A154292 (program): Integers of the form m*(6*m -+ 1)/2.
  • A154293 (program): Integers of the form t/6, where t is a triangular number (A000217).
  • A154295 (program): a(n) = 81*n^2 - 90*n + 26.
  • A154306 (program): a(n) = (n+1)^3*(3+n)!/6.
  • A154307 (program): a(n) = (n+1)^4*(4+n)!/24.
  • A154308 (program): a(n) = (n+1)^5*(5+n)!/120.
  • A154312 (program): Triangle T(n,k), 0<=k<=n, read by rows, given by [0,1/2,-1/2,0,0,0,0,0,0,0,…] DELTA [2,-1/2,-1/2,2,0,0,0,0,0,0,0 …] where DELTA is the operator defined in A084938 .
  • A154318 (program): Numbers n such that nonprime(prime(n))+1 is prime.
  • A154319 (program): Primes p such that p^2 + 2*p - 4 is also prime.
  • A154320 (program): Primes p such that p^2 + 8*p - 4 is also prime.
  • A154322 (program): a(n) = 1 + n + binomial(n+3,5).
  • A154323 (program): Central coefficients of number triangle A113582.
  • A154324 (program): Diagonal sums of number triangle A113582.
  • A154325 (program): Triangle with interior all 2’s and borders 1.
  • A154327 (program): Diagonal sums of number triangle A132046.
  • A154331 (program): Numbers m such that 12 m^2 is the average of a twin prime pair.
  • A154333 (program): Difference between n^3 and the next smaller square
  • A154334 (program): A triangular sequence of coefficients of polynomials: p(x,n) = ((x - 1)^n *(Sum_{k>=0} (((-1)^n*(2*k + 1)^(n - 1)))*x^k) + (x - 1)^(n + 1)*(Sum_{k>=0} ((-1)^(n + 1)*k^n)*x^k)/x)/2.
  • A154335 (program): A triangular sequence of coefficients of polynomials: p(x,n) = (2*(x - 1)^n * (Sum_{k>=0} (((-1)^n*(2*k + 1)^(n - 1)))*x^k) - (x - 1)^(n + 1)*(Sum_{k>=0} ((-1)^(n + 1)*k^n)*x^k)/x).
  • A154336 (program): A triangular sequence of coefficients of polynomials: p(x,n)=(3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}] -2*(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x).
  • A154337 (program): A triangular sequence of coefficients of polynomials: p(x,n)=(3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}] -(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x)/2.
  • A154338 (program): A triangular sequence of coefficients of polynomials: p(x,n)=(-(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}]+2*(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x).
  • A154340 (program): a(n) = ( (5 + 2*sqrt(2))^n - (5 - 2*sqrt(2))^n )/(4*sqrt(2)).
  • A154346 (program): a(n) = 12*a(n-1) - 28*a(n-2) for n > 1, with a(0)=1, a(1)=12.
  • A154347 (program): a(n) = ( (7 + 2*sqrt(2))^n - (7 - 2*sqrt(2))^n )/(4*sqrt(2)).
  • A154348 (program): a(n) = 16*a(n-1) - 56*a(n-2) for n>1, with a(0)=1, a(1)=16.
  • A154350 (program): a(n) = ( (9 + 2*sqrt(2))^n - (9 - 2*sqrt(2))^n )/(4*sqrt(2)).
  • A154351 (program): a(n) = number of distinct values of A056239(m) when A153452(m) is equal to n.
  • A154355 (program): a(n) = 25*n^2 - 36*n + 13.
  • A154356 (program): Primes of the form 25n^2-14n+2 for n >= 0.
  • A154357 (program): a(n) = 25*n^2 - 14*n + 2.
  • A154358 (program): a(n) = 1250*n^2 - 1800*n + 649.
  • A154359 (program): a(n) = 1250*n^2 - 700*n + 99.
  • A154360 (program): a(n) = 250*n - 180.
  • A154361 (program): a(n) = 250*n - 70.
  • A154370 (program): Numbers k such that gpf(composite(k)) - lpf(composite(k)) is prime.
  • A154371 (program): Composites with largest prime factor - smallest prime factor = prime.
  • A154372 (program): Triangle T(n,k) = (k+1)^(n-k)*binomial(n,k).
  • A154374 (program): a(n) = 1250*n^2 - 100*n + 1.
  • A154375 (program): a(n) = 1250*n^2 + 100*n + 1.
  • A154376 (program): a(n) = 25*n^2 - 2*n.
  • A154377 (program): a(n) = 25*n^2 + 2*n.
  • A154378 (program): a(n) = 250*n - 10.
  • A154379 (program): a(n) = 250*n + 10.
  • A154381 (program): Row sums of Bell related number triangle A154380.
  • A154383 (program): Powers of 4 at even indices, two times powers of 4 at odd indices.
  • A154384 (program): Odd nonprimes with odd sum of digits.
  • A154387 (program): Composite numbers with even sum of digits.
  • A154388 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,-1,0,0,0,0,0,0,0,…] DELTA [1,-1,-1,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A154392 (program): Number of zeros of sin(x^2) in integer intervals starting with (0,1).
  • A154402 (program): Inverse Moebius transform of Fredholm-Rueppel sequence, cf. A036987.
  • A154405 (program): Primes of the form 20n^2+8n+1.
  • A154406 (program): Larger twin primes in A061237.
  • A154407 (program): a(n) = 5*2^(n-1) + 3*6^n/2.
  • A154409 (program): Primes of the form 10n^2+6n+1.
  • A154410 (program): a(n) = 5*(3*6^n + 2^n)/2.
  • A154412 (program): Primes of the form 10n^2+14n+5, n >= 0.
  • A154414 (program): Primes of the form 20n^2+32n+13.
  • A154419 (program): Primes of the form 20*k^2 + 36*k + 17.
  • A154420 (program): Maximal coefficient of MacMahon polynomial (cf. A060187) p(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; that is, a(n) = Max(coefficients(p(x,n)).
  • A154426 (program): a(n) = n + (sum of preceding terms) mod n; a(0) = 0.
  • A154428 (program): Primes of the form 50n^2 + 10n + 1.
  • A154432 (program): Numbers k such that 5k^2-k+1 is prime.
  • A154435 (program): Permutation of nonnegative integers induced by Lamplighter group generating wreath recursion, variant 3: a = s(b,a), b = (a,b), starting from the state a.
  • A154436 (program): Permutation of nonnegative integers induced by Lamplighter group generating wreath recursion, variant 1: a = s(a,b), b = (a,b), starting from the state a.
  • A154437 (program): Permutation of nonnegative integers: A059893-conjugate of A154435.
  • A154438 (program): Permutation of nonnegative integers: A059893-conjugate of A154436.
  • A154503 (program): Numbers n of A144571
  • A154506 (program): Primes of the form concatenation(A141468(k), k).
  • A154508 (program): Numbers k such that appending k to the k-th nonprime yields a prime.
  • A154510 (program): Primes of the form 648*n^2 + 72*n + 1.
  • A154511 (program): Primes of the form 648n^2 - 72n + 1.
  • A154514 (program): a(n) = 648*n^2 - 72*n + 1.
  • A154515 (program): a(n) = 648*n^2 + 72*n + 1.
  • A154516 (program): a(n) = 9n^2 - n.
  • A154517 (program): a(n) = 9*n^2 + n.
  • A154518 (program): a(n) = 216*n - 12.
  • A154519 (program): a(n) = 216*n + 12.
  • A154529 (program): A090040 mod 9.
  • A154533 (program): Number of constants of the form a^3*u + b*c*v, where a, b, c are linear, u of order n-3 and v of order n-2.
  • A154546 (program): Numbers n in A154276.
  • A154549 (program): a(n) = 111111*n.
  • A154554 (program): Primes p such that m=p-1 is the least number such that p divides m!+1.
  • A154556 (program): Exponential Riordan array [exp(-x), x(1+x/2)]
  • A154557 (program): Production array of A122848, read by row.
  • A154558 (program): Triangle read by rows, A007318 * (A001006 * 0^(n-k))
  • A154560 (program): (n+3)^2*n/2 + 1.
  • A154563 (program): Averages of twin prime pairs of A074378.
  • A154565 (program): One-half of averages of twin prime pairs of A001318.
  • A154569 (program): Partial sums of (2n-1)^(2n+1)+(2n+1)^(2n-1).
  • A154570 (program): The main diagonal of the successive differences of A154127.
  • A154571 (program): Numbers that are congruent to {0, 3, 4, 5, 7, 8} mod 12.
  • A154575 (program): a(n) = 2*n^2 + 12*n + 4.
  • A154576 (program): a(n) = 2*n^2 + 14*n + 5.
  • A154577 (program): Primes of the form 2n^2+14n+5.
  • A154585 (program): a(n) = abs(Sum_{k=1..n} (-1)^k * (n-k+1 mod k)).
  • A154589 (program): a(n)=A154570(n)+A154570(n+1).
  • A154590 (program): 2n^2+16n+6.
  • A154591 (program): a(n) = 2*n^2 + 18*n + 7.
  • A154592 (program): Primes of the form 2n^2+18n+7, n>=0.
  • A154595 (program): Period 6: repeat [1, 3, 3, -1, -3, -3].
  • A154597 (program): a(n) = 15*a(n-1) + a(n-2) with a(0) = 0, a(1) = 1.
  • A154599 (program): a(n) = 2*n^2 + 20*n + 8.
  • A154600 (program): a(n) = 2*n^2 + 22*n + 9.
  • A154601 (program): Primes of the form 2*n^2 + 22*n + 9.
  • A154603 (program): Binomial transform of reduced tangent numbers (A002105).
  • A154604 (program): Hankel transform of reduced tangent numbers.
  • A154605 (program): Decimal expansion of 2/(4th root of 3).
  • A154607 (program): Numbers n such that 11*n + 4 is prime.
  • A154608 (program): Primes p such that 11*p + 4 is also prime.
  • A154609 (program): a(n) = 13*n + 5.
  • A154610 (program): Numbers n such that 13n + 5 is prime.
  • A154611 (program): Numbers n such that 7*n+3 is not prime.
  • A154612 (program): 17n + 7.
  • A154613 (program): Prime p such that 23p + 10 is prime.
  • A154614 (program): Triangle read by rows where T(m,n) = m*n + m + n - 1, 1<=n<=m.
  • A154615 (program): a(n) = A022998(n)^2.
  • A154616 (program): Primes of the form (4*n^2-8*n-9)/3.
  • A154617 (program): Eleven times hexagonal numbers: 11*n*(2*n-1).
  • A154618 (program): Triangle read by rows: integer values of T(n,m) = (4*m*n+2*m+2*n-3)/3.
  • A154619 (program): Primes of the form (4k^2 + 4k - 5)/5.
  • A154620 (program): Primes p such that 31p+14 is prime.
  • A154621 (program): Primes congruent to 32 mod 67.
  • A154623 (program): Sequence with g.f. 1+(x/(1-5*x))*c(x/(1-5*x)), c(x) the g.f. of A000108.
  • A154624 (program): Primes congruent to 34 mod 71.
  • A154626 (program): a(n) = 2^n*A001519(n).
  • A154627 (program): Expansion of (1-5x)/(1-8x+4x^2).
  • A154628 (program): Primes congruent to 35 mod 73
  • A154629 (program): Period 9: repeat [9, 3, 1, 3, 3, 1, 3, 9, 1].
  • A154631 (program): Triangle read by rows: T(m,n) = 2mn + m + n + 5.
  • A154633 (program): a(n) = (4*n+1)*(4*n+3)*(4*n+5)*(4*n+7).
  • A154635 (program): Ratio of the sum of the bends of the 5-dimensional spheres added in the n-th generation of Apollonian packing to the sum of the bends of the initial configuration of seven mutually tangent spheres.
  • A154636 (program): a(n) is the ratio of the sum of the bends of the circles that are drawn in the n-th generation of Apollonian packing to the sum of the bends of the circles in the initial configuration of 3 circles.
  • A154637 (program): a(n) is the ratio of the sum of squares of the bends of the circles that are added in the n-th generation of Apollonian packing, to the sum of squares of the bends of the initial three circles.
  • A154638 (program): a(n) is the number of distinct reduced words of length n in the Coxeter group of “Apollonian reflections” in three dimensions.
  • A154648 (program): Primes of the form n^2 - 13.
  • A154669 (program): Averages k of twin prime pairs such that 2*k^3 + 12*k^2 is a square.
  • A154670 (program): Averages of twin prime pairs k such that k*2 and k/2 are squares.
  • A154671 (program): Averages of twin prime pairs k such that k*3 and k/3 are squares.
  • A154680 (program): Triangle read by rows where T(m,n)=2*m*n + m + n - 2.
  • A154681 (program): Triangle read by rows where T(m,n) = 2*m*n + m + n +3.
  • A154682 (program): (2n-1)^(2n+1) + (2n+1)^(2n-1).
  • A154684 (program): Triangle read by rows where T(m,n)=2mn + m + n - 3, 1<=n<=m.
  • A154685 (program): Triangle read by rows where T(m,n)=2mn+m+n+4
  • A154686 (program): Numbers k such that k^3 + 2*k^2 + k + 1 is prime.
  • A154687 (program): Period 6: repeat [1, 4, 7, 8, 5, 2].
  • A154690 (program): Triangle read by rows: T(n,m) = (2^(n-m) + 2^m)*binomial(n,m), 0 <= m <= n.
  • A154691 (program): Expansion of (1+x+x^2) / ((1-x-x^2)*(1-x)).
  • A154693 (program): Triangle T(n,m) = ( 2^(n-m)+2^m )*A008292(n+1,m+1) read by rows.
  • A154695 (program): Generalized Sierpinski-Pascal-MacMahon gasket triangular sequence defined by T(n, m) = (r^(n-m)*q^m + r^m*q^(n-m))*b(n), where b(n) = coefficients of p(x, n) = 2^n*(1-x)^(n+1) * LerchPhi(x, -n, 1/2), and r=2, q=1.
  • A154699 (program): Terms in A014217 pairwise swapped.
  • A154708 (program): Numbers a such that b and c exist with b <= a < c and a*(a+1) + b^2 = c^2.
  • A154715 (program): Triangle interpolating between the subsets of an n-set (A000079) and the trees on n labeled nodes (A000272) (read by rows).
  • A154728 (program): Products of three consecutive primes of the form 6n+1 (see A002476).
  • A154736 (program): Define k(0) = 2 and k(m) = m^2-k(m-1) for m >= 1. This is a list of those m for which k(m)+1 and k(m)-1 are both prime.
  • A154739 (program): Decimal expansion of sqrt(1 - 1/sqrt(2)), the abscissa of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
  • A154743 (program): Decimal expansion of 2^(1/4) - 2^(-1/4), the ordinate of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
  • A154747 (program): Decimal expansion of sqrt(sqrt(2) - 1), the radius vector of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant.
  • A154760 (program): Final digit of n!! (A006882).
  • A154764 (program): Primes with exactly one odd decimal digit.
  • A154766 (program): Numbers n with exactly one even decimal digit in prime(n).
  • A154777 (program): Numbers of the form x^2 + 2*y^2 with positive integers x and y.
  • A154778 (program): Numbers of the form a^2 + 5b^2 with positive integers a,b.
  • A154783 (program): Row sums of triangle in A154720.
  • A154784 (program): Row sums of triangle in A154721.
  • A154785 (program): Row sums of triangle in A154724.
  • A154786 (program): Row sums of triangle in A154725.
  • A154787 (program): a(n) = A061357(n)*n = A154786(n)/2.
  • A154804 (program): Number of ways to represent 2n as the sum of two distinct primes (counting 1 as a prime).
  • A154806 (program): Numbers such that every run length in base 2 is 4.
  • A154808 (program): Numbers such that every run length in base 2 is 5.
  • A154809 (program): Numbers whose binary expansion is not palindromic.
  • A154810 (program): Nonpalindromic numbers with binary digits only.
  • A154811 (program): a(n) = Fibonacci(2n+1) mod 9.
  • A154815 (program): Period 6: repeat [8, 7, 4, 5, 2, 1].
  • A154817 (program): Triangle T(n,k) = A060187(n+2,k+2), 1<=k<=n.
  • A154825 (program): Reversion of x*(1-2*x)/(1-3*x).
  • A154840 (program): Distance to nearest cube different from n.
  • A154870 (program): Period 6: repeat [7, 5, 1, -7, -5, -1].
  • A154879 (program): Third differences of the Jacobsthal sequence A001045.
  • A154890 (program): Jacobsthal numbers A001045 alternatingly incremented by 3 and 5.
  • A154893 (program): Numbers whose number of proper divisors is not a prime number.
  • A154920 (program): Denominators of a ternary BBP-type formula for log(3).
  • A154921 (program): Triangle read by rows, T(n,k) = C(n,k)*Sum_{j=0..n-k} E(n-k,j)*2^j, where E(n,k) are the Eulerian numbers A173018(n,k), n >= 0, 0 <= k <= n.
  • A154926 (program): Signed version of Pascal’s triangle. Diagonal positive, rest negative.
  • A154929 (program): A Fibonacci convolution triangle.
  • A154930 (program): Inverse of Fibonacci convolution array A154929.
  • A154931 (program): Third column of A154921.
  • A154948 (program): Riordan array ((1+x)/(1-x^2)^2, x(1+x)/(1-x)).
  • A154949 (program): Diagonal sums of Riordan array A154948.
  • A154955 (program): a(1) = 1, a(2) = -1, followed by 0, 0, 0, … .
  • A154957 (program): A symmetric (0,1)-triangle.
  • A154958 (program): Antidiagonal sums of number triangle A154957 regarded as a lower triangular infinite matrix.
  • A154964 (program): a(n) = 3*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=1, a(2)=5.
  • A154968 (program): a(n) = 4*a(n-1) + 12*a(n-2), n>2 with a(0)=1, a(1)=1, a(2)=7.
  • A154990 (program): Triangle read by rows. Main diagonal is positive. The rest of the terms are negative.
  • A154992 (program): A048473 prefixed by two zeros.
  • A154996 (program): a(n) = 5*a(n-1) + 20*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=9.
  • A154997 (program): a(n) = 6*a(n-1) + 30*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=11.
  • A154999 (program): a(n) = 7*a(n-1) + 42*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=13.
  • A155000 (program): a(n) = 8*a(n-1) + 56*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=15.
  • A155001 (program): a(n) = 9*a(n-1) + 72*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=17.
  • A155013 (program): Integer part of square root of A000584.
  • A155014 (program): a(n) = floor(sqrt(n^7)).
  • A155015 (program): Integer part of square root of n^11 = A008455(n).
  • A155016 (program): Integer part of square root of A010801.
  • A155017 (program): a(n) = 10*a(n-1) + 90*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=19 .
  • A155018 (program): Integer part of square root of n^15 = A010803(n).
  • A155019 (program): Integer part of square root of n^17 = A010805(n).
  • A155020 (program): a(n) = 2*a(n-1) + 2*a(n-2) for n>2, a(0)=1, a(1)=1, a(2)=3.
  • A155029 (program): Complement to A051731 with the identity matrix A023531 included.
  • A155031 (program): Triangle T(n, k) = 0 if n==0 (mod k) otherwise -1 with T(n, n) = 1 and T(n, 0) = 0, read by rows.
  • A155037 (program): Numbers n such that n^3+2*n^2+1 is prime.
  • A155038 (program): Triangle read by rows: T(n,k) is the number of compositions of n with first part k.
  • A155040 (program): A symmetric (1,-1)-triangle.
  • A155041 (program): Diagonal sums of symmetric (1,-1)-triangle A155040.
  • A155043 (program): a(0)=0; for n >= 1, a(n) = 1 + a(n-d(n)), where d(n) is the number of divisors of n (A000005).
  • A155046 (program): List of pairs: first pair is (1,1); then follow (x,y) with (x+2y, x+y).
  • A155047 (program): a(1) = 1, a(2) = 2, then a(n) = largest prime factor of the partial sum up to a(n-1).
  • A155049 (program): Expansion of (1+5*x)/(1-13*x+10*x^2).
  • A155050 (program): A symmetric Catalan based triangle.
  • A155051 (program): Expansion of c(x^2)*(1+x)/(1-x), c(x) the g.f. of A000108.
  • A155058 (program): Primes with odd largest digit.
  • A155067 (program): First differences of A031368.
  • A155069 (program): Expansion of (3 - x - sqrt(1 - 6*x + x^2))/2.
  • A155071 (program): Primes with two odd digits.
  • A155072 (program): Positive integers n such that the base-2 MR-expansion of 1/n is periodic with period (n-1)/4.
  • A155073 (program): Expansion of (1+6*x)/(1-12*x-8*x^2).
  • A155076 (program): Triangle read by rows. The main diagonal is positive. If rowindex >= 2*columnindex then -1 else 0.
  • A155084 (program): A Catalan transform of x^n (A002605).
  • A155085 (program): a(n) = n + sum of divisors of n.
  • A155086 (program): Numbers n such that n^2 == -1 (mod 13).
  • A155090 (program): Composites k such that composite(k) is odd.
  • A155091 (program): Triangle read by rows. Signed version of A145362. Main diagonal positive, rest of the nonzero terms negative.
  • A155095 (program): Numbers k such that k^2 == -1 (mod 17).
  • A155096 (program): Numbers k such that k^2 == -1 (mod 29).
  • A155097 (program): Numbers k such that k^2 == -1 (mod 37).
  • A155098 (program): Numbers k such that k^2 == -1 (mod 41).
  • A155099 (program): Third column of A155092.
  • A155102 (program): Triangle T(n,k) read by rows. If n=k then T(n,k)=1, elseif n=2*k then T(n,k)=-(k+1), else T(n,k)=0.
  • A155104 (program): Numbers appearing in the fourth column of A155103.
  • A155107 (program): Numbers that are 23 or 30 (mod 53).
  • A155108 (program): Primes k such that the k-th composite is even.
  • A155110 (program): a(n) = 8*Fibonacci(2n+1).
  • A155111 (program): Odd numbers k such that composite(k) is odd.
  • A155112 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [0,2,-1/2,-1/2,0,0,0,0,0,0,0,0,…] DELTA [1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A155116 (program): a(n) = 3*a(n-1) + 3*a(n-2), n>2, a(0)=1, a(1)=2, a(2)=8.
  • A155117 (program): a(n) = 4*a(n-1) + 4*a(n-2), n>2, a(0)=1, a(1)=3, a(2)=15.
  • A155118 (program): Array T(n,k) read by antidiagonals: the k-th term of the n-th iterated differences of A140429.
  • A155119 (program): a(n) = 5*a(n-1) + 5*a(n-2), n > 2, a(0)=1, a(1)=4, a(2)=24.
  • A155120 (program): a(n) = 2*(n^3 + n^2 + n - 1).
  • A155121 (program): a(n) = 2*n*(1 + n + n^2 + n^3) - 3.
  • A155122 (program): a(n) = 4*(3*n+2)*(2*n+1)*(n+2)*(n+1).
  • A155124 (program): Triangle T(n, k) = 1-n if k=0 else 2, read by rows.
  • A155127 (program): a(n) = 6*a(n-1) + 6*a(n-2), n>2, a(0)=1, a(1)=5, a(2)=35.
  • A155130 (program): a(n) = 7*a(n-1) + 7*a(n-2), n>2, a(0)=1, a(1)=6, a(2)=48.
  • A155132 (program): a(n) = 8*a(n-1) + 8*a(n-2), n > 2, a(0)=1, a(1)=7, a(2)=63.
  • A155133 (program): Numbers n >= 0 such that 5n^2+4n+1 is prime.
  • A155135 (program): Integers n such that n^3+28*n^2 is a square.
  • A155136 (program): Integers n such that n+28 is a square.
  • A155138 (program): a(n) = nonnegative value y such that (A155136(n), y) is a solution to the Diophantine equation x^3+28*x^2 = y^2.
  • A155144 (program): a(n) = 9*a(n-1) + 9*a(n-2), n>2; a(0)=1, a(1)=8, a(2)=80.
  • A155148 (program): Numbers n such that n^4 has exactly 2 different decimal digits.
  • A155151 (program): Triangle T(n, k) = 4*n*k + 2*n + 2*k + 2, read by rows.
  • A155152 (program): Numbers n such that 13n^2+3n+1 is prime.
  • A155155 (program): a(n) = 2*(10*3^n - 1).
  • A155156 (program): Triangle T(n, k) = 4*n*k + 2*n + 2*k, read by rows.
  • A155157 (program): a(n) = 10*a(n-1) + 10*a(n-2), with a(0)=1, a(1)=9, a(2)=99.
  • A155158 (program): Period 4: repeat [1, 5, 7, 3].
  • A155159 (program): a(n) = 1 + 2*n*n!.
  • A155160 (program): a(n) = 2^n * (n + 3)!!.
  • A155161 (program): A Fibonacci convolution triangle: Riordan array (1, x/(1 - x - x^2)). Triangle T(n,k), 0 <= k <= n, read by rows.
  • A155167 (program): (L)-sieve transform of A004767 = {3,7,11,15,…,4n-1,…}.
  • A155171 (program): Numbers p such that if q = p+1 then (a = q^2-p^2, b = 2*p*q, c = q^2 + p^2) is a primitive Pythagorean triple with s-1 and s+1 primes, where s = a+b+c.
  • A155173 (program): Short leg A of primitive Pythagorean triangles such that perimeter s is average of twin prime pairs, q=p+1, A=q^2-p^2, C=q^2+p^2, B=2*p*q, s=A+B+C; s -/+ 1 are primes.
  • A155174 (program): Long leg B of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.*)
  • A155175 (program): Hypotenuse C of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.
  • A155176 (program): Perimeter s/6 (divided by 6) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, s=a+b+c, s-+1 are primes.
  • A155177 (program): Area ar/6 (divided by 6) of primitive Pythagorean triangles such that perimeters are Averages of twin prime pairs, q=p+1, a=q^2-p^2, c=q^2+p^2, b=2*p*q, ar=a*b/2; s=a+b+c, s-+1 are primes.
  • A155179 (program): a(n)=4*a(n-1)+a(n-2), n>2; a(0)=1, a(1)=3, a(2)=12.
  • A155181 (program): a(n)=5*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=4, a(2)=20 .
  • A155189 (program): Square-weak primes.
  • A155195 (program): a(n)=6*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=5, a(2)=30 .
  • A155196 (program): a(n)=7*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=6, a(2)=42 .
  • A155197 (program): a(n) = 8*a(n-1) + a(n-2) for n>2, with a(0)=1, a(1)=7, a(2)=56.
  • A155198 (program): a(n)=9*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=8, a(2)=72 .
  • A155199 (program): a(n)=10*a(n-1)+a(n-2), n>2 ; a(0)=1, a(1)=9, a(2)=90 .
  • A155200 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2) * x^n/n ), a power series in x with integer coefficients.
  • A155201 (program): G.f.: A(x) = exp( Sum_{n>=1} (2^n + 1)^n * x^n/n ), a power series in x with integer coefficients.
  • A155202 (program): G.f.: A(x) = exp( Sum_{n>=1} (2^n - 1)^n * x^n/n ), a power series in x with integer coefficients.
  • A155203 (program): G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients.
  • A155204 (program): G.f.: A(x) = exp( Sum_{n>=1} (3^n + 1)^n * x^n/n ), a power series in x with integer coefficients.
  • A155207 (program): G.f.: A(x) = exp( Sum_{n>=1} 4^(n^2) * x^n/n ), a power series in x with integer coefficients.
  • A155209 (program): G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n * x^n/n ), a power series in x with integer coefficients.
  • A155210 (program): G.f.: A(x) = exp( Sum_{n>=1} (4^n - 1)^n/3^(n-1) * x^n/n ), a power series in x with integer coefficients.
  • A155211 (program): Numbers n such that n^4+(n+1)^4 is a prime.
  • A155212 (program): a(n) = (n^2 + 9*n + 4)/2.
  • A155213 (program): a(n) = floor(prime(n)/9).
  • A155449 (program): Numbers k == 6 or 11 (mod 17).
  • A155450 (program): Numbers equal to 5 or 18 mod 23.
  • A155455 (program): a(n)=5*a(n-1)+16*a(n-2), n>1 ; a(0)=0, a(1)=1.
  • A155456 (program): Write (1+1/x)*log(1+x) = Sum c(n)*x^n; then a(n) = (n+1)!*c(n).
  • A155457 (program): a(n) = exp(Lambda(n)), where Lambda(n) is the von Mangoldt function for odd (!) primes.
  • A155458 (program): a(n)=6*a(n-1)+25*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=6 .
  • A155459 (program): a(n)=7*a(n-1)+36*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=7 .
  • A155460 (program): a(n)=8*a(n-1)+49*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=8 .
  • A155461 (program): a(n) = n^2 + 52*n + 30.
  • A155462 (program): Frequency of n in A155213.
  • A155464 (program): a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.
  • A155465 (program): a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555.
  • A155466 (program): a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248.
  • A155469 (program): Numbers that are the sum of 2 (not-distinct) numbers; nonzero square and cube, including repetitions.
  • A155477 (program): a(n) = 43^(2*n+1).
  • A155482 (program): Signed-digit binary expansion of Pi/4
  • A155483 (program): a(n)=A000040(A043489(n+1)).
  • A155485 (program): a(n) = 5^n + (1 - 4^n)/3.
  • A155487 (program): Difference between n-th composite number and twice its least prime factor.
  • A155494 (program): Triangle T(n, k) = (k+1)*(n-k+1)*binomial(n,k) with T(n, 0) = T(n, n) = 1, read by rows.
  • A155495 (program): Triangle read by rows: t(n,m) = binomial(2*n,2*m) * binomial(n,m).
  • A155497 (program): Triangle T(n, k) = binomial(n, k)*binomial(n+1, k+1)*binomial(2*n, 2*k)/(n-k+1), read by rows.
  • A155498 (program): Number of odd digits in the concatenation of first n primes.
  • A155499 (program): a(n) = n + (n+1)^(n+2).
  • A155504 (program): Numbers of the form (3h+1)*3^(k+1) listed in increasing order.
  • A155516 (program): Triangle T(n, k) = binomial(2*n, 2*k)*binomial(2*n+1, 2*k+1)/(2*n-2*k+1), read by rows.
  • A155519 (program): a(n) = Sum (J(p): p is a permutation of {1,2,…,n}), where J(p) is the number of j <= ceiling(n/2) such that p(j) + p(n+1-j) = n+1.
  • A155521 (program): Smallest fixed point summed over all non-derangement permutations of {1,2,…,n}.
  • A155537 (program): Triangle T(n,k,p,q) = (p^n + q^n)*A001263(n, k) with p=2 and q=1, read by rows.
  • A155538 (program): Take square root of previous term.
  • A155539 (program): a(n) = n^(n+3) + (n+3)^n.
  • A155542 (program): Expansion of (2+2*x)/(1-8*x-25*x^2).
  • A155543 (program): a(n)=2*A081294(n).
  • A155546 (program): Triangle read by rows where T(m,n)=2mn + m + n - 5, 1<=n<=m.
  • A155547 (program): a(n) = prime(n) without prime digits in n.
  • A155550 (program): Triangle read by rows where T(m,n)=2*m*n + m + n - 6.
  • A155551 (program): Triangle read by rows where T(m,n)=2*m*n + m + n - 9.
  • A155557 (program): A proximate-prime polynomial sequence generated by 2*n^2 - 2*n + 53089.
  • A155559 (program): a(n) = 2*A131577(n).
  • A155579 (program): Recursive sequence (n+1)*a(n) = 3*(3*n-2)*a(n-1).
  • A155585 (program): a(n) = 2^n*E(n, 1) where E(n, x) are the Euler polynomials.
  • A155586 (program): A modified Catalan sequence array.
  • A155587 (program): Expansion of (1 + x*c(x))/(1 - x), where c(x) is the g.f. of A000108.
  • A155588 (program): a(n) = 5^n + 2^n - 1^n.
  • A155589 (program): 6^n+2^n-1.
  • A155590 (program): a(n) = 7^n+2^n-1^n.
  • A155592 (program): 8^n+2^n-1^n.
  • A155593 (program): a(n) = 9^n + 2^n - 1.
  • A155594 (program): 10^n+2^n-1.
  • A155595 (program): 11^n+2^n-1.
  • A155596 (program): a(n) = 5^n - 2^n + 1^n.
  • A155597 (program): a(n) = 6^n - 2^n + 1.
  • A155598 (program): a(n) = 7^n-2^n+1.
  • A155599 (program): a(n) = 8^n - 2^n + 1^n.
  • A155600 (program): a(n) = 9^n-2^n+1^n.
  • A155601 (program): a(n) = 10^n - 2^n + 1^n.
  • A155602 (program): 4^n + 3^n - 1.
  • A155603 (program): a(n) = 5^n+3^n-1.
  • A155604 (program): 6^n+3^n-1.
  • A155605 (program): 7^n+3^n-1.
  • A155606 (program): a(n) = 8^n + 3^n - 1.
  • A155607 (program): 9^n+3^n-1.
  • A155608 (program): 10^n + 3^n - 1.
  • A155609 (program): a(n) = 4^n - 3^n + 1.
  • A155610 (program): 5^n - 3^n + 1.
  • A155611 (program): 6^n - 3^n + 1.
  • A155612 (program): 7^n - 3^n + 1.
  • A155613 (program): 8^n - 3^n + 1.
  • A155614 (program): 9^n - 3^n + 1.
  • A155615 (program): 10^n - 3^n + 1.
  • A155616 (program): 5^n + 4^n - 1.
  • A155617 (program): 6^n + 4^n - 1.
  • A155618 (program): a(n) = 7^n+4^n-1^n.
  • A155619 (program): 8^n+4^n-1^n
  • A155620 (program): 9^n+4^n-1.
  • A155621 (program): 10^n+4^n-1^n
  • A155622 (program): a(n) = 11^n - 2^n + 1.
  • A155623 (program): a(n) = 11^n + 3^n - 1.
  • A155624 (program): 11^n-3^n+1.
  • A155625 (program): 11^n+4^n-1.
  • A155626 (program): a(n) = 5^n-4^n+1.
  • A155627 (program): a(n) = 6^n - 4^n + 1.
  • A155628 (program): a(n) = 7^n-4^n+1^n.
  • A155629 (program): a(n) = 8^n-4^n+1^n.
  • A155630 (program): a(n) = 9^n-4^n+1^n.
  • A155631 (program): 10^n-4^n+1^n
  • A155632 (program): a(n) = 11^n - 4^n + 1^n.
  • A155633 (program): 6^n+5^n-1.
  • A155634 (program): 7^n + 5^n - 1.
  • A155635 (program): 8^n+5^n-1.
  • A155636 (program): 9^n+5^n-1.
  • A155637 (program): 10^n+5^n-1.
  • A155638 (program): a(n) = 11^n+5^n-1^n.
  • A155639 (program): a(n) = 6^n-5^n+1^n.
  • A155640 (program): a(n) = 7^n - 5^n + 1^n.
  • A155641 (program): 8^n-5^n+1^n.
  • A155642 (program): 9^n - 5^n + 1.
  • A155643 (program): 10^n-5^n+1.
  • A155644 (program): 11^n-5^n+1.
  • A155645 (program): 7^n+6^n-1.
  • A155646 (program): a(n) = 8^n + 6^n - 1.
  • A155647 (program): a(n) = 9^n+6^n-1^n.
  • A155648 (program): a(n) = 10^n + 6^n - 1.
  • A155649 (program): a(n) = 11^n+6^n-1^n.
  • A155650 (program): 7^n - 6^n + 1.
  • A155651 (program): 8^n-6^n+1^n
  • A155652 (program): 9^n-6^n+1.
  • A155653 (program): 10^n-6^n+1.
  • A155654 (program): 11^n - 6^n + 1.
  • A155655 (program): 8^n+7^n-1^n.
  • A155656 (program): 9^n+7^n-1.
  • A155657 (program): 10^n+7^n-1.
  • A155658 (program): a(n) = 11^n + 7^n - 1.
  • A155659 (program): 8^n-7^n+1.
  • A155660 (program): 9^n-7^n+1.
  • A155661 (program): 10^n-7^n+1.
  • A155662 (program): 11^n-7^n+1.
  • A155663 (program): 9^n+8^n-1.
  • A155664 (program): 10^n+8^n-1
  • A155665 (program): 11^n+8^n-1.
  • A155666 (program): 9^n-8^n+1.
  • A155667 (program): 10^n-8^n+1.
  • A155668 (program): 11^n-8^n+1.
  • A155669 (program): 10^n+9^n-1.
  • A155670 (program): 11^n+9^n-1^n
  • A155671 (program): a(n) = 10^n - 9^n + 1^n.
  • A155672 (program): 11^n-9^n+1^n
  • A155673 (program): 11^n+10^n-1^n
  • A155674 (program): 11^n-10^n+1^n
  • A155689 (program): a(n) = Sum_{k >= 1} floor(n * sqrt(2) / 2^k).
  • A155698 (program): a(n)=a(n-1)+a(n-2)^a(n-3); a(1)=a(2)=a(3)=1.
  • A155701 (program): a(n) = (4^n + 8)/3.
  • A155702 (program): Primes of the form 2n^2-9.
  • A155704 (program): Triangle read by rows where T(m,n)=2*m*n + m + n + 10.
  • A155705 (program): Triangle read by rows where T(m,n) = 2*m*n + m + n + 2.
  • A155706 (program): A119468 made symmetrical using a matrix polynomial system: A(n,m,k)=If[m less than n, 1, -1]; p(x,k)=(-1)^n*CharacteristicPolynomial[A[n,m,k],x]; t(n,m)=coefficients(p(x,n)+x^n*p(1/x,n))
  • A155716 (program): Numbers of the form N = a^2 + 6b^2 for some positive integers a,b.
  • A155721 (program): Positions of parity change in A033035.
  • A155722 (program): Numbers k such that 2*k + 9 is prime.
  • A155723 (program): Numbers k such that 2*k + 9 is not prime.
  • A155724 (program): Triangle read by rows: T(m,n) = 2mn + m + n - 4.
  • A155726 (program): Production matrix for Fibonacci numbers, read by row.
  • A155727 (program): Production matrix of the Jacobsthal numbers, read by row.
  • A155728 (program): INVERTi transform of A054765: (1, 3, 19, 160, 1744, …).
  • A155730 (program): Indices of Bell numbers divisible by 5.
  • A155734 (program): Binomial transform of A154879.
  • A155736 (program): Numbers n such that 4*n^2+2*n-1 is a prime.
  • A155737 (program): Primes of the form 4*n^2 + 2*n -1.
  • A155738 (program): Primes p such that 4*p^2+2*p-1 is also prime
  • A155750 (program): First differences of A031215.
  • A155752 (program): Where 2’s occur in the prime differences A001223.
  • A155753 (program): a(n) = (n^3 - n + 9)/3.
  • A155754 (program): A variation on 10^n mod 19
  • A155757 (program): (n^3 - n + 15)/3.
  • A155761 (program): Riordan array (c(2*x^2), x*c(2*x^2)) where c(x) is the g.f. of A000108.
  • A155769 (program): a(n) = 2n^2 + 2n - 41.
  • A155770 (program): Primes of form: 2*n^2+2*n-41.
  • A155771 (program): Numbers n such that 2*n^2+2*n-41 is a prime.
  • A155794 (program): Triangle read by rows: t(n,m)=(m*(m-n))!
  • A155795 (program): Triangle read by rows: t(n,k)=n!/(n - k*(n - k)).
  • A155797 (program): Triangle read by rows: t(n,k)=Binomial[k*(n - k), n]
  • A155798 (program): Triangle read by rows: t(n,k)=Binomial[n, k] + Binomial[k*(n - k), n]
  • A155803 (program): A023001 interleaved with 2*A023001 and 4*A023001.
  • A155816 (program): First nonzero digit in the decimal expansion of (cos Pi/4)^n
  • A155819 (program): a(n) = p(n+1)^2 + 2*p(n) + 1; p(n) is the n-th prime number and n >= 1.
  • A155820 (program): Primes of the form prime(k)^2 + 2*prime(k-1) where prime(k) is the k-th prime number.
  • A155822 (program): Number of compositions of n with no part greater than 3 such that no two adjacent parts are equal.
  • A155828 (program): Number of integers k in {1,2,3,..,n} such that kn+1 is a square.
  • A155836 (program): 2^(2^n) mod n.
  • A155851 (program): n is prime and is the sum of the first k primes for some k, start from 5.
  • A155853 (program): Numbers n such that 13*n + 3 is a prime.
  • A155854 (program): Numbers n such that 13*n + 3 is not prime.
  • A155856 (program): Triangle T(n,k) = binomial(2*n-k, k)*(n-k)!, read by rows.
  • A155857 (program): Row sums of triangle A155856.
  • A155859 (program): a(n) = (1/162)*(61*10^n + 18*n + 20).
  • A155862 (program): A ‘Morgan Voyce’ transform of A007854.
  • A155863 (program): Triangle T(n,k) = n*(n^2 - 1)*binomial(n-2, k-1) for 1 <= k <= n-1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
  • A155864 (program): Triangle T(n,k) = n*(n-1)*binomial(n-2, k-1) for 1 <= k <= n-1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
  • A155865 (program): Triangle T(n,k) = (n-1)*binomial(n-2, k-1) for 1 <= k <= n-1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
  • A155866 (program): A ‘Morgan Voyce’ transform of the Bell numbers A000110.
  • A155867 (program): A ‘Morgan Voyce’ transform of the large Schroeder numbers A006318.
  • A155872 (program): a(n) = 10^n + 11^n.
  • A155874 (program): Smallest positive composite number such that a(n)+n is also composite.
  • A155875 (program): Smallest positive composite number such that a(n) - n is also composite.
  • A155879 (program): a(0) = 4; for n > 0, a(n) is the smallest composite number c > a(n-1) such that c - n is also composite.
  • A155883 (program): a(n) = 14*n^3 - 30*n^2 + 24*n - 7.
  • A155887 (program): Riordan array (1, (1/(1-x))c(x/(1-x))), c(x) the g.f. of A000108.
  • A155888 (program): a(n) = dimension of the space of n-boxes in the unshaded subfactor planar algebra of type E8.
  • A155902 (program): Arises in Connell’s game, a variation of Wythoff’s Nim game.
  • A155912 (program): Let d(i) be the i-th digit of the decimal expansion of Pi = 3.1415926535897932384626433832795…, so that d(0) = 3, d(1) = 1, d(2) = 4, etc. Then a(0) = 3, a(n) = d(d(n)) for n>0.
  • A155919 (program): Number of squared hypotenuses mod n in three dimensions.
  • A155933 (program): Primes of the form n^2 + (n+1)^3.
  • A155934 (program): The sequence k(m) defined in A005991.
  • A155935 (program): Numbers n such that 13*n + 5 is not prime.
  • A155937 (program): Numbers n such that 13*n + 8 is a prime.
  • A155938 (program): Primes p such that 13*p + 8 is also prime.
  • A155939 (program): Numbers n such that 13*n + 8 is not a prime.
  • A155941 (program): Numbers n such that 16*n+1 is not prime.
  • A155942 (program): Numbers n such that 16n+1 is a prime.
  • A155943 (program): Primes p such that 16*p + 1 is also prime.
  • A155944 (program): Jacobsthal numbers A001045, every second term incremented by 1.
  • A155945 (program): Numbers n such that 24*n + 13 is not prime.
  • A155946 (program): Numbers d for which the volume of the regular d-dimensional simplex of unit edge is rational.
  • A155954 (program): a(0)=2, a(1)=3, a(2)=5, a(n) = smallest prime greater than or equal to a(n-1) + a(n-2) + a(n-3).
  • A155955 (program): Triangle read by rows: T(n,k) = (k*n)^k, 0 <= k <= n.
  • A155956 (program): a(n) = Sum_{k=0..n} (k*n)^k.
  • A155957 (program): a(n) = (2*n^2)^n.
  • A155965 (program): a(n) = n*(n^2+4).
  • A155966 (program): a(n) = 2*n^2 + 8.
  • A155972 (program): The Partition Ruler
  • A155977 (program): a(n) = n^5 + n^3.
  • A155978 (program): The primes (p-11)/10 arising in A089442.
  • A155980 (program): First differences of A135351.
  • A155988 (program): a(n) = (2*n+1)*9^n.
  • A155989 (program): List of numbers prime(k) as k runs through the numbers with a single prime digit.
  • A155990 (program): Numbers prime(k) as k runs through the numbers whose digits are all prime.
  • A155996 (program): Nearest integer to 2^n*Pi/4.
  • A155997 (program): Triangle read by rows: T(n, k) = f(n, k) + f(n, n-k), where f(n, k) = binomial(n, k)*(1 + (-1)^k)/2.
  • A155998 (program): Triangle read by rows: T(n, k) = f(n, k) + f(n, n-k), where f(n, k) = binomial(n, k)*(1 - (-1)^k)/2.
  • A156002 (program): Partial sums of round(7^n/9).
  • A156004 (program): Primes p such that 8*p+21 is prime.
  • A156005 (program): Primes p such that 16*p+45 is prime.
  • A156016 (program): Expansion of (1-x-sqrt(1-6x-3x^2))/(2x).
  • A156017 (program): Schroeder paths with two rise colors and two level colors.
  • A156018 (program): Primes of the form k^3 + k^2 + k - 1.
  • A156022 (program): Maximum number of positive numbers represented by substrings of an n-bit number’s binary representation
  • A156023 (program): n(n+1)/2 - A112509(n)
  • A156024 (program): n(n+1)/2 - A156022(n)
  • A156033 (program): Numerator of (Sum_{k=1..n} k^3)/n!.
  • A156034 (program): Denominator of (Sum_{k=1..n} k^3)/n!.
  • A156035 (program): Decimal expansion of 3 + 2*sqrt(2).
  • A156036 (program): Numerators in expansion of log(z^2/(cosh(z)-cos(z))).
  • A156037 (program): Largest nonprime < n-th prime.
  • A156039 (program): Number of compositions (ordered partitions) of n into 4 parts, where the first is at least as great as each of the others.
  • A156040 (program): Number of compositions (ordered partitions) of n into 3 parts (some of which may be zero), where the first is at least as great as each of the others.
  • A156056 (program): n-th triangular number modulo n-th prime.
  • A156057 (program): Decimal expansion of log(3)/2.
  • A156058 (program): a(n) = 5^n * Catalan(n).
  • A156060 (program): Jacobsthal numbers A001045 mod 9.
  • A156061 (program): a(n) = product of indices of distinct prime factors of n, where index(prime(k)) = k.
  • A156062 (program): Riordan array (1/(1-x^4), x/(1-x^4)).
  • A156065 (program): Diagonal sums of inverse of Riordan array (1/(1-x^4),x/(1-x^4)).
  • A156066 (program): Numbers n with property that n^2 is a square arising in A154138.
  • A156067 (program): a(0)=1. a(n)= -2^(n-1)-3*(-1)^n, n>1.
  • A156077 (program): a(n) = #{1<=k<=n : A000002(k)=1}.
  • A156078 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k) = 1}.
  • A156079 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k) = 2}.
  • A156080 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k-1) = 2}.
  • A156081 (program): a(n) = #{1 <= k <= ceiling(n/2) : A000002(2k-1) = 1}.
  • A156084 (program): Sum of the squares of the first n Fibonacci numbers with index divisible by 3.
  • A156085 (program): One fourth of the sum of the squares of the first n Fibonacci numbers with index divisible by 3.
  • A156086 (program): Sum of the squares of the first n Fibonacci numbers with index divisible by 4.
  • A156087 (program): One ninth of the sum of the squares of the first n Fibonacci numbers with index divisible by 4.
  • A156088 (program): Alternating sum of the squares of the first n even-indexed Fibonacci numbers.
  • A156089 (program): Alternating sum of the squares of the first n odd-indexed Fibonacci numbers.
  • A156090 (program): Alternating sum of the squares of the first n Fibonacci numbers with index divisible by 3.
  • A156091 (program): One fourth of the alternating sum of the squares of the first n Fibonacci numbers with index divisible by 3.
  • A156092 (program): Alternating sum of the squares of the first n Fibonacci numbers with index divisible by 4.
  • A156093 (program): One ninth of the alternating sum of the squares of the first n Fibonacci numbers with index divisible by 4.
  • A156094 (program): 5 F(2n) (F(2n) - 1) + 1 where F(n) denotes the n-th Fibonacci number.
  • A156095 (program): 5 F(2n) (F(2n) + 1) + 1 where F(n) denotes the n-th Fibonacci number.
  • A156096 (program): Inverse binomial transform of A030186.
  • A156104 (program): Primes p such that p+36 is also prime.
  • A156105 (program): Primes p such that p + 72 is also prime.
  • A156107 (program): Primes p such that p + 144 is also prime.
  • A156125 (program): a(n)=10^n*C(2n,n)/C(n+3,3).
  • A156126 (program): Sequence related to Hankel transform of super-ballot numbers.
  • A156127 (program): a(n) = 7*2^n - 3.
  • A156128 (program): a(n) = 6^n * Catalan(n).
  • A156136 (program): A triangle of polynomial coefficients related to Mittag-Leffler polynomials: p(x,n)=Sum[Binomial[n, k]*Binomial[n - 1, n - k]*2^k*x^k, {k, 0, n}]/(2*x).
  • A156143 (program): P_n(1)*Q_n(1) (see A155100 and A104035), defining Q_{-1} = 0.
  • A156156 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53.
  • A156157 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 17, a(2) = 85.
  • A156158 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 25, a(2) = 137.
  • A156160 (program): a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=169, a(2)=2809.
  • A156161 (program): a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=289, a(2)=7225.
  • A156162 (program): a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=625, a(2)=18769.
  • A156163 (program): Decimal expansion of (19+6*sqrt(2))/17.
  • A156164 (program): Decimal expansion of 17 + 12*sqrt(2).
  • A156168 (program): A bisection of A002437.
  • A156169 (program): A bisection of A002437.
  • A156171 (program): G.f.: A(x) = exp( Sum_{n>=1} x^n/(1 - 2^n*x)^n / n ), a power series in x with integer coefficients.
  • A156172 (program): Twice A002437.
  • A156173 (program): A q-factorial type triangle sequence: t(n,m)=Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}].
  • A156174 (program): Period 5: repeat [1,-1,1,-1,0].
  • A156177 (program): A bisection of A000436.
  • A156178 (program): A bisection of A000436.
  • A156180 (program): Denominator of Euler(n,1/3).
  • A156183 (program): Denominator of Euler(n, 1/5).
  • A156189 (program): Denominator of Euler(n, 1/6).
  • A156192 (program): Denominator of Euler(n, 1/7).
  • A156194 (program): Period 12: 1,2,7,1,7,2,1,1,4,2,4,1 repeated.
  • A156195 (program): a(2n+2) = 6*a(2n+1), a(2n+1) = 6*a(2n) - 5^n*A000108(n), a(0)=1.
  • A156198 (program): a(n) = 2*a(n-1)+3 with n>1, a(1)=8.
  • A156199 (program): Period 12: repeat 1, 1, 4, 2, 4, 1, 1, 2, 7, 1, 7, 2 .
  • A156201 (program): Numerator of Euler(n, 1/8).
  • A156202 (program): a(n) = 2*a(n-1)+3 for n > 1, a(1) = 10.
  • A156203 (program): a(n) = 2*a(n-1) + 3 for n>1, a(1)=14.
  • A156207 (program): Sum of the products of the digits in n and their position m in n.
  • A156208 (program): Primes appearing as the products of digits and positions in A156207(i) in the order of appearance.
  • A156213 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)*C(2*n-1,n)*x^n/n ), a power series in x with integer coefficients.
  • A156216 (program): G.f.: A(x) = exp( Sum_{n>=1} A000204(n)^n * x^n/n ), a power series in x with integer coefficients.
  • A156217 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^n*x^n/n ), a power series in x with integer coefficients.
  • A156218 (program): Denominator of Euler(n, 1/9).
  • A156226 (program): Primes of the form 9*n^2 + 1.
  • A156227 (program): Period 12: repeat [0,1,3,8,3,1,0,8,6,1,6,8].
  • A156229 (program): Partial sums of A052343.
  • A156230 (program): Sum of the products of the digits of n and the positions of the digits m in n starting from the last digit.
  • A156232 (program): a(n) is the number of induced subgraphs with odd number of edges in the cycle graph C(n).
  • A156234 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*A000204(n)*x^n/n ).
  • A156242 (program): Bisection of A054353.
  • A156243 (program): Bisection of A054353.
  • A156244 (program): Bisection of A078649.
  • A156245 (program): Bisection of A078649.
  • A156246 (program): a(n)=sum(k=1,n,A000002(2*k-1))
  • A156247 (program): a(n)=sum(k=1,n,A000002(2*k))
  • A156248 (program): a(n)=sum(k=1,n,(-1)^k*A000002(2*k))
  • A156249 (program): a(n)=sum(k=1,n,(-1)^k*A000002(2*k-1))
  • A156250 (program): Least k such that A078649(k)>= A054353(n).
  • A156251 (program): Least k such that A078649(k)>=n
  • A156252 (program): Primes of the form 4*n^2+6*n+43.
  • A156253 (program): Least k such that A054353(k) >= n.
  • A156256 (program): Number of 1’s separating successive 2’s in the Kolakoski sequence A000002.
  • A156257 (program): Digit of runs of length 2 in the Kolakoski sequence A000002: a(n) = A000002(A078649(n)).
  • A156258 (program): a(n)=(1/2)*(A000002(A078649(n))-A000002(A078649(n)+2)+1)
  • A156259 (program): a(n)=(1/2)*(A000002(A078649(n)+2)-A000002(A078649(n))+1)
  • A156260 (program): Row sums of A156254.
  • A156261 (program): a(n)=n/2+(1/2)*sum(k=1,n,A000002(A078649(k)+2)-A000002(A078649(k)))
  • A156262 (program): a(n)=n/2-(1/2)*sum(k=1,n,A000002(A078649(k)+2)-A000002(A078649(k)))
  • A156263 (program): a(n)=A000002(3*n-1)
  • A156264 (program): a(n) = A000002(3*n-2), where A000002 is the Kolakoski sequence.
  • A156265 (program): a(n)=3*n-A078649(n)
  • A156266 (program): a(n) = 7^n*Catalan(n).
  • A156267 (program): a(n)=A054353(2*n)-A078649(n)
  • A156270 (program): a(n) = 8^n*Catalan(n).
  • A156271 (program): a(n)=sum(k=1,n,A000002(A078649(k)))
  • A156273 (program): a(n) = 9^n*Catalan(n).
  • A156275 (program): a(n) = 10^n*Catalan(n).
  • A156276 (program): Denominator of Euler(n, 1/10).
  • A156277 (program): Numbers appearing at every third row in the third column of A156241.
  • A156279 (program): 4 times the Lucas number A000032(n).
  • A156283 (program): Period 6: repeat [1, 2, 4, -4, -2, -1].
  • A156286 (program): Triangle T(n, k) = (1/k^n)*Product_{j=1..n} ( (k-1)*(k+1)^j + 1 ), read by rows.
  • A156287 (program): Numbers k such that 4*k-5 is a prime number.
  • A156288 (program): Numbers n such that 4*n-5 is not a prime number.
  • A156290 (program): Triangle read by rows: alternating binomial coefficients with signs.
  • A156293 (program): Denominator of Euler(n, 1/11).
  • A156294 (program): Sum of products of the digits of prime numbers and the position of the digits in the prime numbers.
  • A156296 (program): a(1)=1, a(n) = 2 * Sum_{k=1..n-1} (3^k-1)/2 * a(k) for n>=2.
  • A156297 (program): Triangle T(n,k) read by rows. If n = k^2 then 1 else 0.
  • A156300 (program): Primes p such that 4*p - 5 is also prime.
  • A156301 (program): a(n) = ceiling( n * (log_3 2)) = ceiling(n * 0.6309297535714574371…).
  • A156302 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^2*x^n/n ), a power series in x with integer coefficients.
  • A156303 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n^2)*x^n/n ), a power series in x with integer coefficients.
  • A156304 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n^3)*x^n/n ), a power series in x with integer coefficients.
  • A156308 (program): Inverse of triangle S(n,m) defined by sequence A156290, n >= 1, 1 <= m <= n.
  • A156309 (program): Decimal expansion of the absolute value of the larger solution of (n^2+n)/2 = -1/12. (Real root q of 6n^2 + 6n + 1, the other root being p = -1-q.)
  • A156319 (program): Triangle by columns: (1, 2, 0, 0, 0, …) in every column.
  • A156320 (program): List of prime pairs of the form (p, p+8).
  • A156324 (program): a(1)=0, a(n+1) is smallest nonprime >= a(n)+n.
  • A156330 (program): Numerator of Euler(n, 1/12).
  • A156331 (program): a(n)=8*A154811(n).
  • A156334 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^[n^2/2+1]*x^n/n ), a power series in x with integer coefficients.
  • A156335 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.
  • A156337 (program): G.f.: A(x) = exp( Sum_{n>=1} 4^[(n^2+1)/2]*x^n/n ), a power series in x with integer coefficients.
  • A156339 (program): Denominator of Euler(n, 1/13).
  • A156340 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2-n+1) * x^n/n ), a power series in x with integer coefficients.
  • A156341 (program): Expansion of (2-6*x)/(1-12*x+11*x^2).
  • A156346 (program): Palindromic period of length 12: repeat 1,2,-4,4,-2,-1,-1,-2,4,-4,2,1.
  • A156348 (program): Triangle T(n,k) read by rows. Column of Pascal’s triangle interleaved with k-1 zeros.
  • A156349 (program): a(n)=sum_{k=1..n} r(k) where r(k)=A000002(k) if A000002(k+1)=2 and r(k)=0 if A000002(k+1)=1
  • A156351 (program): a(n) = Sum_{k=1..n} (-1)^K(k+1)*(K(k+1)-K(k)) where K(k) = A000002(k).
  • A156352 (program): a(n)=A078649(A054353(n)-n+1)-A054353(n)
  • A156353 (program): A symmetrical powers triangle sequence: t(n,m) = (m^(n - m) + (n - m)^m).
  • A156354 (program): Triangle T(n, k) = k^(n-k) + (n-k)^k with T(0, 0) = 1, read by rows.
  • A156359 (program): Denominator of Euler(n, 1/14).
  • A156360 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma_n(2n)*x^n/n ), where sigma_n(2n) is the sum of the n-th powers of the divisors of 2*n.
  • A156361 (program): a(2*n+2) = 7*a(2*n+1), a(2*n+1) = 7*a(2*n) - 6^n*A000108(n), a(0) = 1.
  • A156362 (program): a(2*n+2) = 8*a(2*n+1), a(2*n+1) = 8*a(2*n) - 7^n*A000108(n), a(0)=1.
  • A156365 (program): T(n, k) = E(n, k)*2^k where E(n,k) are the Eulerian numbers A173018, for n > 0 and 0 <= k <= n-1, additionally T(0,0) = 1.
  • A156367 (program): Triangle T(n, k) = binomial(n+k, 2*k)*k!, read by rows.
  • A156372 (program): Denominator of Euler(n, 1/15).
  • A156376 (program): a(n) = 30*n + 19.
  • A156377 (program): Numerator of Euler(n, 1/16).
  • A156384 (program): The number of solutions to x^2 + y^2 + 2*z^2 = n in nonnegative integers x,y,z.
  • A156531 (program): Denominator of Euler(n, 1/17).
  • A156536 (program): Period length 12: repeat 7,5,-1,1,-5,-7,-7,-5,1,-1,5,7.
  • A156540 (program): Array A(n, k) = Product_{j=1..n} ( (k+1)^j - 1 ) with A(n, 0) = n!, read by antidiagonals.
  • A156542 (program): Number of distinct Sophie Germain prime factors of n.
  • A156543 (program): Multiplicative closure of primes that are not Sophie Germain primes (A053176).
  • A156548 (program): Decimal expansion of the real part of the limit of f(f(…f(0)…)) where f(z)=sqrt(i+z).
  • A156550 (program): a(n) = 5*(-1)^n*A078008(n).
  • A156551 (program): Period 10: repeat [8,6,0,4,2,2,4,0,6,8].
  • A156552 (program): Unary-encoded compressed factorization of natural numbers.
  • A156554 (program): The number of integer sequences of length d = 2n+1 such that the sum of the terms is 0 and the sum of the absolute values of the terms is d-1.
  • A156558 (program): a(n) = Sum_{k=1..n} (n^k mod (n-k+1)).
  • A156561 (program): Floor(Fibonacci(2n+1)/9).
  • A156562 (program): a(n) = (-1)^n*Sum_{k=1..n} A054353(k)*(-1)^k.
  • A156563 (program): a(n) = (-1)^n*Sum_{k=1..n} A078649(k)*(-1)^k.
  • A156566 (program): a(2n+2) = 9*a(2n+1), a(2n+1) = 9*a(2n) - 8^n*A000108(n), a(0)=1.
  • A156568 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=23, a(2)=115.
  • A156569 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205.
  • A156570 (program): a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=17, a(2)=65.
  • A156571 (program): Decimal expansion of (27 + 10*sqrt(2))/23.
  • A156573 (program): a(n) = 34*a(n-1) - a(n-2) - 4232 for n > 2; a(1)=529, a(2)=13225.
  • A156574 (program): a(n) = 34*a(n-1) - a(n-2) - 4232 for n > 2; a(1)=1369, a(2)=42025.
  • A156575 (program): a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=289, a(2)=4225.
  • A156577 (program): a(2*n+2) = 10*a(2*n+1), a(2*n+1) = 10*a(2*n) - 9^n*A000108(n), a(0) = 1.
  • A156578 (program): Triangle of coefficients of 1 - (n+1)*x^n + n*x^(n+1), read by rows.
  • A156581 (program): Triangle T(n, k, m) = (m+2)^(k*(n-k)) with m = 15, read by rows.
  • A156589 (program): a(n) = 4^n - 2^n - 1.
  • A156590 (program): Decimal expansion of the imaginary part of the limit of f(f(…f(0)…)) where f(z)=sqrt(i+z).
  • A156591 (program): First differences of A154570.
  • A156592 (program): Product p*q of two primes with q = 2*p + 1.
  • A156595 (program): Fixed point of the morphism 0->011, 1->010.
  • A156596 (program): Infinite Fibonacci word fractal sequence.
  • A156605 (program): a(n) = (4^n + 20)/3.
  • A156611 (program): a(1) = 2, a(n+1) is smallest prime >= a(n)+2*n.
  • A156615 (program): a(1)=2, a(n+1) is the smallest prime > n*final digit of a(n).
  • A156616 (program): G.f.: Product_{n>0} ((1+x^n)/(1-x^n))^n.
  • A156619 (program): Numbers congruent to {7, 18} mod 25.
  • A156622 (program): Values of register a when register b becomes 0 for the two-register machine {i[1], i[1], i[1], d[2,1], d[1,6], i[2], d[1,5], d[2,3]}.
  • A156623 (program): Values of register b when register a becomes 0 for the two register machine {i[1], i[1], i[1], d[2,1], d[1,6], i[2], d[1,5], d[2,3]}
  • A156626 (program): a(0)=1; a(1)=2; a(2)=6; a(n+1) = 2*(n+1)*a(n) - n^2*a(n-1), n > 1.
  • A156627 (program): a(n) = 4394*n - 1820.
  • A156634 (program): Denominator of Euler(n, 1/18).
  • A156635 (program): 144*n^2 - n.
  • A156636 (program): a(n) = 4394*n + 1820.
  • A156637 (program): Pell numbers A000129 mod 9. Period 24: repeat 0,1,2,5,3,2,7,7,3,4,2,8,0,8,7,4,6,7,2,2,6,5,7,1.
  • A156638 (program): Numbers k such that k^2 + 2 == 0 (mod 9).
  • A156639 (program): a(n) = 169*n^2 - 140*n + 29.
  • A156640 (program): a(n) = 169*n^2 + 140*n + 29.
  • A156641 (program): a(n) = 13*(100^(n+1) - 1)/99.
  • A156642 (program): Number of decompositions of 4n+2 into unordered sums of two primes of the form 4k+3.
  • A156644 (program): Mirror image of triangle A080233.
  • A156649 (program): Decimal expansion of (9+4*sqrt(2))/7.
  • A156655 (program): Primes of the form 1000*k + 1.
  • A156657 (program): Numbers that are not safe primes.
  • A156659 (program): Characteristic function of safe primes.
  • A156660 (program): Characteristic function of Sophie Germain primes.
  • A156661 (program): Denominator of Euler(n, 1/19).
  • A156663 (program): Triangle by columns, powers of 2 interleaved with zeros.
  • A156664 (program): Binomial transform of A052551.
  • A156665 (program): Triangle read by rows, A156663 * A007318
  • A156672 (program): a(1)=2, a(n+1) is the smallest prime >= a(n) + sum of digits of a(n).
  • A156674 (program): Numbers k such that k^2 - 2 == 0 (mod 49).
  • A156675 (program): a(n) = 17*((100^(n+1) - 1)/99).
  • A156676 (program): a(n) = 81*n^2 - 44*n + 6.
  • A156677 (program): a(n) = 81n^2 - 118n + 43.
  • A156683 (program): Integers that can occur as either leg in more than one primitive Pythagorean triple
  • A156685 (program): Number of primitive Pythagorean triples A^2 + B^2 = C^2 with 0 < A < B < C and gcd(A,B)=1 that have a hypotenuse C that is less than or equal to n.
  • A156686 (program): The ordered set of a + b - c as (a,b,c) runs through all Pythagorean triples with a<b<c.
  • A156688 (program): The total number of distinct Pythagorean triples with an area numerically equal to n times their perimeters
  • A156701 (program): a(n) = 4*n^4 + 17*n^2 + 4.
  • A156702 (program): Numbers k such that k^2 - 1 == 0 (mod 24^2).
  • A156706 (program): For all numbers k(n) congruent to +1 or -1 (mod 6) starting with k(n) = {5,7,11,13,…}, a(k(n)) is the congruence (mod 6) if k(n) is prime and 0 if k(n) is composite.
  • A156707 (program): For all numbers k(n) congruent to +1 or -1 (mod 4) starting with k(n) = {3,5,7,9,11,…}, a(k(n)) is the congruence (mod 4) if k(n) is prime and 0 if k(n) is composite.
  • A156708 (program): Triangle read by rows, binomial transform of A154325
  • A156709 (program): For all numbers k(n) congruent to -1 or +1 (mod 6) starting with k(n) = {5,7,11,13,…}, a(k(n)) is incremented by the congruence (mod 6) if k(n) is prime and by 0 if k(n) is composite.
  • A156711 (program): a(n) = 144*n^2 - 161*n + 45.
  • A156712 (program): Star numbers (A003154) that are also triangular numbers (A000217).
  • A156717 (program): Triangle read by rows: T(n,m) = binomial(n + m - 1, 2*m) + binomial(2*n - m - 2, 2*(n - m - 1)).
  • A156718 (program): Numbers k such that k^2 == -1 (mod 13^2).
  • A156719 (program): a(n) = 144*n^2 - 127*n + 28.
  • A156721 (program): a(n) = 57122*n^2 - 47320*n + 9801.
  • A156723 (program): a(n)=A156253(n)-A156251(n)
  • A156724 (program): a(n)=A156253(2n)-A156251(2n)
  • A156726 (program): a(n)=A156253(2n-1)-A156251(2n-1)
  • A156728 (program): a(n) = abs(A054354(n)).
  • A156729 (program): a(n)=(v(2*n+2)-v(2*n))/2 where v(n)=A156253(n)-A156251(n).
  • A156731 (program): a(n)=(v(2*n+1)-v(2*n-1))/2 where v(n)=A156253(n)-A156251(n).
  • A156732 (program): Triangle T(n, k) = ((n-2*k)^2/(n-k+1))*binomial(n+1, k+1), read by rows.
  • A156733 (program): Euler transform of n*A065958(n).
  • A156734 (program): Square array read by antidiagonals up. T(n,k) = if k divides n then +1 else -1.
  • A156735 (program): a(n) = 57122*n^2 + 47320*n + 9801.
  • A156745 (program): a(n) = Sum_{k=1..n} floor((n+k)/k) = n + Sum_{k=1..n} sigma_0(k), where sigma_0(k) is A000005(k). Also a(n) = n + A006218(n).
  • A156746 (program): Numerator of Euler(n, 1/20).
  • A156749 (program): For all numbers k(n) congruent to -1 or +1 (mod 4) starting with k(n) = {3,5,7,9,11,…}, a(k(n)) is incremented by the congruence (mod 4) if k(n) is prime and by 0 if k(n) is composite.
  • A156752 (program): a(n) = floor(Catalan(n+1)/Catalan(n)).
  • A156755 (program): Period 9: repeat 1,1,2,1,1,2,2,2,3.
  • A156760 (program): 5*4^n-1.
  • A156762 (program): Denominator of Euler(n, 1/21).
  • A156763 (program): Triangle T(n, k) = binomial(2*k, k)*binomial(n+k, n-k) + binomial(2*n-k, k)*binomial(2*(n-k), n-k), read by rows.
  • A156769 (program): a(n) = denominator(2^(2*n-2)/factorial(2*n-1)).
  • A156771 (program): a(n) = 729*n - 531.
  • A156772 (program): a(n) = 729*n - 198.
  • A156773 (program): a(n) = 6561*n^2 - 9558*n + 3482.
  • A156774 (program): a(n) = 6561*n^2 - 3564*n + 485.
  • A156778 (program): n*A007504(n)/2 = n*(sum of first n primes)/2
  • A156779 (program): Sum( d | n, sp(d)), where sp(d) = A034387(d) = sum of primes <= d.
  • A156780 (program): sp(n)*pi(n) = A034387(n)*A000720(n) = (sum of primes <= n)*(number of primes <= n).
  • A156789 (program): Irregular triangle, read by rows, T(n, k) = binomial(2*n, k)*binomial(2*k, k).
  • A156795 (program): a(n) = 81*n - 59.
  • A156796 (program): a(n) = 81*n - 22.
  • A156797 (program): Numbers k such that k^2 + 2 == 0 (mod (9^2)).
  • A156798 (program): a(n) = n^4 + 5*n^2 + 4.
  • A156810 (program): a(n) = 225*n^2 - 251*n + 70.
  • A156812 (program): a(n) = 225*n^2 - 199*n + 44.
  • A156813 (program): a(n) = 225*n^2 - n.
  • A156814 (program): a(n) = 225*n^2 + n.
  • A156815 (program): Triangle T(n, k) = n!*StirlingS2(n, k)/binomial(n, k), read by rows.
  • A156820 (program): T(n,m) = Sum_{j=0..m} (-1)^(j + m)*(j + 1)^n*binomial(m, j) + Sum_{j=0..(n-m) (-1)^(j - m + n )*(1 + j)^n*binomial(n-m, j).
  • A156821 (program): Prime factors of 13! listed with multiplicity.
  • A156827 (program): A001792*A008683.
  • A156828 (program): a(1) = 2. a(n) = the smallest prime >= a(n-1) + 4.
  • A156829 (program): a(1) = 2. a(n) = the smallest prime >= a(n-1) + 6.
  • A156834 (program): A156348 * A000010
  • A156836 (program): Triangle read by rows, A156348 * A130207
  • A156838 (program): Row sums of triangle A156837
  • A156840 (program): Numbers k >= 1 such that k^2 == 1 (mod 900).
  • A156841 (program): 529n^2 - 312n + 46.
  • A156842 (program): 529n^2 - 746n + 263.
  • A156843 (program): 279841n^2 - 165048n + 24335.
  • A156844 (program): 279841n^2 - 394634n + 139128.
  • A156845 (program): 12167n - 8579.
  • A156846 (program): 12167n - 3588.
  • A156849 (program): Numbers k such that k^2 == 2 (mod 23^2).
  • A156850 (program): a(1)=2, a(n+1) is the smallest prime > (a(n) + sum of digits of a(n)).
  • A156853 (program): a(n) = 2025*n^2 - 649*n + 52.
  • A156854 (program): a(n) = 2025*n^2 - 3401*n + 1428.
  • A156855 (program): a(n) = 2025*n^2 - n.
  • A156856 (program): a(n) = 2025*n^2 + n.
  • A156857 (program): Expansion of (1+2*x)/(1+x+4*x^2)^2.
  • A156859 (program): The main column of a version of the square spiral.
  • A156861 (program): Triangle read by rows: T(n, k) = 2^k - binomial(n, k+1).
  • A156862 (program): Triangle read by rows: T(n, k) = 2^k - binomial(n, k+1) + 2^(n-k) - binomial(n, n-k+1).
  • A156863 (program): Denominator of Euler(n, 1/22).
  • A156864 (program): Triangle read by rows: T(n, k) = 2^k - binomial(n+1, k+1) - ((2*k-n)/(k+1)) * binomial(n+1, k).
  • A156865 (program): a(n) = 729000*n - 612180.
  • A156866 (program): a(n) = 729000*n - 116820.
  • A156867 (program): a(n) = 729000*n - 180.
  • A156868 (program): a(n) = 729000*n + 180.
  • A156872 (program): Period 12: 1,3,-1,3,1,0,-1,-3,1,-3,-1,0 repeated.
  • A156874 (program): Number of Sophie Germain primes <= n.
  • A156875 (program): Number of safe primes <= n.
  • A156877 (program): Number of primes <= n that are safe primes and also Sophie Germain primes.
  • A156886 (program): a(n) = Sum_{k=0..n} C(n,k)*C(3*n+k,k)
  • A156887 (program): a(n) = Sum_{k=0..n} C(n,k)*C(4*n+k,k).
  • A156892 (program): Denominator of Euler(n, 1/23).
  • A156894 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2*n+k-1,k).
  • A156898 (program): a(n) = the smallest squarefree integer >= the n-th prime power.
  • A156899 (program): a(n) = the largest prime power <= the n-th positive squarefree integer.
  • A156900 (program): a(n) = the smallest prime power >= the n-th positive squarefree integer.
  • A156906 (program): Transform of Fibonacci(n+1) with Hankel transform (-1)^binomial(n+1,2) * Fibonacci(n+1).
  • A156909 (program): G.f.: A(x) = 1 + x*exp( Sum_{k>=1} [A(-(-1)^k*x) - 1]^k/k ).
  • A156910 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^(n^2)/(1 - 2^n*x)^n * x^n/n ).
  • A156911 (program): G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2)/(1 - 3^n*x)^n * x^n/n ).
  • A156922 (program): Third right hand column (n-m=2) of the A156920 triangle
  • A156926 (program): Row sums of the FP2 polynomials of A156925.
  • A156928 (program): G.f. of the z^1 coefficients of the FP1 in the second column of the A156921 matrix.
  • A156934 (program): G.f. of the z^1 coefficients of the FP2 in the second column of the A156925 matrix
  • A156944 (program): Let d(i) be the i-th digit of the decimal expansion of e = 2.71828182845…, so that d(1) = 2, d(2) = 7, d(3) = 1, etc. Then a(n) = d(10 - d(n)).
  • A156959 (program): Numerator of Euler(n, 1/24).
  • A156965 (program): Denominator of Euler(n, 1/25).
  • A156991 (program): Triangle T(n,k) read by rows: T(n,k) = n! * binomial(n + k - 1, n).
  • A156992 (program): Triangle T(n,k) = n!*binomial(n-1, k-1) for 1 <= k <= n, read by rows.
  • A156995 (program): Triangle T(n, k) = 2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), with T(0, 0) = 2, read by rows.
  • A157000 (program): Triangle T(n,k) = (n/k)*binomial(n-k-1, k-1) read by rows.
  • A157001 (program): Fractions x/y, with 1<=x,y<=n, that reduce to (odd)/(even).
  • A157002 (program): Transform of Catalan numbers whose Hankel transform gives the Somos-4 sequence.
  • A157003 (program): Transform of Catalan numbers whose Hankel transform gives the Somos-4 sequence.
  • A157004 (program): Transform of central binomial coefficients A000984 whose Hankel transform obeys a Somos-4 recurrence.
  • A157005 (program): A Somos-4 variant.
  • A157010 (program): a(n) = 1681*n^2 - 756*n + 85.
  • A157014 (program): Expansion of x*(1-x)/(1 - 22*x + x^2).
  • A157019 (program): a(n) = Sum_{d|n} binomial(n/d+d-2, d-1).
  • A157020 (program): a(n) = Sum_{d|n} d*binomial(n/d+d-2,d-1).
  • A157024 (program): a(0)=1, a(n) = (3n-1)*3n*(3n+1)/2 for n>0.
  • A157027 (program): Denominator of Euler(n, 1/26).
  • A157029 (program): A007318 * A157019.
  • A157031 (program): Triangle A054521 * A157019, where A054521 = an infinite lower triangular matrix and A157019 = a vector [1, 2, 2, 4, 2, 8, 2, 10, 8, …].
  • A157032 (program): Let d(i) be the i-th digit of the decimal expansion of phi=1.6180339887498948482045868…,so that d(0) = 1, d(1) = 6, d(2) = 1, etc. Then a(0) = 1, thereafter a(n) = d(d(n)).
  • A157037 (program): Numbers with prime arithmetic derivative A003415.
  • A157040 (program): 121n^2 - 2n.
  • A157052 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 6.
  • A157053 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 8.
  • A157054 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 10.
  • A157055 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 12.
  • A157056 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 14.
  • A157057 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 16.
  • A157058 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 18.
  • A157059 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 20.
  • A157060 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 22.
  • A157061 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 24.
  • A157062 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 26.
  • A157063 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 28.
  • A157064 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 30.
  • A157065 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 32.
  • A157066 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 34.
  • A157067 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 36.
  • A157068 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 38.
  • A157069 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 40.
  • A157070 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 42.
  • A157071 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 44.
  • A157072 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 46.
  • A157073 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 48.
  • A157074 (program): Number of integer sequences of length n+1 with sum zero and sum of absolute values 50.
  • A157075 (program): Positive integers n for which the Diophantine equation x^2 + y^2 = n^2/2 has relatively prime solutions.
  • A157077 (program): Triangle read by rows, coefficients of the Legendre polynomials P(n, x) times 2^n: T(n, k) = 2^n * [x^k] P(n, x), n >= 0, 0 <= k <= n.
  • A157078 (program): a(n) = 32805000*n^2 - 55096200*n + 23133601.
  • A157079 (program): a(n) = 32805000*n^2 - 10513800*n + 842401.
  • A157080 (program): a(n) = 32805000*n^2 - 16200*n + 1.
  • A157081 (program): a(n) = 32805000*n^2 + 16200*n + 1.
  • A157084 (program): Consider all consecutive integer Pythagorean quintuples (X, X+1, X+2, Z-1, Z) ordered by increasing Z; sequence gives X values.
  • A157085 (program): Consider all Consecutive Integer Pythagorean quintuples (X, X+1, X+2, Z-1, Z) ordered by increasing Z; sequence gives Z values.
  • A157088 (program): Consider all consecutive integer Pythagorean septuples (X, X+1, X+2, X+3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives X values.
  • A157089 (program): Consider all Consecutive Integer Pythagorean septuples (X, X+1, X+2, X+3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives Z values.
  • A157092 (program): Consider all consecutive integer Pythagorean 9-tuples (X, X+1, X+2, X+3, X+4, Z-3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives X values.
  • A157093 (program): Consider all Consecutive Integer Pythagorean 9-tuples (X,X+1,X+2,X+3,X+4,Z-3,Z-2,Z-1,Z) ordered by increasing Z; sequence gives Z values.
  • A157094 (program): Denominator of Euler(n, 1/27).
  • A157096 (program): Consider all consecutive integer Pythagorean 11-tuples (X, X+1, X+2, X+3, X+4, X+5, Z-4, Z-3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives X values.
  • A157097 (program): Consider all Consecutive Integer Pythagorean 11-tuples (X, X+1, X+2, X+3, X+4, X+5, Z-4, Z-3, Z-2, Z-1, Z) ordered by increasing Z; sequence gives Z values.
  • A157100 (program): Transform of Catalan numbers whose Hankel transform satisfies the Somos-4 recurrence.
  • A157101 (program): A Somos-4 variant.
  • A157102 (program): Tuple-chromatic Van der Waerden numbers.
  • A157103 (program): Array A(n, k) = Fibonacc(n+1, k), with A(n, 0) = A(n, n) = 1, read by antidiagonals.
  • A157104 (program): Arithmetic derivative of cubefree numbers.
  • A157105 (program): a(n) = 137842*n - 30996.
  • A157106 (program): 5651522n^2 - 2541672n + 285769.
  • A157108 (program): Triangle, read by rows, T(n, k) = binomial(n*binomial(n, k), k).
  • A157110 (program): a(n) = 1681*n^2 - 2606*n + 1010.
  • A157111 (program): a(n) = 137842*n - 106846.
  • A157112 (program): a(n) = 5651522*n^2 - 8761372*n + 3395619.
  • A157121 (program): Decimal expansion of 11+3*sqrt(2).
  • A157122 (program): Decimal expansion of 11 - 3*sqrt(2).
  • A157123 (program): Decimal expansion of (11 + 3*sqrt(2))/(11 - 3*sqrt(2)).
  • A157124 (program): a(1)=1; a(n) = floor((n-1)*Sum_{k=1..n-1} 1/a(k)).
  • A157125 (program): A transform of the Catalan numbers.
  • A157126 (program): Expansion of (1-2x-3x^2+x^3-x^5)/(1+4x^3+x^6).
  • A157127 (program): A transform of the Catalan numbers with a simple Hankel transform.
  • A157128 (program): Expansion of (1 - x - x^2 + x^3 - x^5) / ((1 + x)^2*(1 - x + x^2)^2).
  • A157129 (program): An analog of the Kolakoski sequence A000002, only now a(n) = (length of n-th run divided by 2) using 1 and 2 and starting with 1,1.
  • A157130 (program): Partial sums of A128201.
  • A157132 (program): Factorial of primes divided by prime numbers’ respective places in the sequence of primes.
  • A157142 (program): Signed denominators of Leibniz series for Pi/4.
  • A157194 (program): Fibonacci sequence beginning 41, 43.
  • A157195 (program): a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of the proper divisors of n.
  • A157196 (program): a(n)=(1/2)*(sum of elements of n-th run) using 1 and 2 starting with 1,1.
  • A157201 (program): Numbers k such that 66*k + 1 is prime.
  • A157202 (program): Numbers k such that 66*k + 5 is prime.
  • A157206 (program): Numerator of Euler(n, 1/28).
  • A157214 (program): Decimal expansion of 18 + 5*sqrt(2).
  • A157215 (program): Decimal expansion of 18 - 5*sqrt(2).
  • A157216 (program): Decimal expansion of (18 + 5*sqrt(2))/(18 - 5*sqrt(2)).
  • A157219 (program): Triangle T(n, k) = binomial(n*f(n,k), f(n,k)), where f(n, k) = k if k <= floor(n/2) otherwise n-k, read by rows.
  • A157223 (program): Number of primitive inequivalent oblique sublattices of centered rectangular lattice of index n.
  • A157224 (program): Number of primitive inequivalent (up to Pi/2 rotation) nonsquare sublattices of square lattice of index n.
  • A157226 (program): Number of primitive inequivalent sublattices of square lattice having mirrors parallel to the sides of the unit cell of the parent lattice of index n.
  • A157227 (program): Number of primitive inequivalent (up to Pi/3 rotation) non-hexagonal sublattices of hexagonal (triangular) lattice of index n.
  • A157228 (program): Number of primitive inequivalent inclined square sublattices of square lattice of index n.
  • A157230 (program): Number of primitive inequivalent sublattices of square lattice having mirrors parallel to the diagonals of the unit cell of the parent lattice of index n.
  • A157233 (program): Numerator of Euler(n, 5/28).
  • A157234 (program): Numerator of Euler(n, 9/28).
  • A157235 (program): Number of primitive inequivalent oblique sublattices of hexagonal (triangular) lattice of index n (equivalence and symmetry of sublattices are determined using only parent lattice symmetries).
  • A157236 (program): Numerator of Euler(n, 11/28).
  • A157239 (program): Numerator of Euler(n, 13/28).
  • A157240 (program): a(n) = A128018(n) + 1.
  • A157241 (program): Expansion of x / ((1-x)*(4*x^2-2*x+1)).
  • A157249 (program): Generalized Wilson quotients (or Wilson quotients for composite moduli).
  • A157252 (program): Denominator of Euler(n, 1/29).
  • A157258 (program): Decimal expansion of 7 + 2*sqrt(2).
  • A157259 (program): Decimal expansion of 7 - 2*sqrt(2).
  • A157260 (program): Decimal expansion of (7 + 2*sqrt(2))/(7 - 2*sqrt(2)).
  • A157262 (program): a(n) = 36*n^2 - 55*n + 21.
  • A157263 (program): a(n) = 1728*n - 1320.
  • A157264 (program): a(n) = 10368*n^2 - 15840*n + 6049.
  • A157265 (program): a(n) = 36*n^2 - 17*n + 2.
  • A157266 (program): a(n) = 1728*n - 408.
  • A157267 (program): a(n) = 10368*n^2 - 4896*n + 577.
  • A157279 (program): Product 1*2*…*r mod n, where r = integer part of sqrt(n).
  • A157282 (program): Maximum cardinality of a weakly triple-free subset of {1, 2, …, n}.
  • A157284 (program): Triangle T(n, k, m) = (m+1)^n*binomial(n,k)*f(n,m)*f(k,n-m)/n!, with T(n, 0, m) = 1, where f(n, k) = Product_{j=1..n} ( (1 - (k+1)^J)/(-k)^j ), f(n, 0) = n!, and m = 0, read by rows.
  • A157286 (program): a(n) = 36*n^2 - n.
  • A157287 (program): a(n) = 1728*n - 24.
  • A157288 (program): a(n) = 10368*n^2 - 288*n + 1.
  • A157298 (program): Decimal expansion of (251+66*sqrt(2))/233.
  • A157300 (program): Decimal expansion of (1683 + 58*sqrt(2))/41^2.
  • A157317 (program): G.f. A(x) = Product_{n>=1} 1/(1 - 2^(n^2)*x^n).
  • A157319 (program): Possible total points for a single team in a game of American football, ignoring safeties (and time constraints).
  • A157320 (program): Symmetrical Hahn weights on q-form factorials:m=1;q=2; q-form:t(n,m)=If[m == 0, n!, Product[Sum[(m + 1)^i, {i, 0, k - 1}], {k, 1, n}]]; Hahn weight:b(n,k,m)=If[n == 0, 1, (n!*t[m + 1, k]*t[m + 1, n - k])/(k!*(n - k)!*t[1, n])].
  • A157324 (program): a(n) = 36*n^2 + n.
  • A157325 (program): a(n) = 1728*n + 24.
  • A157326 (program): a(n) = 10368*n^2 + 288*n + 1.
  • A157328 (program): Expansion of 1/(1-2x*c(4x)) with c(x) g.f. of Catalan numbers (A000108).
  • A157330 (program): a(n) = 64*n - 8.
  • A157331 (program): a(n) = 128*n^2 - 32*n + 1.
  • A157335 (program): Expansion of 1/( (1+x)*(1-7*x+x^2) ).
  • A157336 (program): a(n) = 8*(8*n + 1).
  • A157337 (program): a(n) = 128*n^2 + 32*n + 1.
  • A157338 (program): First primes in successive prime centuries.
  • A157349 (program): Decimal expansion of (297 + 68*sqrt(2))/281.
  • A157351 (program): Row sums of triangle T(j,k) = (j^k) mod (j*k) for 1 <= k <= j (see A096133).
  • A157358 (program): Triple-safe primes p: p, (p-1)/2, (p-3)/4, and (p-7)/8 are all prime.
  • A157361 (program): Triangle read by rows, A051731 * (A114810 * 0^(n-k))
  • A157362 (program): a(n) = 49*n^2 - 2*n.
  • A157363 (program): 686n - 14.
  • A157364 (program): a(n) = 4802*n^2 - 196*n + 1.
  • A157365 (program): a(n) = 49*n^2 + 2*n.
  • A157366 (program): a(n) = 686*n + 14.
  • A157367 (program): a(n) = 4802*n^2 + 196*n + 1.
  • A157368 (program): a(n) = 49*n^2 - 78*n + 31.
  • A157369 (program): a(n) = 343*n - 273.
  • A157370 (program): a(n) = 2401*n^2 - 3822*n + 1520.
  • A157371 (program): a(n) = (n+1)*(9-9*n+5*n^2-n^3).
  • A157373 (program): a(n) = 49*n^2 - 20*n + 2.
  • A157374 (program): a(n) = 343*n - 70.
  • A157375 (program): a(n) = 2401*n^2 - 980*n + 99.
  • A157376 (program): a(n) = 6561*n^2 - 7732*n + 2278.
  • A157377 (program): a(n) = 531441*n - 313146.
  • A157378 (program): a(n) = 43046721*n^2 - 50729652*n + 14945957.
  • A157391 (program): A partition product of Stirling_1 type [parameter k = 1] with biggest-part statistic (triangle read by rows).
  • A157410 (program): Final primes in successive prime centuries.
  • A157411 (program): a(n) = 30*n^4 - 120*n^3 + 120*n^2 - 19.
  • A157416 (program): Length of maximal uncrossed cycle of knight moves on n X n board.
  • A157417 (program): Primes of the form floor((4*n^2-8*n-9)/3).
  • A157418 (program): a(n) is the number of ways to insert single pairs of parenthesis to completely separate n identical objects in a straight line such that at least one of the objects at the two ends is not enclosed.
  • A157423 (program): Triangle read by rows, T(n,k) = 0 if (n-k+1) is prime, else 1.
  • A157431 (program): a(n) = 4*n^2 + 73*n + 333.
  • A157432 (program): 64n + 584.
  • A157433 (program): 128n^2 + 2336n + 10657.
  • A157434 (program): a(n) = 4*n^2 + 79*n + 390.
  • A157435 (program): 64n + 632.
  • A157436 (program): a(n) = 128*n^2 + 2528*n + 12481.
  • A157437 (program): Primes congruent to 1, 5, 7, or 11 modulo 24.
  • A157440 (program): a(n) = 121*n^2 - 204*n + 86.
  • A157441 (program): a(n) = 1331*n - 1122.
  • A157442 (program): a(n) = 14641*n^2 - 24684*n + 10405.
  • A157443 (program): a(n) = 121*n^2 - 38*n + 3.
  • A157444 (program): a(n) = 1331*n - 209.
  • A157445 (program): a(n) = 14641*n^2 - 4598*n + 362.
  • A157446 (program): a(n) = 16*n^2 - n.
  • A157447 (program): a(n) = 512*n - 16.
  • A157448 (program): a(n) = 2048*n^2 - 128*n + 1.
  • A157449 (program): Difference between n and the sum of its divisors except 1 and itself.
  • A157451 (program): Number generated by regarding the numbers in row n of A139038 as digits of a base n number.
  • A157452 (program): Number generated by regarding the numbers in row n of A003983 as digits of a base n number.
  • A157454 (program): Triangle read by rows: T(n, m) = min(2*m - 1, 2*(n - m) + 1).
  • A157455 (program): Number generated by regarding the numbers in row n of A157454 as digits of a base n number.
  • A157456 (program): Expansion of x*(1-x) / ( 1 - 16*x + x^2 ).
  • A157457 (program): Read n-th row of triangle in A157458 and regard it as the expansion of a number in base n+1.
  • A157458 (program): Triangle, read by rows, double tent function: T(n,k) = min(1 + 2*k, 1 + 2*(n-k), n).
  • A157459 (program): Expansion of 72*x^2 / (1 - 323*x + 323*x^2 - x^3).
  • A157460 (program): Expansion of 88*x^2 / (1-483*x+483*x^2-x^3).
  • A157461 (program): Expansion of x*(x+1) / (x^2-26*x+1).
  • A157462 (program): Denominator of Euler(n, 1/30).
  • A157467 (program): Primes of the form p^2 + 2*p + 2 where p is prime.
  • A157470 (program): Decimal expansion of (99+14*sqrt(2))/97.
  • A157472 (program): Decimal expansion of (627 + 238*sqrt(2))/23^2.
  • A157474 (program): a(n) = 16n^2 + n.
  • A157475 (program): 512n + 16.
  • A157476 (program): 2048n^2 + 128n + 1.
  • A157491 (program): A050165*A130595 as infinite lower triangular matrices.
  • A157492 (program): Apply partial sum operator twice to sequence of squares of the first n primes.
  • A157493 (program): Apply partial sum operator thrice to sequence of squares of the first n primes.
  • A157497 (program): Triangle read by rows, A156348 * A127648
  • A157499 (program): Denominator of Euler(n, 1/31).
  • A157502 (program): Even numbers without the squares.
  • A157505 (program): a(n) = 1458*n + 18.
  • A157506 (program): a(n) = 13122*n^2 + 324*n + 1.
  • A157507 (program): a(n) = 81*n^2 - 2*n.
  • A157508 (program): a(n) = 1458*n - 18.
  • A157509 (program): a(n) = 13122*n^2 - 324*n + 1.
  • A157510 (program): a(n) = 1000*n + 20.
  • A157511 (program): a(n) = 5000*n^2 + 200*n + 1.
  • A157512 (program): Partial sums of A157502.
  • A157514 (program): a(n) = 25*n^2 - n.
  • A157515 (program): a(n) = 1000*n - 20.
  • A157516 (program): a(n) = 5000*n^2 - 200*n + 1.
  • A157517 (program): a(n) = 7 + 12*n - 6*n^2.
  • A157522 (program): Triangle T(n, k) = f(n, k) + f(n, n-k) - 1, where f(n, k) = k if k <= floor(n/4), floor(n/2) - k if floor(n/4) < k <= floor(n/2), k - floor(n/2) if floor(n/2) < k <= floor(3*n/4), otherwise n-k, read by rows.
  • A157524 (program): a(n) = A140783(n+4)/9.
  • A157528 (program): Triangle read by rows: T(n, k) = 2*k*(n - k) with T(n, 0) = T(n, n) = 1.
  • A157531 (program): Triangle T(n, k) = binomial(2*n, n) + binomial(n, k)^2, read by rows.
  • A157532 (program): a(1) = 2; for n > 1, a(n) = 3.
  • A157603 (program): Triangle read by rows: T(n,k) = 1 for k <= n/2, T(n,k)=A055248 otherwise.
  • A157606 (program): a(1)=1. a(n) = the largest integer coprime to a(n-1) and less than n^2.
  • A157609 (program): 2662n - 22.
  • A157610 (program): 29282n^2 - 484n + 1.
  • A157613 (program): a(n) = 2662*n + 22.
  • A157614 (program): a(n) = 29282*n^2 + 484*n + 1.
  • A157615 (program): On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding path made of alternated vertical and horizontal unitary steps.
  • A157616 (program): On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding path that starts from a corner and is made of alternated vertical and horizontal unitary steps.
  • A157617 (program): On an n X n board, a(n) is the maximal number of squares covered by a self-avoiding cycle made of alternated vertical and horizontal unit length steps.
  • A157618 (program): a(n) = 625*n^2 - 886*n + 314.
  • A157619 (program): 31250n - 22150.
  • A157620 (program): 781250n^2 - 1107500n + 392499.
  • A157621 (program): a(n) = 625n^2 - 364n + 53.
  • A157622 (program): 31250n - 9100.
  • A157623 (program): 781250n^2 - 455000n + 66249.
  • A157625 (program): Product of the composite numbers between n+1 and 2n, both inclusive.
  • A157626 (program): a(n) = 100n^2 - 151n + 57.
  • A157627 (program): 8000n - 6040.
  • A157628 (program): 80000n^2 - 120800n + 45601.
  • A157632 (program): Triangle T(n,m) read by rows: 1 in column m=0 and on the diagonal, else 3*n*m*(n-m).
  • A157633 (program): Triangle T(n,m) read rows: 1 in column m=0 and on the diagonal, 2*m*(n-m)*(m^2-n*m+2*n^2) otherwise.
  • A157635 (program): Triangle read by rows: T(n,m) = 1 if n*m*(n-m) = 0, and n*m*(n-m) otherwise.
  • A157636 (program): Triangle read by rows: T(n, k) = 1 if k=0 or k=n, otherwise = n*k*(n-k)/2.
  • A157639 (program): Least number of lattice points from which every point of a square n X n lattice is visible.
  • A157645 (program): A157644(n+39)-A157644(n).
  • A157647 (program): Decimal expansion of (33+8*sqrt(2))/31.
  • A157648 (program): Decimal expansion of (1539+850*sqrt(2))/31^2.
  • A157649 (program): Decimal expansion of (387 + 182*sqrt(2))/17^2.
  • A157651 (program): a(n) = 100*n^2 - 49*n + 6.
  • A157652 (program): a(n) = 40*(200*n - 49).
  • A157653 (program): a(n) = 80000*n^2 - 39200*n + 4801.
  • A157657 (program): a(1) = 1, a(n) = -mu(n) for n >= 2.
  • A157658 (program): a(1) = 0, a(n) = -mu(n) for n >= 2.
  • A157659 (program): a(n) = 100*n^2 - n.
  • A157660 (program): a(n) = 8000*n - 40.
  • A157661 (program): a(n) = 80000*n^2 - 800*n + 1.
  • A157663 (program): a(n) = 8000*n + 40.
  • A157664 (program): a(n) = 80000*n^2 + 800*n + 1.
  • A157665 (program): a(n) = 729*n^2 - 1016*n + 354.
  • A157666 (program): a(n) = 19683*n - 13716.
  • A157667 (program): a(n) = 531441*n^2 - 740664*n + 258065.
  • A157668 (program): a(n) = 729*n^2 - 442*n + 67.
  • A157669 (program): a(n) = 19683*n - 5967.
  • A157670 (program): a(n) = 531441*n^2 - 322218*n + 48842.
  • A157671 (program): Numbers whose ternary representation begins with 2.
  • A157672 (program): Number of unordered factorizations of n! into two distinct proper factors.
  • A157674 (program): G.f.: A(x) = 1 + x/exp( Sum_{k>=1} (A((-1)^k*x) - 1)^k/k ).
  • A157676 (program): Numbers n such that n + (product of digits of n) is prime.
  • A157681 (program): Fibonacci sequence beginning 29, 31.
  • A157684 (program): a(n)=#{1<=k<=n : [K(k),K(k+1)]=[1,2]} where K=A000002
  • A157685 (program): a(n)=#{1<=k<=n : [K(k),K(k+1)]=[2,1]} where K=A000002
  • A157686 (program): a(n) = A157684(n) - A157685(n).
  • A157687 (program): a(n)=n-A054353(A156351(n)).
  • A157694 (program): Triangle read by rows: the Pascal triangle A007318 with all elements replaced by 1 which do not equal the central binomial coefficients.
  • A157695 (program): Composite numbers that are not multiples of 3.
  • A157696 (program): Define k(n) to be the sequence of integers such that k(n)F(n)=F(2n)(Fibonacci sequence) (A000204); in turn define g(n) to be the sequence of integers such that g(n)k(n)=k(3n)(A110391); finally a(n) is the sequence of integers such that a(n)g(n)=g(5n).
  • A157697 (program): Decimal expansion of sqrt(2/3).
  • A157706 (program): The z^2 coefficients of the polynomials in the GF1 denominators of A156921.
  • A157707 (program): The z^2 coefficients of the polynomials in the GF3 denominators of A156927 divided by 2
  • A157713 (program): a(n)=(2*n+1)!*(2*n-2)!/((n-1)!*(n!)^2*6) ,n=1,2… .
  • A157716 (program): One-eighth of triangular numbers (integers only).
  • A157721 (program): a(n) = 0 if n is 1 or a prime, otherwise a(n) = product of composite (nonprime) divisors of n.
  • A157725 (program): a(n) = Fibonacci(n) + 2.
  • A157726 (program): a(n) = Fibonacci(n) + 3.
  • A157727 (program): a(n) = Fibonacci(n) + 4.
  • A157728 (program): a(n) = Fibonacci(n) - 4.
  • A157729 (program): a(n) = Fibonacci(n) + 5.
  • A157730 (program): a(n) = 441*n^2 - 488*n + 135.
  • A157731 (program): a(n) = 18522*n - 10248.
  • A157732 (program): a(n) = 388962*n^2 - 430416*n + 119071.
  • A157734 (program): a(n) = 441*n^2 - 394*n + 88.
  • A157735 (program): 18522n - 8274.
  • A157736 (program): a(n) = 388962*n^2 - 347508*n + 77617.
  • A157737 (program): a(n) = 441*n^2 - 2*n.
  • A157738 (program): 18522n - 42.
  • A157739 (program): a(n) = 388962*n^2 - 1764*n + 1.
  • A157740 (program): 18522n + 42.
  • A157741 (program): a(n) = 388962*n^2 + 1764*n + 1.
  • A157742 (program): A006094(n+3) mod 9.
  • A157751 (program): Triangle of coefficients of polynomials F(n,x) in descending powers of x generated by F(n,x)=(x+1)*F(n-1,x)+F(n-1,-x), with initial F(0,x)=1.
  • A157757 (program): a(n) = 2809*n^2 - 4618*n + 1898.
  • A157758 (program): a(n) = 297754*n - 244754.
  • A157759 (program): a(n) = 15780962*n^2 - 25943924*n + 10662963.
  • A157760 (program): a(n) = 2809*n^2 - 1000*n + 89.
  • A157761 (program): a(n) = 297754*n - 53000.
  • A157762 (program): a(n) = 15780962*n^2 - 5618000*n + 500001.
  • A157765 (program): Expansion of (2 - 2*x) / (1 - 10*x - 7*x^2).
  • A157767 (program): Numerator of Euler(n, 1/32).
  • A157768 (program): 27225n^2 - 39202n + 14112.
  • A157769 (program): 8984250n - 6468330.
  • A157770 (program): 1482401250n^2 - 2134548900n + 768398401.
  • A157772 (program): Numbers n such that 100n + 13 is prime.
  • A157779 (program): Numerator of Bernoulli(n, 1/2).
  • A157780 (program): Denominator of Bernoulli(n, 1/2).
  • A157782 (program): Denominator of Bernoulli(n, -1/2).
  • A157786 (program): a(n) = 27225*n^2 - 15248*n + 2135.
  • A157787 (program): 8984250n - 2515920.
  • A157788 (program): 1482401250n^2 - 830253600n + 116250751.
  • A157791 (program): Least number of lattice points on two adjacent sides from which every point of a square n X n lattice is visible.
  • A157792 (program): Least number of lattice points on one side from which every point of a square n X n lattice is visible.
  • A157795 (program): Largest subset of the discrete triangular grid { (a,b,c): a+b+c = n, a,b,c >= 0 } that does not contain any upward-pointing triangles (i.e., triples (a+r,b,c), (a,b+r,c), (a,b,c+r) with r positive).
  • A157796 (program): a(n) = 27225*n^2 - 12098*n + 1344.
  • A157797 (program): a(n) = 8984250*n - 1996170.
  • A157798 (program): a(n) = 1482401250*n^2 - 658736100*n + 73180801.
  • A157800 (program): Denominator of Bernoulli(n, 1/3).
  • A157802 (program): a(n) = 27225*n^2 - 51302*n + 24168.
  • A157803 (program): a(n) = 8984250*n - 8464830.
  • A157804 (program): a(n) = 1482401250*n^2 - 2793393900*n + 1315947601.
  • A157805 (program): Numerator of Euler(n,3).
  • A157806 (program): Absolute value of the difference between numerator and denominator of fractions arranged by Cantor’s ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, …) with equivalent fractions removed.
  • A157807 (program): Numerators of fractions arranged in Cantor’s ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, 5/2, …) with equivalent fractions removed.
  • A157810 (program): Period 4: repeat [2, 1, 3, 2].
  • A157813 (program): Denominators of fractions arranged in Cantor’s ordering (1/1, 2/1, 1/2, 1/3, 3/1, 4/1, 3/2, 2/3, 1/4, 1/5, 5/1, 6/1, 5/2, …) with equivalent fractions removed.
  • A157814 (program): a(n) = 27225*n^2 - 2*n.
  • A157815 (program): a(n) = 8984250*n - 330.
  • A157816 (program): a(n) = 1482401250*n^2 - 108900*n + 1.
  • A157818 (program): Denominator of Bernoulli(n, 1/4).
  • A157820 (program): 27225n^2 + 2n.
  • A157821 (program): 8984250n + 330.
  • A157822 (program): 1482401250n^2+108900n+1.
  • A157823 (program): a(n) = A156591(n) + A156591(n+1).
  • A157824 (program): 3600n^2 - 6751n + 3165.
  • A157825 (program): 1728000n - 1620240.
  • A157826 (program): 103680000n^2 - 194428800n + 91152001.
  • A157834 (program): Numbers n such that 3n-2 and 3n+2 are both prime.
  • A157838 (program): 3600n^2 - 6049n + 2541.
  • A157839 (program): 1728000n - 1451760.
  • A157840 (program): 103680000n^2 - 174211200n + 73180801.
  • A157842 (program): a(n) = 3600*n^2 - 5599*n + 2177.
  • A157843 (program): 1728000n - 1343760.
  • A157844 (program): 103680000n^2 - 161251200n + 62697601.
  • A157845 (program): a(0) = 1, a(n) = sum of binary digits of all prior terms, expressed in binary.
  • A157853 (program): 3600n^2 - 1601n + 178.
  • A157854 (program): 1728000n - 384240.
  • A157855 (program): 103680000n^2 - 46108800n + 5126401.
  • A157857 (program): a(n) = 3600*n^2 - n.
  • A157858 (program): a(n) = 1728000*n - 240.
  • A157859 (program): a(n) = 103680000*n^2 - 28800*n + 1.
  • A157861 (program): a(n) = 3600*n^2 + n.
  • A157862 (program): a(n) = 1728000*n + 240.
  • A157863 (program): a(n) = 103680000*n^2 + 28800*n + 1.
  • A157865 (program): a(n) is the number of numbers of the form 4n+2 in A082542.
  • A157867 (program): Denominator of Bernoulli(n, 1/5).
  • A157870 (program): a(n) = (4n+1)*(4n+2) = (4n+2)!/(4n)!.
  • A157872 (program): a(n) = 9*n^2 - 3.
  • A157874 (program): Expansion of 104*x^2 / (-x^3+675*x^2-675*x+1).
  • A157877 (program): Expansion of (1-x)*x/(x^2-30*x+1).
  • A157878 (program): Expansion of x*(1+x)/(x^2-30*x+1).
  • A157879 (program): Expansion of 120*x^2 / (-x^3+899*x^2-899*x+1).
  • A157880 (program): Expansion of 136*x^2 / (-x^3+1155*x^2-1155*x+1).
  • A157881 (program): Expansion of 152*x^2 / (-x^3+1443*x^2-1443*x+1).
  • A157884 (program): For each positive integer m there exist at least one prime Q=Q(m) and at least one prime P=P(m) such that (2m-1)^2 < Q < (2m)^2 - (2m-1) <= P < (2m)^2. Sequence lists pairs P(m), Q(m) for m >= 1. If more than one prime for P or Q exists, we take the smallest.
  • A157887 (program): The domatic number of the n-cube.
  • A157888 (program): a(n) = 81*n^2 + 9.
  • A157889 (program): a(n) = 18*n^2 + 1.
  • A157892 (program): Values of k in A080075.
  • A157893 (program): Values of m in A080075.
  • A157909 (program): a(n) = 81*n^2 - 9.
  • A157910 (program): a(n) = 18*n^2 - 1.
  • A157911 (program): Nonprimes whose digits are all cubes.
  • A157912 (program): 64*n^2 + 16.
  • A157913 (program): a(n) = 64*n^2 - 16.
  • A157914 (program): a(n) = 8*n^2 - 1.
  • A157915 (program): a(n) = 625*n^2 + 25.
  • A157916 (program): a(n) = 50*n^2 + 1.
  • A157918 (program): a(n) = 625*n^2 - 25.
  • A157919 (program): a(n) = 50*n^2 - 1.
  • A157921 (program): a(n) = 72*n - 1.
  • A157923 (program): a(n) = 49*n^2 - n.
  • A157924 (program): a(n) = 98*n - 1.
  • A157928 (program): a(n) = 0 if n < 2, = 1 otherwise.
  • A157931 (program): Numbers that are both the sum and the product of two primes.
  • A157932 (program): Numbers k such that (3^(35*k) + 5^(21*k) + 7^(15*k)) mod 105 is prime.
  • A157947 (program): a(n) = 98n + 1.
  • A157948 (program): a(n) = 64*n^2 - n.
  • A157949 (program): a(n) = 128*n - 1.
  • A157951 (program): a(n) = 128*n + 1.
  • A157952 (program): a(n) = 162*n + 1.
  • A157953 (program): a(n) = 81n^2 - n.
  • A157954 (program): 162n - 1.
  • A157955 (program): 200n - 1.
  • A157956 (program): a(n) = 200*n + 1.
  • A157958 (program): a(n) = 242*n + 1.
  • A157960 (program): a(n) = 121*n^2 - n.
  • A157961 (program): a(n) = 242*n - 1.
  • A157966 (program): Number of 3’s in A157733(n).
  • A157970 (program): Evil twin locations: first members of pairs of consecutive evil numbers.
  • A157971 (program): Odious twin locations: first members of pairs of consecutive odious numbers.
  • A157974 (program): Primes p such that 12*p + 11 is also prime.
  • A157975 (program): Primes p such that 16*p + 15 is also prime.
  • A157976 (program): Primes p such that 18*p + 17 is also prime.
  • A157977 (program): Primes p such that 20*p + 19 is also prime.
  • A157978 (program): Primes p such that 4*p - 3 is also a prime.
  • A157983 (program): a(n)=3!*n!/(8!*19!)
  • A157984 (program): a(n) = n!/(7 * 20!).
  • A157988 (program): a(n)=16*n!/(253*43!).
  • A157990 (program): a(n) = 288*n + 1.
  • A157996 (program): Primes which are sum of 1 and two nonconsecutive primes p1 and p2, p2 - p1 > 2.
  • A157997 (program): 288n - 1.
  • A157998 (program): 169n^2 - n.
  • A157999 (program): 338n - 1.
  • A158000 (program): a(n) = 338*n + 1.
  • A158001 (program): Period 6: repeat [9, 10, 9, 4, 4, 1].
  • A158002 (program): a(n) = 392*n + 1.
  • A158003 (program): a(n) = 196*n^2 - n.
  • A158004 (program): a(n) = 392*n - 1.
  • A158010 (program): a(n) = 256*n^2 - n.
  • A158011 (program): a(n) = 512n - 1.
  • A158012 (program): A000796(n)*A000796(n+1) mod 9.
  • A158014 (program): Primes p such that (p-1)/8 is also prime.
  • A158015 (program): Primes p such that 6*p-1 is also prime.
  • A158016 (program): Primes p such that 8*p-1 is also prime.
  • A158017 (program): Primes p such that 10*p-1 is also prime.
  • A158018 (program): Primes p such that (p - 1)/12 is also prime.
  • A158019 (program): Numbers such that (n-1)/2 and 10*n-1 are both prime.
  • A158037 (program): A106044 sorted and duplicates removed.
  • A158038 (program): Difference between n-th prime and next cube.
  • A158040 (program): Determinant of power series of gamma matrix with determinant 2!.
  • A158054 (program): a(1)=2, a(n+1) is the smallest prime > n*(sum of decimal digits of a(n)).
  • A158055 (program): a(1)=2, a(n+1) is the smallest prime > n*first digit of a(n).
  • A158056 (program): a(n) = 16*n^2 + 2*n.
  • A158057 (program): First differences of A051870: 16*n + 1.
  • A158058 (program): a(n) = 16*n^2 - 2*n.
  • A158059 (program): a(1)=2, a(n+1) is the smallest prime >= n*sum of digits of a(n).
  • A158060 (program): a(n) = 25*n + 1.
  • A158062 (program): a(n) = 36*n^2 - 2*n.
  • A158064 (program): a(n) = 36*n^2 + 2*n.
  • A158065 (program): a(n) = 36*n + 1.
  • A158066 (program): a(n) = 49*n + 1.
  • A158067 (program): a(n) = 64*n^2 - 2*n.
  • A158068 (program): Period 6: repeat [1, 2, 2, 1, 5, 5].
  • A158070 (program): a(n) = 64*n^2 + 2*n.
  • A158071 (program): a(n) = 64*n + 1.
  • A158082 (program): Squares whose decimal expansion contains no digit greater than 4.
  • A158083 (program): a(n) = Fibonacci(n+3) for n < 5 and 9*n - 15 otherwise.
  • A158090 (program): Period 9: repeat [0, 6, 0, 6, 0, 0, 3, 3, 0].
  • A158095 (program): G.f.: A(x) = exp( Sum_{n>=1} 2*sigma(n,n-1)*x^n/n ).
  • A158096 (program): G.f.: A(x) = exp( Sum_{n>=1} x^n/n * 2^(n^2)/(1 + 2^(n^2)*x^n) ).
  • A158099 (program): Euler transform of square powers of 2: [2,2^4,2^9,…,2^(n^2),…].
  • A158111 (program): E.g.f.: sm^-1(x) = Sum_{n>=0} a(n)*x^(3n+1)/(3n+1)!; a(n) = coefficient of x^(3n+1)/(3n+1)! in the Maclaurin expansion of the inverse of the Dixon elliptic function sm(x,0).
  • A158116 (program): Triangle T(n,k) = 6^(k*(n-k)), read by rows.
  • A158117 (program): Triangle T(n, k) = 10^(k*(n-k)), read by rows.
  • A158121 (program): Given n points in the complex plane, let M(n) the number of distinct Moebius transformations that take 3 distinct points to 3 distinct points. Note that the triples may have some or all of the points in common.
  • A158123 (program): a(n) = 81*n + 1.
  • A158127 (program): a(n) = 100*n^2 + 2*n.
  • A158128 (program): 100n + 1.
  • A158129 (program): 100n^2 - 2n.
  • A158130 (program): 121n - 1.
  • A158131 (program): a(n) = 121*n + 1.
  • A158132 (program): 144n^2 + 2n.
  • A158133 (program): 144n + 1.
  • A158134 (program): Fourth quadrisection of A157261.
  • A158135 (program): a(n) = 144*n^2 - 2*n.
  • A158136 (program): a(n) = 144*n - 1.
  • A158137 (program): Period 9: repeat [-2,4,-2,4,-2,-2,1,1,-2].
  • A158138 (program): Number of nondecreasing integer sequences of length 4 with sum zero and sum of absolute values 2n.
  • A158186 (program): a(n) = 10*n^2 - 7*n + 1.
  • A158187 (program): a(n) = 10*n^2 + 1.
  • A158190 (program): Nonprime numbers with final digit prime.
  • A158196 (program): Expansion of (1-x^2*c(x)^4)/(1-3*x*c(x)^2), c(x) the g.f. of A000108.
  • A158197 (program): Expansion of (1-x^2*c(x)^4)/(1-4*x*c(x)^2), c(x) the g.f. of A000108.
  • A158198 (program): Triangle T(n, k) = Sum_{j=0..k-1} (-1)^j*binomial(k, j+1)*(k-j)^(n-k), read by rows.
  • A158204 (program): Terms in A178335 not divisible by 10.
  • A158210 (program): Number omega(n) of distinct primes dividing n multiplied by -1 when n is squarefree (thus Omega(n) = omega(n)).
  • A158218 (program): 169n^2 - 2n.
  • A158219 (program): 169n - 1.
  • A158220 (program): a(n) = 169*n^2 + 2*n.
  • A158221 (program): a(n) = 169n + 1.
  • A158222 (program): a(n) = 196*n^2 + 2*n.
  • A158223 (program): a(n) = 196*n + 1.
  • A158224 (program): a(n) = 196*n^2 - 2*n.
  • A158225 (program): 196n - 1.
  • A158226 (program): 225n^2-2n.
  • A158227 (program): 225n - 1.
  • A158228 (program): 225n^2 + 2n.
  • A158229 (program): 225n + 1.
  • A158230 (program): 256n^2+2n.
  • A158231 (program): a(n) = 256*n + 1.
  • A158241 (program): Decimal expansion of theta = arctan((sqrt(10-2*sqrt(5))-2)/(sqrt(5)-1)).
  • A158243 (program): Derangements with at least one 2-cycle.
  • A158249 (program): a(n) = 256*n^2 - 2*n.
  • A158250 (program): a(n) = 256*n - 1.
  • A158251 (program): a(n)=S(S(n)) where S=A054353 gives the partial sums of Kolakoski sequence.
  • A158252 (program): 289n^2 - 2n.
  • A158253 (program): 289n - 1.
  • A158254 (program): 289n^2 + 2n.
  • A158255 (program): 289n + 1.
  • A158265 (program): G.f.: A(x) = exp( Sum_{n>=1} 2*sigma(n,n+1)*x^n/n ).
  • A158266 (program): G.f.: A(x) = exp( Sum_{n>=1} C(2n-1,n)^2*x^n/n ).
  • A158270 (program): Single-digit numbers in A061049.
  • A158271 (program): 324n^2 + 2n.
  • A158272 (program): 324n + 1.
  • A158273 (program): Indices of single-digit numbers in A061049.
  • A158274 (program): Numerators of antiharmonic means of divisors of n.
  • A158275 (program): Denominators of antiharmonic means of divisors of n.
  • A158276 (program): Numbers k such that sigma_1(k) not divides sigma_2(k).
  • A158277 (program): The lesser of twin prime pairs with each prime in a different century.
  • A158280 (program): Octosection: A145511(8n+4) or A145501(8n+4).
  • A158289 (program): Period 18 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1].
  • A158293 (program): Primes whose digit sum is a multiple of 10.
  • A158298 (program): Denominators of averages of squares of the divisors of n.
  • A158299 (program): Numerators of averages of squares of the divisors of n.
  • A158302 (program): “1” followed by repeats of 2^k deleting all 4^k, k>0
  • A158303 (program): Triangle read by rows, A007318 * ((A158300 * 0^(n-k)).
  • A158304 (program): Numbers k such that k^2 contains no digit greater than 4.
  • A158305 (program): 324n^2 - 2n.
  • A158306 (program): 324n - 1.
  • A158307 (program): 361n^2 - 2n.
  • A158308 (program): 361n - 1.
  • A158309 (program): 361n^2 + 2n.
  • A158310 (program): 361n + 1.
  • A158312 (program): 400n^2 + 2n.
  • A158313 (program): a(n) = 400 * n + 1.
  • A158315 (program): A158280(n)/7.
  • A158316 (program): 400n^2 - 2n.
  • A158317 (program): a(n) = 400*n - 1.
  • A158318 (program): Primes p such that 5p-2 is prime.
  • A158319 (program): 441n - 1.
  • A158321 (program): a(n) = 441n^2 + 2n.
  • A158322 (program): a(n) = 441*n + 1.
  • A158324 (program): Successive powers of two, represented as binary coded decimal. (0x1, 0x2, 0x4, 0x8, 0x16, 0x32, etc.)
  • A158325 (program): a(n) = 484n^2 + 2n.
  • A158326 (program): 484n + 1.
  • A158327 (program): a(n) = A145444(n)-A145511(n).
  • A158329 (program): 484n^2 - 2n.
  • A158330 (program): 484n - 1.
  • A158333 (program): Position of number of digits increment in the sequence of powers of 3.
  • A158338 (program): Composite numbers k such that k - number of divisors of k = prime.
  • A158362 (program): a(n)=binomial((n+1)^3,n+2), n=1,2… .
  • A158363 (program): a(n)=binomial((n+2)^3,n+1),n=0,1… .
  • A158364 (program): 529n^2 - 2n.
  • A158365 (program): 529n - 1.
  • A158366 (program): Least k such that n! divides (n+k)!/(n+1)!.
  • A158367 (program): 529n^2 + 2n.
  • A158368 (program): 529n + 1.
  • A158369 (program): 576n^2 + 2n.
  • A158370 (program): 576n + 1.
  • A158371 (program): 576n^2 - 2n.
  • A158372 (program): 576n - 1.
  • A158373 (program): 625n^2 - 2n.
  • A158374 (program): 625n - 1.
  • A158378 (program): a(1) = 0, a(n) = gcd(A051904(n), A051903(n)) for n >= 2.
  • A158382 (program): a(n) = 625*n^2 + 2*n.
  • A158383 (program): 625n + 1.
  • A158385 (program): a(n) = 676*n^2 + 2*n.
  • A158386 (program): 676n + 1.
  • A158387 (program): a(n) = -1 if n is a square, 1 if n is not a square.
  • A158388 (program): -1 followed by infinitely many 1’s.
  • A158392 (program): 676n^2 - 2n.
  • A158393 (program): a(n) = 676*n - 1.
  • A158394 (program): 729n^2 - 2n.
  • A158395 (program): 729n - 1.
  • A158396 (program): 729n^2 + 2n.
  • A158397 (program): 729n + 1.
  • A158398 (program): 784n^2 - 2n.
  • A158399 (program): 784n - 1.
  • A158401 (program): a(n) = 841*n^2 - 2*n.
  • A158402 (program): a(n) = 841*n - 1.
  • A158403 (program): 841n^2 + 2n.
  • A158404 (program): 841n + 1.
  • A158405 (program): Triangle T(n,m) = 1+2*m of odd numbers read along rows, 0<=m<n.
  • A158406 (program): a(n) = 900*n^2 + 2*n.
  • A158407 (program): a(n) = 900*n + 1.
  • A158408 (program): a(n) = 900*n^2 - 2*n.
  • A158409 (program): a(n) = 900*n - 1.
  • A158410 (program): a(n) = 961*n^2 - 2*n.
  • A158411 (program): Maximum number of colors required to paint a map having n regions.
  • A158412 (program): 961n - 1.
  • A158413 (program): 961n^2 + 2n.
  • A158414 (program): 961n + 1.
  • A158416 (program): Expansion of (1+x-x^3)/(1-x^2)^2.
  • A158420 (program): 1024n^2 - 2n.
  • A158421 (program): a(n) = 1024*n - 1.
  • A158440 (program): Triangle T(n,k) read by rows: row n contains n times n+1 followed by n 1’s.
  • A158443 (program): 16n^2 - 4.
  • A158444 (program): a(n) = 16*n^2 + 4.
  • A158445 (program): 25n^2 + 5.
  • A158446 (program): 25n^2 - 5.
  • A158447 (program): a(n) = 10*n^2 - 1.
  • A158454 (program): Riordan array (1/(1-x^2), x/(1+x)^2).
  • A158455 (program): a(n) = 2^(n-1)*(n-1)!*(4*n+1).
  • A158456 (program): Signature sequence for log(3)/log(2).
  • A158458 (program): Numbers k such that k + bigomega(k) is prime.
  • A158459 (program): Period 4: repeat [0, 3, 2, 1].
  • A158461 (program): A102370(n) mod 3 .
  • A158462 (program): a(n) = 36*n^2 - 6.
  • A158463 (program): a(n) = 12*n^2 - 1.
  • A158464 (program): Number of distinct squares in row n of Pascal’s triangle.
  • A158478 (program): Number of colors needed to paint n sectors of a circle.
  • A158479 (program): 36n^2 + 6.
  • A158480 (program): a(n) = 12*n^2 + 1.
  • A158481 (program): 49n^2 + 7.
  • A158482 (program): a(n) = 14*n^2 + 1.
  • A158483 (program): Triangle read by rows: T(n,k) = (4k+3)/(n+2k+2)*binomial(2n,n+2k+1).
  • A158484 (program): 49n^2 - 7.
  • A158485 (program): a(n) = 14*n^2 - 1.
  • A158487 (program): a(n) = 64*n^2 - 8.
  • A158488 (program): a(n) = 64*n^2 + 8.
  • A158490 (program): 100n^2 - 10.
  • A158491 (program): 20n^2 - 1.
  • A158492 (program): a(n) = 100*n^2 + 10.
  • A158493 (program): a(n) = 20*n^2 + 1.
  • A158494 (program): Boundary area of the T-square fractal.
  • A158495 (program): Expansion of ((1-4x)+sqrt(1-4x))/(2(1-2x)).
  • A158496 (program): Expansion of (1-4x+x^2)/(1+x^2)^2.
  • A158497 (program): Triangle T(n,k) formed by the coordination sequences and the number of leaves for trees.
  • A158498 (program): a(n) = (1/2)*(n^3 - 6*n^2 + 13*n - 6).
  • A158499 (program): Expansion of (1+sqrt(1-4x))/(2-4x).
  • A158500 (program): Expansion of (1+sqrt(1+4x))*(1+2x)/(2*sqrt(1+4x)).
  • A158501 (program): Hankel transform of A158500.
  • A158510 (program): Generalized Fibonacci numbers Fib(n + 0.5) rounded to an integer.
  • A158513 (program): a(n) = Hermite(n,5).
  • A158515 (program): Number of colors needed to paint a wheel graph on n nodes.
  • A158516 (program): a(n) = Hermite(n,6).
  • A158522 (program): Dirichlet inverse of number of unitary divisors of n (A034444).
  • A158523 (program): Moebius transform of negate primes in factorization of n.
  • A158525 (program): Number of connected spanning subgraphs and number of forests of the wheel graph W_n.
  • A158526 (program): n and (1 + 2*n + 2*n^2) are primes.
  • A158528 (program): Sum of primes between consecutive positive cubes.
  • A158530 (program): a(n) = Hermite(n,7).
  • A158531 (program): a(n) = Hermite(n,8).
  • A158532 (program): a(n) = Hermite(n,9).
  • A158534 (program): a(n) = Hermite(n,10).
  • A158535 (program): a(n) = Hermite(n,11).
  • A158536 (program): 121n^2 + 11.
  • A158537 (program): a(n) = 22*n^2 + 1.
  • A158538 (program): a(n) = Hermite(n,12).
  • A158539 (program): a(n) = 121*n^2 - 11.
  • A158540 (program): a(n) = 22*n^2 - 1.
  • A158542 (program): a(n) = Hermite(n,13).
  • A158543 (program): a(n) = 144*n^2 - 12.
  • A158544 (program): a(n) = 24*n^2 - 1.
  • A158545 (program): a(n) = Hermite(n,14).
  • A158546 (program): a(n) = 144*n^2 + 12.
  • A158547 (program): a(n) = 24*n^2 + 1.
  • A158548 (program): a(n) = 169*n^2 + 13.
  • A158549 (program): a(n) = 26*n^2 + 1.
  • A158550 (program): a(n) = 169*n^2 - 13.
  • A158551 (program): a(n) = 26*n^2 - 1.
  • A158552 (program): a(n) = A144433(n) - A106833(n).
  • A158553 (program): a(n) = 196*n^2 - 14.
  • A158554 (program): a(n) = 28*n^2 - 1.
  • A158555 (program): a(n) = 196*n^2 + 14.
  • A158556 (program): a(n) = 28*n^2 + 1.
  • A158557 (program): a(n) = 225*n^2 + 15.
  • A158558 (program): a(n) = 30n^2 + 1.
  • A158559 (program): a(n) = 225*n^2 - 15.
  • A158560 (program): a(n) = 30n^2 - 1.
  • A158561 (program): a(n)=((2^n)*((2^n)+1) - (2^(n-1))*((2^(n-1))+1))/2, a(1)=3.
  • A158562 (program): a(n) = 256*n^2 - 16.
  • A158563 (program): a(n) = 32*n^2 - 1.
  • A158569 (program): a(n) = Sum_{i=1..F(n)} F(i), n >= 1, where F(k) is A000045, Fibonacci numbers.
  • A158570 (program): a(n) = A007814((2n-1)!! + 1).
  • A158572 (program): a(n) = A007814((2n-1)!! - 1).
  • A158573 (program): Numbers k such that 30*k + 7 is prime.
  • A158574 (program): a(n) = 256*n^2 + 16.
  • A158575 (program): a(n) = 32*n^2 + 1.
  • A158580 (program): a(n) = Hermite(n, 15).
  • A158581 (program): Numbers having in binary representation at least two ones and two zeros.
  • A158582 (program): Numbers having in binary representation at least two zeros.
  • A158585 (program): a(n) = 289*n^2 + 17.
  • A158586 (program): a(n) = 34*n^2 + 1.
  • A158587 (program): a(n) = 289*n^2 - 17.
  • A158588 (program): a(n) = 34*n^2 - 1.
  • A158589 (program): a(n) = 324*n^2 - 18.
  • A158590 (program): a(n) = 324*n^2 + 18.
  • A158591 (program): a(n) = 36*n^2 + 1.
  • A158592 (program): a(n) = 361*n^2 + 19.
  • A158593 (program): a(n) = 38*n^2 + 1.
  • A158595 (program): a(n) = 361*n^2 - 19.
  • A158596 (program): a(n) = 38*n^2 - 1.
  • A158597 (program): a(n) = 400*n^2 - 20.
  • A158598 (program): a(n) = 40*n^2 - 1.
  • A158601 (program): a(n) = 400*n^2 + 20.
  • A158602 (program): a(n) = 40*n^2 + 1.
  • A158603 (program): a(n) = 441*n^2 + 21.
  • A158604 (program): a(n) = 42*n^2 + 1.
  • A158607 (program): Period 5: repeat 9,11,13,5,7.
  • A158608 (program): a(n) = a(n-1) + 16*a(n-2), starting a(0)=1, a(1)=4.
  • A158609 (program): Expansion of (1+8*x)/(1-x-81*x^2).
  • A158610 (program): Expansion of (1+15*x)/(1-x-256*x^2).
  • A158611 (program): 0, 1 and the primes.
  • A158613 (program): Expansion of (1 - 2*x^3 - x^4 - x^5 + x^6 + x^7 - x^8)/(1 - x^3)^3.
  • A158614 (program): Numbers n such that 30*n + 11 is prime.
  • A158617 (program): a(n) = Hermite(n, 16).
  • A158618 (program): Number of gates in Ladner-Fisher prefix circuit.
  • A158619 (program): Twin prime pairs concatenated in binary representation.
  • A158620 (program): Partial products of A068601.
  • A158621 (program): Partial products of A001093.
  • A158622 (program): Numerator of the reduced fraction A158620(n)/A158621(n).
  • A158623 (program): Denominator of the reduced fraction A158620(n)/A158621(n).
  • A158626 (program): a(n) = 42*n^2 - 1.
  • A158627 (program): a(n) = 484*n^2-22.
  • A158628 (program): a(n) = 44*n^2 - 1.
  • A158629 (program): a(n) = 484*n^2 + 22.
  • A158630 (program): a(n) = 44*n^2+1.
  • A158631 (program): a(n) = 529*n^2 + 23.
  • A158632 (program): a(n) = 46*n^2 + 1.
  • A158633 (program): a(n) = 529*n^2 - 23.
  • A158634 (program): a(n) = 46*n^2 - 1.
  • A158635 (program): 6n - A008578(n).
  • A158636 (program): a(n) = 576*n^2 - 24.
  • A158637 (program): a(n) = 576*n^2 + 24.
  • A158638 (program): a(n) = 48*n^2 + 1.
  • A158639 (program): a(n) = 676*n^2 - 26.
  • A158640 (program): 52*n^2 - 1.
  • A158643 (program): a(n) = 676*n^2 + 26.
  • A158644 (program): a(n) = 52*n^2 + 1.
  • A158645 (program): a(n) = 729*n^2 + 27.
  • A158646 (program): a(n) = 54*n^2 + 1.
  • A158647 (program): A145501(16n+8).
  • A158648 (program): Numbers n such that 30*n + 17 is prime.
  • A158654 (program): Denominator of Bernoulli(n, 1/8).
  • A158655 (program): a(n) = 729*n^2 - 27.
  • A158656 (program): a(n) = 54*n^2 - 1.
  • A158657 (program): a(n) = 784*n^2 - 28.
  • A158658 (program): a(n) = 56*n^2 - 1.
  • A158659 (program): a(n) = 784*n^2 + 28.
  • A158660 (program): a(n) = 56*n^2 + 1.
  • A158662 (program): Sum of primes <= n if 1 is counted as a prime.
  • A158665 (program): a(n) = 841*n^2 + 29.
  • A158666 (program): a(n) = 58*n^2 + 1.
  • A158667 (program): 841*n^2 - 29.
  • A158668 (program): a(n) = 58*n^2 - 1.
  • A158669 (program): a(n) = 900*n^2 - 30.
  • A158670 (program): a(n) = 60*n^2 - 1.
  • A158672 (program): a(n) = 900*n^2 + 30.
  • A158673 (program): a(n) = 60*n^2 + 1.
  • A158674 (program): Period 18: repeat 3, 4, 0, 8, 6, 3, 3, 7, 0, 2, 6, 6, 3, 1, 0, 5, 6, 0.
  • A158675 (program): a(n) = 961*n^2 + 31.
  • A158676 (program): a(n) = 62*n^2 + 1.
  • A158677 (program): Period 6: repeat [3, 4, 0, 5, 6, 3].
  • A158678 (program): Period 18: repeat 0,0,0,3,0,0,0,3,0,-3,0,3,0,-3,0,0,0,-3.
  • A158679 (program): a(n) = 961*n^2 - 31.
  • A158680 (program): a(n) = 62*n^2 - 1.
  • A158681 (program): Wiener indexes of the complete binary trees with n levels, root being at level 0.
  • A158683 (program): a(n) = 1024*n^2 - 32.
  • A158684 (program): a(n) = 64*n^2 - 1.
  • A158685 (program): 32*(32*n^2+1).
  • A158686 (program): 64n^2 + 1.
  • A158687 (program): Riordan array (1/(1-x),x(1+x)^2/(1-x)).
  • A158688 (program): a(n) = 1089*n^2 + 33.
  • A158689 (program): a(n) = 66*n^2 + 1.
  • A158692 (program): a(n) = 1089*n^2 - 33.
  • A158693 (program): a(n) = 66*n^2 - 1.
  • A158696 (program): a(n) = Hermite(n, 17).
  • A158698 (program): Numbers not occurring in A073627.
  • A158699 (program): Start with 0; then add one to each single digit.
  • A158700 (program): a(n) = Hermite(n, 18).
  • A158702 (program): a(n) = Hermite(n, 19).
  • A158703 (program): a(n) = Hermite(n, 20).
  • A158704 (program): Nonnegative integers with an even number of even powers of 2 in their base-2 representation.
  • A158705 (program): Nonnegative integers with an odd number of even powers of 2 in their base-2 representation.
  • A158708 (program): Primes p such that p + floor(p/2) is prime.
  • A158709 (program): Primes p such that p + ceiling(p/2) is prime.
  • A158721 (program): Primes p such that (p + 1)/3 + p is prime.
  • A158724 (program): Numbers n such that prime(n)^2 + 1 is a semiprime.
  • A158727 (program): a(n) = Hermite(n, 21).
  • A158729 (program): a(n) = 1156*n^2 - 34.
  • A158730 (program): a(n) = 68*n^2 - 1.
  • A158731 (program): a(n) = 1156*n^2 + 34.
  • A158732 (program): a(n) = 68*n^2 + 1.
  • A158733 (program): a(n) = 1225*n^2 + 35.
  • A158734 (program): a(n) = 70*n^2 + 1.
  • A158735 (program): a(n) = 1225*n^2 - 35.
  • A158736 (program): a(n) = 70*n^2 - 1.
  • A158737 (program): a(n) = 1296*n^2 - 36.
  • A158738 (program): a(n) = 72*n^2 - 1.
  • A158739 (program): 1296*n^2 + 36.
  • A158740 (program): a(n) = 72*n^2 + 1.
  • A158741 (program): a(n) = 1369*n^2 + 37.
  • A158742 (program): a(n) = 74*n^2 + 1.
  • A158743 (program): a(n) = 1369*n^2 - 37.
  • A158744 (program): a(n) = 74*n^2 - 1.
  • A158745 (program): a(3n)=A130750(n). a(3n+1)=A130752(n). a(3n+2)=A130755(n).
  • A158746 (program): Numbers n such that 30*n + 13 is prime.
  • A158747 (program): Triangle read by rows: T(n,m)=prime( 1+prime(n+1)-prime(m+1) ).
  • A158749 (program): a(n) = n * 9^n.
  • A158751 (program): a(n) = Hermite(n, 22).
  • A158752 (program): a(n) = Hermite(n, 23).
  • A158753 (program): Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.
  • A158764 (program): 38*(38*n^2-1).
  • A158765 (program): a(n) = 76*n^2 - 1.
  • A158766 (program): a(n) = 1444*n^2 + 38.
  • A158767 (program): a(n) = 76*n^2 + 1.
  • A158768 (program): a(n) = 1521*n^2 + 39.
  • A158769 (program): a(n) = 78*n^2 + 1.
  • A158770 (program): a(n) = 1521*n^2 - 39.
  • A158771 (program): a(n) = 78*n^2 - 1.
  • A158772 (program): a(n) = A138635(n+18)-A138635(n).
  • A158773 (program): a(n) = 1600*n^2 - 40.
  • A158774 (program): a(n) = 80*n^2 - 1.
  • A158775 (program): a(n) = 1600*n^2 + 40.
  • A158776 (program): a(n) = 80*n^2 + 1.
  • A158780 (program): a(2n) = A131577(n). a(2n+1) = A011782(n).
  • A158783 (program): a(n) = Hermite(n, 24).
  • A158791 (program): Numbers n such that 30*n + 23 is prime.
  • A158793 (program): Triangle read by rows: product of A130595 and A092392 considered as infinite lower triangular arrays.
  • A158797 (program): a(n) = a(n-1) + 36*a(n-2), a(0)=1, a(1)=6.
  • A158798 (program): a(n) = a(n-1) + 64*a(n-2), a(0)=1, a(1)=8.
  • A158799 (program): a(0)=1, a(1)=2, a(n)=3 for n>=2.
  • A158802 (program): a(n) = n * n! * b(n), where b(n) = ((n-1)*(n-3)*b(n-1) - b(n-2) + b(n-3))/(n*(n - 1)) and b(0) = b(1) = 1, b(2) = -1.
  • A158803 (program): Numbers k such that k^2 == 2 (mod 41).
  • A158806 (program): Numbers n such that 30*n + 19 is prime.
  • A158808 (program): Denominator of Bernoulli(n, 1/9).
  • A158811 (program): Numerator of Hermite(n, 1/3).
  • A158815 (program): Triangle T(n,k) read by rows, matrix product of A046899(row-reversed) * A130595.
  • A158821 (program): Triangle read by rows: row n (n>=0) ends with 1, and for n>=1 begins with n; other entries are zero.
  • A158822 (program): Triangle read by rows, matrix triple product A000012 * A145677 * A000012.
  • A158823 (program): Triangle read by rows: matrix product A004736 * A158821.
  • A158824 (program): Triangle T(n,k) = A000292(n) if k = 1 otherwise (k-1)*(n-k+1)*(n-k+2)/2, read by rows.
  • A158841 (program): Triangle read by rows, matrix product of A145677 * A004736.
  • A158842 (program): 1 + n*(n+1)*(n-1)/2.
  • A158845 (program): Numbers k such that prepending 1 to the k-th triangular number produces a prime.
  • A158849 (program): a(10n+m) is the integer with n+m concatenations of the digit m in base 10, 0<=m<=9.
  • A158850 (program): Numbers n such that 30*n + 29 is prime.
  • A158851 (program): a(n) = lcm(1,2,3,…,n) mod (n+1).
  • A158854 (program): Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial (1-x)^(1+floor(n/2))* (1+x)^floor((n-1)/2) in row n, column k.
  • A158859 (program): a(n) is formed by 2n+1 concatenations of the digit 2r+1 where n=r (mod 5).
  • A158860 (program): Triangle T(n,k)= ( 1 +T(n-1,k)*T(n,k-1) ) / T(n-1,k-1) initialized by T(n,0)=3n-2, T(n,k)=0 if k>=n, read by rows 0<=k<n.
  • A158863 (program): Maximal excess of a 3-normalized Hadamard matrix of order 4n.
  • A158869 (program): Number of ways of filling a 2 X 3 X 2n hole with 1 X 2 X 2 bricks.
  • A158874 (program): a(n) = (n + 4)*(n + 3)*(n + 2)*(n + 1)*n / 5 = 24*A000389(n+4).
  • A158875 (program): Row sums of A099884, the XOR difference triangle of the powers of 2.
  • A158876 (program): Expansion of e.g.f.: exp( Sum_{n>=1} (n-1)! * x^n ).
  • A158879 (program): a(n) = 4^n + n.
  • A158881 (program): a(n) = (n*2^n + 1)^(n-1).
  • A158882 (program): G.f. A(x) satisfies: [x^n] A(x)^n = [x^n] A(x)^(n-1) for n>1 with A(0)=A’(0)=1.
  • A158886 (program): a(n) = (n+1)^n * n! * C(1/(n+1), n).
  • A158887 (program): a(n) = (n+1)^n * n! * binomial(n-1 + 1/(n+1), n).
  • A158893 (program): Triangle read by rows: T(n,1)=7n-6; T(n,m)= 1+n-m, 1<m<=n.
  • A158894 (program): Sawtooth pattern of one, then two, then three, then four etc. consecutive odd numbers, starting each time at 3.
  • A158897 (program): The elements of A059100 at indices of triangular numbers, padded with zeros.
  • A158899 (program): These are numbers n such that the reciprocal, 1/n, is a repeating fraction whose period is n/2 - 1.
  • A158901 (program): A051731 * (1, 1, 2, 3, 4, 5, …).
  • A158903 (program): Numerator of Hermite(n, 2/3).
  • A158906 (program): Triangle read by rows: the matrix product A158821 * A051731.
  • A158907 (program): Row sums of triangle A158906.
  • A158908 (program): First differences of A061238.
  • A158909 (program): Riordan array (1/((1-x)(1-x^2)), x/(1-x)^2). Triangle read by rows, T(n,k) for 0 <= k <= n.
  • A158910 (program): First Differences of A061240.
  • A158911 (program): Numbers of the form 2^i*5^j - 1.
  • A158916 (program): Inverse binomial transform of A153130.
  • A158919 (program): Beatty sequence for the tribonacci constant tau (A058265): a(n) = floor(n*tau).
  • A158920 (program): Binomial transform of A008805 (triangular numbers with repeats).
  • A158926 (program): First differences of A158916.
  • A158927 (program): a(n) = -3a(n-1) - 3a(n-2) - 2a(n-3), n > 3.
  • A158934 (program): Decimal expansion of xi = (cos(Pi/5) - 1/2) / (sin(Pi/5) + 1/2).
  • A158935 (program): a(n)= -3a(n-1)-3a(n-2)-2a(n-3), n>3. a(0)=4, a(1)=4, a(2)=-5, a(3)=4.
  • A158937 (program): Numbers of the form x^2+3y^2 where x and y are positive integers (with repetitions).
  • A158942 (program): Nonsquares coprime to 10.
  • A158943 (program): INVERT transform of A027656: (1, 0, 2, 0, 3, 0, 4, 0, 5, …).
  • A158944 (program): Triangle by columns: the natural numbers interleaved with zeros in every column: (1, 0, 2, 0, 3, 0, 4, …)
  • A158946 (program): Triangle read by rows, A000012(signed) * A145677 * A000012
  • A158948 (program): Triangle read by rows, left border = natural numbers repeated (1, 1, 2, 2, 3, 3, …); all other columns = (1, 0, 1, 0, 1, 0, …).
  • A158949 (program): Inverse Moebius transform of A065958.
  • A158953 (program): Trajectory of 12 under repeated application of the map n –> A102370(n) .
  • A158954 (program): Numerator of Hermite(n, 1/4).
  • A158955 (program): First differences of A061241.
  • A158958 (program): Numerator of Hermite(n, 3/4).
  • A158960 (program): Numerator of Hermite(n, 1/5).
  • A158961 (program): Numerator of Hermite(n, 2/5).
  • A158965 (program): Numerator of Hermite(n, 3/5).
  • A158967 (program): Numerator of Hermite(n, 4/5).
  • A158968 (program): Numerator of Hermite(n, 1/6).
  • A158969 (program): Numerator of Hermite(n, 5/6).
  • A158973 (program): a(n) = count of numbers k <= n such that all proper divisors of k are divisors of n.
  • A158974 (program): a(n) is the number of numbers k <= n such that not all proper divisors of k are divisors of n.
  • A158980 (program): Numerator of Hermite(n, 1/7).
  • A158981 (program): Numerator of Hermite(n, 2/7).
  • A158987 (program): Numerator of Hermite(n, 3/7).
  • A158991 (program): Numerator of Hermite(n, 4/7).
  • A159005 (program): Numerator of Hermite(n, 5/7).
  • A159006 (program): Transformation of prime(n): flip digits in the binary representation, revert the sequence of digits, and convert back to decimal.
  • A159007 (program): Numbers k such that k == 32 or 41 (mod 73).
  • A159008 (program): Positive numbers k such that k^2 == 2 (mod 89).
  • A159013 (program): Numerator of Hermite(n, 6/7).
  • A159014 (program): Numerator of Hermite(n, 1/8).
  • A159017 (program): Numerator of Hermite(n, 3/8).
  • A159018 (program): a(0)=5; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159019 (program): Numerator of Hermite(n, 5/8).
  • A159020 (program): a(0)=11; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159021 (program): a(0)=19; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159022 (program): a(0)=29; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159023 (program): a(0)=41; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159024 (program): a(0)=55; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159025 (program): a(0)=71; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159026 (program): a(0)=89; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159027 (program): a(0)=109; a(n) = a(n-1) + floor(sqrt(a(n-1))), n > 0.
  • A159028 (program): Numerator of Hermite(n, 7/8).
  • A159030 (program): Numerator of Hermite(n, 1/9).
  • A159035 (program): a(0)=1=a(1), a(2)=2, a(3)=5; thereafter a(n+3)=4*a(n+2)-4*a(n+1)+2*a(n) for n>=1.
  • A159036 (program): a(0)=0, a(1)=1, a(2)=4, a(3)=13; thereafter a(n+3)=4*a(n+2)-4*a(n+1)+2*a(n) for n>=1.
  • A159038 (program): a(n) = 8 * n!.
  • A159039 (program): E.g.f. sec(x)/(1-x) = 1/( cos(x) * (1-x) ).
  • A159040 (program): A triangle of polynomial coefficients: p(x,n)=Sum[x^i*If[i == Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= (less than or equal to) Floor[n/2], (-1)^i*A109128[n, i], -(-1)^(n - i)* A109128[n, i]]], {i, 0, n}]/(1 - x).
  • A159047 (program): Primes which are triangular numbers plus 3.
  • A159048 (program): Primes of the form m*(m+1)/2 + 4.
  • A159049 (program): Primes of the form (5+ a triangular number A000217).
  • A159057 (program): a(n) = A102370(n) mod 10.
  • A159058 (program): A102370(n) modulo 8 .
  • A159060 (program): A102370(n) modulo 6 .
  • A159061 (program): Nearest integer to the expected number of tosses of a fair coin required to obtain at least n heads and n tails.
  • A159066 (program): A102370(n) modulo 7 .
  • A159067 (program): A102370(n) modulo 9 .
  • A159068 (program): a(n) = Sum_{k=1..n} binomial(n,k) * gcd(k,n).
  • A159069 (program): a(n) = A159068(n)/n.
  • A159070 (program): Count of numbers k in the range 1 < k <= n such that set of proper divisors of k is a subset of the set of proper divisors of n.
  • A159071 (program): Primes which are the sum of 6 consecutive triangular numbers A000217.
  • A159072 (program): Count of numbers k in the range 1<=k<= n such that set of proper divisors of k is not a subset of the set of the proper divisors of n.
  • A159075 (program): a(1) = -1, otherwise a(n) = 0.
  • A159076 (program): A008474(n) + 2.
  • A159077 (program): a(n) = A008475(n) + 1.
  • A159081 (program): Let d be the largest element of A008578 which divides n, then a(n) is the position of d in A008578.
  • A159083 (program): Products of 7 consecutive integers.
  • A159197 (program): Numerator of Hermite(n, 2/9).
  • A159200 (program): Decimal expansion of Sum_{k >= 1} (1/(10^(4*k + 2) - 1)) - (1/(10^(2*k + 1) - 1)), negated.
  • A159217 (program): 1/8 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 17
  • A159219 (program): Number of n X n arrays of squares of integers with every 2X2 subblock summing to 18
  • A159221 (program): 1/2 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 20
  • A159222 (program): 1/4 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 21
  • A159225 (program): 1/4 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 25
  • A159227 (program): 1/4 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 27
  • A159229 (program): 1/16 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 30
  • A159230 (program): 1/8 the number of n X n arrays of squares of integers with every 2X2 subblock summing to 31
  • A159232 (program): Numerator of Hermite(n, 4/9).
  • A159240 (program): Numerator of Hermite(n, 5/9).
  • A159242 (program): Numerator of Hermite(n, 7/9).
  • A159245 (program): Numerator of Hermite(n, 8/9).
  • A159247 (program): Numerator of Hermite(n, 1/10).
  • A159249 (program): Numerator of Hermite(n, 3/10).
  • A159252 (program): Numerator of Hermite(n, 7/10).
  • A159254 (program): Numbers n with property that n^2 ends with 49.
  • A159256 (program): a(0)=131; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).
  • A159258 (program): a(0)=155; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1))).
  • A159263 (program): a(0)=181; for n > 0, a(n) = a(n-1) + floor(sqrt a(n-1)).
  • A159274 (program): a(0)=209; for n > 0, a(n) = a(n-1) + floor(sqrt(a(n-1)).
  • A159277 (program): Ways to write the identity as a product of n 3-cycles in symmetric group S_4.
  • A159279 (program): Numerator of Hermite(n, 9/10).
  • A159280 (program): Numerator of Hermite(n, 1/11).
  • A159281 (program): Numerator of Hermite(n, 2/11).
  • A159284 (program): Expansion of x*(1+x)/(1-x^2-2*x^3).
  • A159285 (program): Expansion of (1+3*x)/(1-x^2-2*x^3).
  • A159286 (program): Expansion of (x-1)^2/(1-x^2-2*x^3).
  • A159287 (program): Expansion of x^2/(1-x^2-2*x^3)
  • A159288 (program): Expansion of (1 + x + x^2)/(1 - x^2 - 2*x^3).
  • A159289 (program): a(n+1) = 5*a(n) - 2*a(n-1).
  • A159290 (program): A generalized Jacobsthal sequence.
  • A159293 (program): a(n) = smallest prime congruent to 1 mod A051426(n).
  • A159297 (program): Number of 3D matrices with positive integer entries such that sum of all entries equals n
  • A159307 (program): Numerator of Hermite(n, 3/11).
  • A159322 (program): G.f.: A(x) = Sum_{n>=0} log(1+x + 2^n*x^2)^n/n!.
  • A159324 (program): n! times the average number of comparisons required by an insertion sort of n (distinct) elements.
  • A159325 (program): Median number of comparisons used by insertion sort on n (distinct) elements.
  • A159326 (program): Numerator of Hermite(n, 4/11).
  • A159327 (program): Numerator of Hermite(n, 5/11).
  • A159328 (program): Transform of 1 by the T_{1,1} transformation (see link)
  • A159329 (program): Transform of the finite sequence (1, 0, -1) by the T_{1,1} transformation (see link).
  • A159330 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,1} transformation (see link).
  • A159333 (program): Roman factorial of n.
  • A159334 (program): Transform of A056594 by the T_{1,1} transformation (see link)
  • A159335 (program): Triangle read by rows: numerator of n/binomial(n,m).
  • A159336 (program): Transform of the finite sequence (1, 0, -1) by the T_{1,0} transformation (see link).
  • A159337 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{1,0} transformation (see link).
  • A159338 (program): Transform of the finite sequence (1, 0, -1, 0, 1, 0, -1) by the T_{1,0} transformation (see link).
  • A159339 (program): Transform of A056594 by the T_{1,0} transformation (see link).
  • A159340 (program): Transform of the finite sequence (1, 0, -1) by the T_{0,1} transformation (see link).
  • A159341 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,1} transformation (see link).
  • A159343 (program): Transform of A056594 by the T_{0,1} transformation (see link).
  • A159347 (program): Transform of the finite sequence (1, 0, -1) by the T_{0,0} transformation.
  • A159348 (program): Transform of the finite sequence (1, 0, -1, 0, 1) by the T_{0,0} transform (see link).
  • A159350 (program): Transform of A056594 by the T_{0,0} transformation (see link).
  • A159353 (program): a(n) = the smallest positive integer such that a(n) *(2^n -2) is a multiple of n.
  • A159354 (program): Decimal expansion of 18 - 24*log(2).
  • A159355 (program): Number of n X n arrays of squares of integers summing to 4.
  • A159359 (program): Number of n X n arrays of squares of integers summing to 5.
  • A159363 (program): Number of n X n arrays of squares of integers summing to 6.
  • A159367 (program): Number of n X n arrays of squares of integers summing to 7
  • A159449 (program): Numerator of Hermite(n, 6/11).
  • A159450 (program): Numerator of Hermite(n, 7/11).
  • A159454 (program): Numerator of Hermite(n, 8/11).
  • A159460 (program): Numerator of Hermite(n, 9/11).
  • A159461 (program): Numbers of previous and following composites of n-th prime.
  • A159465 (program): Sums of odd numbers, omitting squares.
  • A159467 (program): Decimal expansion of (129+16*sqrt(2))/127.
  • A159469 (program): Maximum remainder when (k + 1)^n + (k - 1)^n is divided by k^2 for variable n and k > 2.
  • A159470 (program): Numerator of Hermite(n, 10/11).
  • A159472 (program): Numerator of Hermite(n, 1/12).
  • A159475 (program): a(1) = 1; for n >= 1, a(n) is the smallest number m > n such that gcd(n,m) > 1.
  • A159476 (program): Expansion of e.g.f.: A(x) = exp( Sum_{n>=1} (n-1)!*x^n/n ).
  • A159477 (program): a(n) = smallest prime >= n, if 1 is counted as a prime.
  • A159480 (program): Numerator of Hermite(n, 5/12).
  • A159481 (program): Number of evil numbers <= n, see A001969.
  • A159482 (program): Greatest odd prime q < 2*n such that p < q and p prime and p = 2*n - q or 0 if no such prime exists.
  • A159485 (program): Numerator of Hermite(n, 7/12).
  • A159486 (program): Numerator of Hermite(n, 11/12).
  • A159488 (program): Numerator of Hermite(n, 1/13).
  • A159490 (program): Denominator of Bernoulli(n, 1/12).
  • A159492 (program): Numerator of Hermite(n, 2/13).
  • A159494 (program): Numerator of Hermite(n, 3/13).
  • A159496 (program): Numerator of Hermite(n, 4/13).
  • A159497 (program): Numerator of Hermite(n, 5/13).
  • A159498 (program): Numerator of Hermite(n, 6/13).
  • A159500 (program): Numerator of Hermite(n, 7/13).
  • A159501 (program): Numerator of Hermite(n, 8/13).
  • A159502 (program): Numerator of Hermite(n, 9/13).
  • A159504 (program): Numerator of Hermite(n, 10/13).
  • A159505 (program): Numerator of Hermite(n, 11/13).
  • A159506 (program): Numerator of Hermite(n, 12/13).
  • A159507 (program): Numerator of Hermite(n, 1/14).
  • A159508 (program): Numerator of Hermite(n, 3/14).
  • A159509 (program): Numerator of Hermite(n, 5/14).
  • A159510 (program): Numerator of Hermite(n, 9/14).
  • A159511 (program): Numerator of Hermite(n, 11/14).
  • A159512 (program): Numerator of Hermite(n, 13/14).
  • A159513 (program): Numerator of Hermite(n, 1/15).
  • A159514 (program): Numerator of Hermite(n, 2/15).
  • A159515 (program): Numerator of Hermite(n, 4/15).
  • A159516 (program): Numerator of Hermite(n, 7/15).
  • A159517 (program): Numerator of Hermite(n, 8/15).
  • A159518 (program): Numerator of Hermite(n, 11/15).
  • A159519 (program): Numerator of Hermite(n, 13/15).
  • A159520 (program): Numerator of Hermite(n, 14/15).
  • A159521 (program): Numerator of Hermite(n, 1/16).
  • A159522 (program): Numerator of Hermite(n, 3/16).
  • A159523 (program): Numerator of Hermite(n, 5/16).
  • A159524 (program): Numerator of Hermite(n, 7/16).
  • A159525 (program): Numerator of Hermite(n, 9/16).
  • A159526 (program): Numerator of Hermite(n, 11/16).
  • A159527 (program): Numerator of Hermite(n, 13/16).
  • A159528 (program): Numerator of Hermite(n, 15/16).
  • A159529 (program): Numerator of Hermite(n, 1/17).
  • A159530 (program): Numerator of Hermite(n, 2/17).
  • A159531 (program): Numerator of Hermite(n, 3/17).
  • A159532 (program): Numerator of Hermite(n, 4/17).
  • A159533 (program): Numerator of Hermite(n, 5/17).
  • A159534 (program): Numerator of Hermite(n, 6/17).
  • A159535 (program): Numerator of Hermite(n, 7/17).
  • A159536 (program): Numerator of Hermite(n, 8/17).
  • A159537 (program): Numerator of Hermite(n, 9/17).
  • A159538 (program): Numerator of Hermite(n, 10/17).
  • A159539 (program): Numerator of Hermite(n, 11/17).
  • A159540 (program): Numerator of Hermite(n, 12/17).
  • A159541 (program): Numerator of Hermite(n, 13/17).
  • A159542 (program): Numerator of Hermite(n, 14/17).
  • A159543 (program): Numerator of Hermite(n, 15/17).
  • A159544 (program): Numerator of Hermite(n, 16/17).
  • A159545 (program): Numerator of Hermite(n, 1/18).
  • A159546 (program): Numerator of Hermite(n, 5/18).
  • A159549 (program): Decimal expansion of (201+20*sqrt(2))/199.
  • A159551 (program): a(n) = 101*n + 10.
  • A159552 (program): Numerator of Hermite(n, 7/18).
  • A159553 (program): a(n) = Sum_{k=0..n} binomial(n,k) * gcd(n,k).
  • A159554 (program): a(n) = A159553(n)/n.
  • A159561 (program): Numerator of Hermite(n, 11/18).
  • A159562 (program): Numerator of Hermite(n, 13/18).
  • A159563 (program): Numerator of Hermite(n, 17/18).
  • A159564 (program): Numerator of Hermite(n, 1/19).
  • A159566 (program): Decimal expansion of (243+22*sqrt(2))/241.
  • A159575 (program): Decimal expansion of (339+26*sqrt(2))/337.
  • A159582 (program): Expansion of (1+6*x+x^2-2*x^3)/((x^2+2*x-1)*(x^2-2*x-1)), bisection is NSW numbers.
  • A159583 (program): Values of A110391(5n)/A110391(n).
  • A159590 (program): Decimal expansion of (451+30*sqrt(2))/449.
  • A159602 (program): G.f.: A(x) = Sum_{n>=0} log(1 + x/(1-2^n*x))^n/n!.
  • A159605 (program): E.g.f: Sum_{n>=1} a(n)*x^(2n-1)/(2n-1)! = Series_Reversion of e.g.f. S(x) of A159601.
  • A159612 (program): INVERT transform of (1, 3, 1, 3, 1, …).
  • A159615 (program): The slowest increasing sequence beginning with a(1)=2 such that a(n) and n are both odious or both not odious.
  • A159616 (program): Expansion of (1-x)/(1-5*x-2*x^2+8*x^3).
  • A159617 (program): G.f.: (1-x)/(1-8*x-8*x^2+8*x^3).
  • A159618 (program): Numerator of Hermite(n, 2/19).
  • A159619 (program): Slowest increasing sequence beginning with 4 such that n and a(n) are either both evil or both odious.
  • A159620 (program): Numerator of Hermite(n, 3/19).
  • A159621 (program): Numerator of Hermite(n, 4/19).
  • A159622 (program): Numerator of Hermite(n, 5/19).
  • A159623 (program): Triangle read by rows: T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 1.
  • A159624 (program): a(n)=A159619(2n)-A159615(2n)
  • A159627 (program): Decimal expansion of (579 + 34*sqrt(2))/577.
  • A159631 (program): Dimension of space of modular forms of weight 1/2, level 4*n and trivial character.
  • A159634 (program): Coefficient for dimensions of spaces of modular & cusp forms of weight k/2, level 4*n and trivial character, where k>=5 is odd.
  • A159637 (program): Start with [0], repeatedly apply the map 0 -> [01/10], 1 -> [10/01] .
  • A159638 (program): Start with [1] and repeatedly apply the map 0 -> [01/10], 1 -> [10/01].
  • A159640 (program): a(1) = a(2) = 1; for n > 2, a(n) = (a(1), a(2), a(3), …) dot (P(1), P(2), P(3), …); P = A000129.
  • A159642 (program): Decimal expansion of (649 + 36*sqrt(2))/647.
  • A159644 (program): Numerator of Hermite(n, 6/19).
  • A159645 (program): Numerator of Hermite(n, 7/19).
  • A159646 (program): Numerator of Hermite(n, 8/19).
  • A159647 (program): Numerator of Hermite(n, 9/19).
  • A159648 (program): Numerator of Hermite(n, 10/19).
  • A159649 (program): Numerator of Hermite(n, 11/19).
  • A159650 (program): Numerator of Hermite(n, 12/19).
  • A159651 (program): Numerator of Hermite(n, 13/19).
  • A159652 (program): Numerator of Hermite(n, 14/19).
  • A159653 (program): Numerator of Hermite(n, 15/19).
  • A159654 (program): Numerator of Hermite(n, 16/19).
  • A159655 (program): Numerator of Hermite(n, 17/19).
  • A159656 (program): Numerator of Hermite(n, 18/19).
  • A159657 (program): Numerator of Hermite(n, 1/20).
  • A159658 (program): Numerator of Hermite(n, 3/20).
  • A159659 (program): Numerator of Hermite(n, 7/20).
  • A159660 (program): Numerator of Hermite(n, 9/20).
  • A159661 (program): The general form of the recurrences are the a(j, b(j) and n(j) solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j) and 13*n(j) + 1 = b(j)*b(j) with positive integer elements. the solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j); 13*n(j) + 1 = b(j)*b(j); with integer numbers.
  • A159663 (program): Numerator of Hermite(n, 11/20).
  • A159664 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j) and 13*n(j) + 1 = b(j)*b(j), with positive integer numbers.
  • A159665 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 11*n(j) + 1 = a(j)*a(j) and 13*n(j) + 1 = b(j)*b(j); with positive integer numbers.
  • A159668 (program): Expansion of (1 - x)/(1 - 28*x + x^2).
  • A159669 (program): Expansion of x*(1 + x)/(1 - 28*x + x^2).
  • A159670 (program): Numerator of Hermite(n, 13/20).
  • A159673 (program): Expansion of 56*x^2/(1 - 783*x + 783*x^2 - x^3).
  • A159674 (program): Expansion of (1 - x)/(1 - 32*x + x^2).
  • A159675 (program): Expansion of x*(1 + x)/(1 - 32*x + x^2).
  • A159676 (program): Numerator of Hermite(n, 17/20).
  • A159677 (program): Expansion of 64*x^2/(1 - 1023*x + 1023*x^2 - x^3).
  • A159678 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2-equation problem 7*n(j) + 1 = a(j)*a(j) and 9*n(j) + 1 = b(j)*b(j) with positive integer numbers.
  • A159679 (program): a(n) are solutions of the 2 equations: 7*a(n) +1 = c(n)^2 and 9*a(n) +1 = b(n)^2.
  • A159680 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 9*n(j) + 1 = a(j)*a(j) and 11*n(j) + 1 = b(j)*b(j) with positive integer numbers.
  • A159681 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 5*n(j)+1=a(j)*a(j) and 7*n(j)+1=b(j)*b(j) with positive integer numbers.
  • A159682 (program): Numerator of Hermite(n, 19/20).
  • A159683 (program): The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 3*n(j) + 1 = a(j)*a(j) and 5*n(j) + 1 = b(j)*b(j) with positive integer numbers.
  • A159684 (program): Sturmian word: limit S(infinity) where S(0) = 0, S(1) = 0,1 and for n>=1, S(n+1) = S(n)S(n)S(n-1).
  • A159689 (program): Fixed point of the morphism 0 -> 0,1,0; 1 -> 1,1; starting from a(0)=0.
  • A159691 (program): Decimal expansion of (883 + 42*sqrt(2))/881.
  • A159693 (program): Partial sums of A000463.
  • A159694 (program): a(n) = 2*a(n-1) + 2^(n-1), for n > 0, with a(0)=6.
  • A159695 (program): a(0)=7, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
  • A159696 (program): a(0)=8, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
  • A159697 (program): a(0)=9, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
  • A159699 (program): Replace 2^k in binary expansion of n with A045623(k+1).
  • A159702 (program): Decimal expansion of (969 + 44*sqrt(2))/967.
  • A159705 (program): Numerator of Hermite(n, 1/21).
  • A159706 (program): Numerator of Hermite(n, 2/21).
  • A159707 (program): Numerator of Hermite(n, 4/21).
  • A159709 (program): Numerator of Hermite(n, 5/21).
  • A159710 (program): Number of permutations of 1..n arranged in a circle with exactly 2 local maxima.
  • A159711 (program): Number of permutations of 1..n arranged in a circle with exactly 3 local maxima.
  • A159715 (program): Number of permutations of 2 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159721 (program): Number of permutations of 3 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159727 (program): Number of permutations of 4 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159733 (program): Number of permutations of 5 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159736 (program): Number of permutations of 6 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159738 (program): Number of permutations of 7 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159739 (program): Number of permutations of 8 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159740 (program): Number of permutations of 9 indistinguishable copies of 1..n arranged in a circle with exactly 1 local maximum.
  • A159741 (program): a(n) = 8*(2^n - 1).
  • A159742 (program): If an array is made of columns of -nacci sequences (Fibonacci, tribonacci, etc.), all starting with 1,1,2,…, the NW-to-SE diagonals can be extended by computation. This sequence is diagonal 6. See A159741 for details.
  • A159745 (program): Numerator of Hermite(n, 8/21).
  • A159751 (program): Decimal expansion of (51 + 14*sqrt(2))/47.
  • A159752 (program): Decimal expansion of (3267 + 1702*sqrt(2))/47^2.
  • A159753 (program): Numerator of Hermite(n, 10/21).
  • A159754 (program): Numbers n with property that n^2 ends with 81.
  • A159755 (program): Triangle of C. A. Laisant for k<=0 (see A062111 and A152920).
  • A159756 (program): Triangle A159755 reversed .
  • A159759 (program): Decimal expansion of (83+18*sqrt(2))/79.
  • A159761 (program): Numerator of Hermite(n, 11/21).
  • A159762 (program): Numerator of Hermite(n, 13/21).
  • A159763 (program): Numerator of Hermite(n, 16/21).
  • A159764 (program): Riordan array (1/(1+4x+x^2), x/(1+4x+x^2)).
  • A159769 (program): Number of n-leaf binary trees that do not contain (((()())())(()(()()))) as a subtree.
  • A159771 (program): Number of n-leaf binary trees that do not contain (()((()())((()())()))) as a subtree.
  • A159772 (program): Number of n-leaf binary trees that do not contain (()((((()())())())())) as a subtree.
  • A159776 (program): Numerator of Hermite(n, 17/21).
  • A159778 (program): Decimal expansion of (171+26*sqrt(2))/167.
  • A159780 (program): Inner product of the binary representation of n and its reverse.
  • A159784 (program): Numerator of Hermite(n, 19/21).
  • A159785 (program): a(n) = A152980(n)*3.
  • A159790 (program): Toothpick number A139250(n) minus triangular number A000217(n).
  • A159791 (program): Bisection of toothpick sequence A139250.
  • A159792 (program): Bisection of toothpick sequence A139250.
  • A159793 (program): a(n) = A153006(n)*2.
  • A159794 (program): a(n) = A153006(n)*3.
  • A159795 (program): a(n) = 4*A153006(n).
  • A159797 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n-1.
  • A159798 (program): Triangle read by rows in which row n lists n terms, starting with 1, such that the difference between successive terms is equal to n-3.
  • A159801 (program): Partial sums of A153001.
  • A159802 (program): Number of primes q with (2m)^2+1 <= q < (2m+1)^2-2m.
  • A159803 (program): Number of primes p with (2m+1)^2 - 2m <= p < (2m+1)^2.
  • A159804 (program): Number of primes q with (2n-1)^2+1 <= q < (2n)^2-(2n-1).
  • A159805 (program): Number of primes p with (2m)^2-(2m-1) <= p < (2m)^2
  • A159806 (program): Numerator of Hermite(n, 1/22).
  • A159807 (program): Numerator of Hermite(n, 3/22).
  • A159808 (program): Numerator of Hermite(n, 5/22).
  • A159810 (program): Decimal expansion of (227+30*sqrt(2))/223.
  • A159814 (program): Expansion of eta(z)^2*eta(4*z)^6/eta(2*z).
  • A159826 (program): Numerator of Hermite(n, 7/22).
  • A159828 (program): a(n) is smallest number m > 0 such that m^2 + n^2 + 1 is prime.
  • A159830 (program): Exponential Riordan array [exp(exp(x)-1-2x),x]
  • A159831 (program): Numerator of Hermite(n, 9/22).
  • A159832 (program): Numerator of Hermite(n, 13/22).
  • A159833 (program): a(n) = n^2*(n^2 + 15)/4.
  • A159834 (program): Coefficient array of Hermite_H(n, (x-1)/sqrt(2))/(sqrt(2))^n.
  • A159840 (program): Numerator of Hermite(n, 15/22).
  • A159841 (program): Triangle T(n,k) = binomial(3*n+1, 2*n+k+1), read by rows.
  • A159845 (program): Decimal expansion of (363 + 38*sqrt(2))/359.
  • A159850 (program): Numerator of Hermite(n, 17/22).
  • A159851 (program): Numerator of Hermite(n, 19/22).
  • A159852 (program): n^2 mod 60.
  • A159853 (program): Riordan array ((1-2*x+2*x^2)/(1-x), x/(1-x)).
  • A159854 (program): Riordan array (1-x,x/(1-x)).
  • A159855 (program): Riordan array ((1-2*x-x^2)/(1-x), x/(1-x)).
  • A159856 (program): Triangle read by rows: T(n,0) = n+1, T(n,k) = 2*T(n-1,k) - T(n-1,k-1), T(n,k) = 0 if k > n and if k < 0.
  • A159857 (program): Numerator of Hermite(n, 21/22).
  • A159858 (program): Numerator of Hermite(n, 1/23).
  • A159859 (program): Numerator of Hermite(n, 2/23).
  • A159864 (program): Difference array of Fibonacci numbers A000045 read by antidiagonals.
  • A159865 (program): Numerator of Hermite(n, 3/23).
  • A159868 (program): Numerator of Hermite(n, 4/23).
  • A159869 (program): Numerator of Hermite(n, 5/23).
  • A159870 (program): Numerator of Hermite(n, 6/23).
  • A159871 (program): Numerator of Hermite(n, 7/23).
  • A159872 (program): Numerator of Hermite(n, 8/23).
  • A159873 (program): Numerator of Hermite(n, 9/23).
  • A159874 (program): Numerator of Hermite(n, 10/23).
  • A159875 (program): Numerator of Hermite(n, 11/23).
  • A159876 (program): Inverse Mobius transform of the rabbit sequence, A051731 * A005614
  • A159877 (program): Numerator of Hermite(n, 12/23).
  • A159880 (program): Infinite string related to Ehrlich’s swap method for generating permutations.
  • A159882 (program): Numerator of Hermite(n, 13/23).
  • A159883 (program): Numerator of Hermite(n, 14/23).
  • A159884 (program): Numerator of Hermite(n, 15/23).
  • A159888 (program): Numbers congruent to {-5,29,39,41,43,45,55,57,59,93,103,105,107,109,119,121} mod 256 .
  • A159889 (program): Numerator of Hermite(n, 16/23).
  • A159891 (program): Decimal expansion of (443+42*sqrt(2))/439.
  • A159894 (program): Decimal expansion of (731+54*sqrt(2))/727.
  • A159897 (program): Decimal expansion of (843+58*sqrt(2))/839.
  • A159904 (program): Numerator of Hermite(n, 17/23).
  • A159912 (program): Partial sums of A159913(k) = 2^bitcount(2k+1)-1 = A038573(2k+1), bitcount=A000120.
  • A159913 (program): a(n) = 2^(A000120(n) + 1) - 1, where A000120(n) = number of nonzero bits in n.
  • A159914 (program): Half the number of (n-3)-element subsets of {1,…,n} whose elements sum up to an odd value.
  • A159915 (program): a(n) = floor((n+1)/4)*floor(n/2).
  • A159916 (program): Triangle T(m,n) = number of subsets of {1,…,m} with n elements having an odd sum, 1 <= n <= m.
  • A159917 (program): Fixed point of the morphism 0 -> 01, 1 -> 2, 2 -> 01, starting from a(0) = 0.
  • A159918 (program): Number of ones in binary representation of n^2.
  • A159919 (program): A square array of numbers, read by antidiagonals, called Sundaram’s sieve.
  • A159920 (program): Sums of the antidiagonals of Sundaram’s sieve (A159919).
  • A159921 (program): Numerator of Hermite(n, 18/23).
  • A159925 (program): Row sums of triangle A159924.
  • A159926 (program): The sum of all terms in row 1 through m of triangle A159924.
  • A159928 (program): a(n) is the sum of the terms of row n of triangle A159927.
  • A159929 (program): INVERT transform of phi(n), A000010.
  • A159930 (program): Triangle read by rows: a(1,1)=1. a(m,n) = a(m-1,n) + (sum of all terms in row m-1), for n<m. a(m,m) = sum of all terms in row m-1.
  • A159933 (program): INVERTi transform of d(n), A000005.
  • A159937 (program): Triangle read by rows, A054525 * A127478, as infinite lower triangular matrices.
  • A159938 (program): The number of homogeneous trisubstituted linear alkanes.
  • A159940 (program): The number of trisubstitution products with composition C_n H_(2n-1) X_2 Y.
  • A159941 (program): Number of trisubstituted linear alkanes of composition C_n H_(2n-1) XYZ.
  • A159943 (program): Numerator of Hermite(n, 19/23).
  • A159946 (program): Numerator of Hermite(n, 20/23).
  • A159947 (program): Numerator of Hermite(n, 21/23).
  • A159948 (program): Numerator of Hermite(n, 22/23).
  • A159949 (program): Numerator of Hermite(n, 1/24).
  • A159952 (program): Skinny numbers (A061909) containing no 3’s.
  • A159954 (program): Numerator of Hermite(n, 5/24).
  • A159955 (program): Period 9: repeat [0, 1, 2, 1, 2, 0, 2, 0, 1].
  • A159956 (program): Period 16 : 0,1,2,3,1,2,3,0,2,3,0,1,3,0,1,2 .
  • A159957 (program): Period 25 : 0,1,2,3,4,1,2,3,4,0,2,3,4,0,1,3,4,0,1,2,4,0,1,2,3 .
  • A159958 (program): Lodumo_3 of A053838 .
  • A159960 (program): Number of permutations of the set 1,2,…, 2n such that at least one pair of adjacent numbers in the permutation differ by n.
  • A159961 (program): Cuban composites: composite numbers equal to the difference of two consecutive cubes.
  • A159964 (program): a(n) = 2^n*(1-n).
  • A159965 (program): Riordan array (1/sqrt(1-4x), (1-2x-(1-3x)c(x))/(x*sqrt(1-4x))), c(x) the g.f. of A000108.
  • A159966 (program): Lodumo_4 of A102370 (sloping binary numbers).
  • A159967 (program): Numerator of Hermite(n, 7/24).
  • A159968 (program): Numerator of Hermite(n, 11/24).
  • A159969 (program): Numerator of Hermite(n, 13/24).
  • A159971 (program): Riordan array (2c(-x)-1, xc(-x)^3), c(x) the g.f. of A000108.
  • A159972 (program): Row sums of number triangle A159971.
  • A159973 (program): Non-refactorable numbers: number of divisors of n does not divide n.
  • A159974 (program): Triangle read by rows, M * Q; M = an infinite lower triangular Toeplitz matrix with (1, 1, 2, 3, 4, 5, …) in every column. Q = a matrix with A034943: (1, 1, 2, 5, 12, 28, …) as the main diagonal and the rest zeros.
  • A159981 (program): Catalan numbers read modulo 4.
  • A159984 (program): Catalan numbers read modulo 5 .
  • A159986 (program): Catalan numbers read modulo 7.
  • A159987 (program): Catalan numbers read modulo 8.
  • A159988 (program): Catalan numbers read modulo 11 .
  • A159989 (program): Catalan numbers read modulo 12.
  • A159991 (program): Powers of 60.
  • A159996 (program): Numerator of Hermite(n, 17/24).
  • A159997 (program): Numerator of Hermite(n, 19/24).
  • A159998 (program): Numerator of Hermite(n, 23/24).
  • A160003 (program): Numerator of Hermite(n, 1/25).
  • A160004 (program): Numerator of Hermite(n, 2/25).
  • A160005 (program): Numerator of Hermite(n, 3/25).
  • A160007 (program): Deficient numbers more than 1 unit away from their predecessors.
  • A160008 (program): Numerator of Hermite(n, 4/25).
  • A160010 (program): Numerator of Hermite(n, 6/25).
  • A160011 (program): Numerator of Hermite(n, 7/25).
  • A160012 (program): Numerator of Hermite(n, 8/25).
  • A160013 (program): Numerator of Hermite(n, 9/25).
  • A160016 (program): Lodumo_2 transform of A159833.
  • A160017 (program): Lodumo_2 of Thue-Morse sequence A010060.
  • A160035 (program): Clausen-normalized numerators of the Bernoulli numbers of order 2.
  • A160037 (program): Numerator of Hermite(n, 11/25).
  • A160038 (program): Numerator of Hermite(n, 12/25).
  • A160039 (program): Numerators of n!*(1 + 1/2 + 1/3 +…+ 1/(n+1))
  • A160042 (program): Decimal expansion of (89+36*sqrt(2))/73.
  • A160043 (program): Decimal expansion of (5907+1802*sqrt(2))/73^2.
  • A160046 (program): Numerator of the Harary number for the cycle graph C_n.
  • A160047 (program): Denominator of the Harary number for the cycle graph C_n.
  • A160048 (program): Numerator of the Harary number for the path graph P_n.
  • A160049 (program): Denominator of the Harary number for the path graph P_n.
  • A160050 (program): Numerator of the Harary number for the star graph s_n.
  • A160056 (program): Decimal expansion of (107+42*sqrt(2))/89.
  • A160057 (program): Decimal expansion of (8979+2990*sqrt(2))/89^2.
  • A160059 (program): Numerator of Hermite(n, 13/25).
  • A160060 (program): Numerator of Hermite(n, 14/25).
  • A160061 (program): Numerator of Hermite(n, 16/25).
  • A160062 (program): Numerator of Hermite(n, 17/25).
  • A160063 (program): Numerator of Hermite(n, 18/25).
  • A160064 (program): Numerator of Hermite(n, 19/25).
  • A160065 (program): Numerator of Hermite(n, 21/25).
  • A160066 (program): Numerator of Hermite(n, 22/25).
  • A160067 (program): Numerator of Hermite(n, 23/25).
  • A160068 (program): Numerator of Hermite(n, 24/25).
  • A160069 (program): Numerator of Hermite(n, 1/26).
  • A160070 (program): Numerator of Hermite(n, 3/26).
  • A160071 (program): Numerator of Hermite(n, 5/26).
  • A160072 (program): Numerator of Hermite(n, 7/26).
  • A160073 (program): Numerator of Hermite(n, 9/26).
  • A160074 (program): Numerator of Hermite(n, 11/26).
  • A160075 (program): Numerator of Hermite(n, 15/26).
  • A160076 (program): Numerator of Hermite(n, 17/26).
  • A160077 (program): Numerator of Hermite(n, 19/26).
  • A160080 (program): Lodumo_4 of Fibonacci numbers .
  • A160082 (program): Numerator of Hermite(n, 21/26).
  • A160083 (program): Numerator of Hermite(n, 23/26).
  • A160084 (program): Numerator of Hermite(n, 25/26).
  • A160087 (program): Numerator of Hermite(n, 1/27).
  • A160088 (program): Numerator of Hermite(n, 2/27).
  • A160091 (program): Decimal expansion of (587+102*sqrt(2))/569.
  • A160093 (program): Number of digits in n, excluding any trailing zeros.
  • A160094 (program): 1 + the number of trailing zeros in n (A122840).
  • A160096 (program): Partial sums of A010815 starting with offset 1, and signed (+ + - - + + …).
  • A160099 (program): Decimal expansion of (843 + 418*sqrt(2))/601.
  • A160103 (program): Numerator of Hermite(n, 4/27).
  • A160104 (program): Numerator of Hermite(n, 5/27).
  • A160107 (program): Numerator of Hermite(n, 7/27).
  • A160117 (program): Number of “ON” cells after n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
  • A160118 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
  • A160119 (program): A three-dimensional version of the cellular automaton A160118, using cubes.
  • A160128 (program): a(n) = number of grid points that are covered after (2^n)th stage of A139250.
  • A160130 (program): 2 x 2 inner (dot) products taken on corresponding digits in Pi and e.
  • A160131 (program): Numerator of Hermite(n, 8/27).
  • A160132 (program): Numerator of Hermite(n, 10/27).
  • A160134 (program): Nonprimitive e-perfect numbers.
  • A160138 (program): a(n) = number of solutions to the system: x + y + z + w = n, -2x - y + z + 2w = 5 with nonnegative x, y, z, w.
  • A160139 (program): Numerator of Hermite(n, 11/27).
  • A160140 (program): Numerator of Hermite(n, 13/27).
  • A160141 (program): Numerator of Hermite(n, 14/27).
  • A160142 (program): Numerator of Hermite(n, 16/27).
  • A160143 (program): a(n) = Numerator((-1)^n*Euler(2*n)*(2*n+1)/(4^(2*n+1)-2^(2*n+1))), where Euler(n) = A122045(n).
  • A160144 (program): Numerator of (2*n+1)/(2^(2*n+1)-1).
  • A160146 (program): Numerator of Hermite(n, 17/27).
  • A160147 (program): Numerator of Hermite(n, 19/27).
  • A160148 (program): Numerator of Hermite(n, 20/27).
  • A160150 (program): Numerator of Hermite(n, 22/27).
  • A160151 (program): Numerator of Hermite(n, 23/27).
  • A160152 (program): Numerator of Hermite(n, 25/27).
  • A160153 (program): Numerator of Hermite(n, 26/27).
  • A160154 (program): 10^n-9n for n>=1
  • A160155 (program): Decimal expansion of the one real root of x^5-x-1.
  • A160156 (program): Partial sums of A007583.
  • A160158 (program): Toothpick sequence starting from a segment of length 4 formed by two toothpicks.
  • A160159 (program): First differences of A160158.
  • A160162 (program): a(n) = A160158(n)/2.
  • A160163 (program): First differences of A160162.
  • A160164 (program): Number of toothpicks after n-th stage in the I-toothpick structure of A139250.
  • A160172 (program): T-toothpick sequence (see Comments lines for definition).
  • A160173 (program): Number of T-toothpicks added at n-th stage to the T-toothpick structure of A160172.
  • A160174 (program): a(n) = (2*n - 1)*(24*n^2 - 42*n + 19).
  • A160175 (program): Expansion of 1/(1 - 2*x - 2*x^2 - 2*x^3 - 2*x^4).
  • A160177 (program): Decimal expansion of (633+100*sqrt(2))/617.
  • A160180 (program): Largest proper divisor of the n-th composite number.
  • A160181 (program): Number of partitions of sets containing from 0 to n elements into blocks of at least 2 elements.
  • A160184 (program): Numerator of Hermite(n, 1/28).
  • A160186 (program): Lodumo_5 of Lucas numbers.
  • A160189 (program): Prime terms subtracted from Fibonacci terms (ignoring first two terms of Fibonacci sequence).
  • A160190 (program): Prime terms multiplied by Fibonacci terms (omitting first two terms of Fibonacci sequence)
  • A160192 (program): Numerator of Hermite(n, 3/28).
  • A160193 (program): Numerator of Hermite(n, 5/28).
  • A160194 (program): Numerator of Hermite(n, 9/28).
  • A160195 (program): Numerator of Hermite(n, 11/28).
  • A160196 (program): Numerator of Hermite(n, 13/28).
  • A160197 (program): Numerator of Hermite(n, 15/28).
  • A160201 (program): Decimal expansion of (1003+462*sqrt(2))/761.
  • A160204 (program): Decimal expansion of (873+232*sqrt(2))/809.
  • A160207 (program): Decimal expansion of (907+210*sqrt(2))/857.
  • A160210 (program): Decimal expansion of (1179+506*sqrt(2))/937.
  • A160213 (program): Decimal expansion of (969+124*sqrt(2))/953.
  • A160215 (program): Primes congruent to 2^k+1 (mod 2^(k+1)), where k is any even integer >=0.
  • A160216 (program): Primes congruent to 2^k+1 (mod 2^(k+1)), where k is any odd integer >=1.
  • A160217 (program): Minimal increasing sequence with a(1)=3 and the property that a(n) and n are both in or both not in A003159.
  • A160219 (program): Numerator of Hermite(n, 17/28).
  • A160220 (program): Numerator of Hermite(n, 19/28).
  • A160221 (program): Numerator of Hermite(n, 23/28).
  • A160222 (program): Numerator of Hermite(n, 25/28).
  • A160223 (program): Numerator of Hermite(n, 27/28).
  • A160224 (program): Numerator of Hermite(n, 1/29).
  • A160225 (program): Numerator of Hermite(n, 2/29).
  • A160226 (program): Numerator of Hermite(n, 3/29).
  • A160230 (program): a(n) = A004760(n+1)-A160217(n), n>=1.
  • A160231 (program): Numerator of Hermite(n, 4/29).
  • A160232 (program): Array read by antidiagonals: row n has g.f. ((1-x)/(1-2x))^n.
  • A160236 (program): Numerator of Hermite(n, 5/29).
  • A160237 (program): Numerator of Hermite(n, 6/29).
  • A160239 (program): Number of “ON” cells in a 2-dimensional cellular automaton (“Fredkin’s Replicator”) evolving according to the rule that a cell is ON in a given generation if and only if there was an odd number of ON cells among the eight nearest neighbors in the preceding generation, starting with one ON cell.
  • A160242 (program): Triangle A(n,m) read by rows: a quarter of the Fourier coefficient [cos(m*t)] of the shifted Boubaker polynomial B_n(2*cos t)-2*cos(n*t).
  • A160243 (program): a(n) = Lucas(n+1) + prime(n).
  • A160244 (program): A104449(n+1)+prime(n), sum of a Lucas and the prime sequence.
  • A160246 (program): Numerator of Hermite(n, 7/29).
  • A160248 (program): Table read by antidiagonals of “less regular” truncated tetrahedron numbers built of face-centered-cubic sphere packing.
  • A160250 (program): a(n) = 64*n^3 - 168*n^2 + 148*n - 43.
  • A160251 (program): Numerator of Hermite(n, 8/29).
  • A160252 (program): Numerator of Hermite(n, 9/29).
  • A160253 (program): Numerator of Hermite(n, 10/29).
  • A160255 (program): The sum of all the entries in an n X n Cayley table for multiplication in Z_n.
  • A160259 (program): Numerator of Hermite(n, 11/29).
  • A160260 (program): Numerator of Hermite(n, 12/29).
  • A160261 (program): Numerator of Hermite(n, 13/29).
  • A160263 (program): Numerator of Hermite(n, 14/29).
  • A160269 (program): Numerator of Hermite(n, 15/29).
  • A160270 (program): Numerator of Hermite(n, 16/29).
  • A160272 (program): Angle between the two hands of a 12 hour analog clock n*12 minutes after noon/midnight, measured in units of minutes.
  • A160273 (program): Successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040).
  • A160278 (program): Angle in degrees between the two hands of a 12-hour analog clock at 12*n minutes after noon/midnight.
  • A160279 (program): Numerator of Hermite(n, 17/29).
  • A160280 (program): Numerator of Hermite(n, 18/29).
  • A160281 (program): Numerator of Hermite(n, 19/29).
  • A160282 (program): Numerator of Hermite(n, 20/29).
  • A160283 (program): Numerator of Hermite(n, 21/29).
  • A160284 (program): Numerator of Hermite(n, 22/29).
  • A160285 (program): Numerator of Hermite(n, 23/29).
  • A160286 (program): Numerator of Hermite(n, 24/29).
  • A160287 (program): Numerator of Hermite(n, 25/29).
  • A160288 (program): Numerator of Hermite(n, 26/29).
  • A160289 (program): Numerator of Hermite(n, 27/29).
  • A160290 (program): Numerator of Hermite(n, 28/29).
  • A160291 (program): Numerator of Hermite(n, 1/30).
  • A160292 (program): Numerator of Hermite(n, 7/30).
  • A160293 (program): Numerator of Hermite(n, 11/30).
  • A160294 (program): Numerator of Hermite(n, 13/30).
  • A160295 (program): Numerator of Hermite(n, 17/30).
  • A160296 (program): Numerator of Hermite(n, 19/30).
  • A160297 (program): Numerator of Hermite(n, 23/30).
  • A160298 (program): Numerator of Hermite(n, 29/30).
  • A160299 (program): Numerator of Hermite(n, 1/31).
  • A160300 (program): Numerator of Hermite(n, 2/31).
  • A160301 (program): Numerator of Hermite(n, 3/31).
  • A160302 (program): Numerator of Hermite(n, 4/31).
  • A160303 (program): Numerator of Hermite(n, 5/31).
  • A160304 (program): Numerator of Hermite(n, 6/31).
  • A160305 (program): Numerator of Hermite(n, 7/31).
  • A160306 (program): Numerator of Hermite(n, 8/31).
  • A160307 (program): Numerator of Hermite(n, 9/31).
  • A160308 (program): Numerator of Hermite(n, 10/31).
  • A160309 (program): Numerator of Hermite(n, 11/31).
  • A160310 (program): Numerator of Hermite(n, 12/31).
  • A160311 (program): Numerator of Hermite(n, 13/31).
  • A160312 (program): Numerator of Hermite(n, 14/31).
  • A160313 (program): Numerator of Hermite(n, 15/31).
  • A160314 (program): Numerator of Hermite(n, 16/31).
  • A160315 (program): Numerator of Hermite(n, 17/31).
  • A160316 (program): Numerator of Hermite(n, 18/31).
  • A160317 (program): Numerator of Hermite(n, 19/31).
  • A160324 (program): Number of ways to express n as the sum of a square, a pentagonal number and a hexagonal number.
  • A160325 (program): Number of ways to express n=0,1,2,… as the sum of a triangular number, an even square and a pentagonal number.
  • A160326 (program): Number of ways to express n=0,1,2,… as the sum of two squares and a pentagonal number.
  • A160327 (program): Decimal expansion of (e-1)/(e+1).
  • A160328 (program): Numerator of Hermite(n, 20/31).
  • A160329 (program): Numerator of Hermite(n, 21/31).
  • A160330 (program): Numerator of Hermite(n, 22/31).
  • A160332 (program): Decimal expansion of the one real root of x^3-8x-10.
  • A160333 (program): Number of pairs of rabbits in month n in the dying rabbits problem, if they become mature after 4 months and give birth to exactly 7 pairs, one per month.
  • A160334 (program): Numerator of Hermite(n, 23/31).
  • A160335 (program): Numerator of Hermite(n, 24/31).
  • A160336 (program): Numerator of Hermite(n, 25/31).
  • A160338 (program): Height (maximum absolute value of coefficients) of the n-th cyclotomic polynomial.
  • A160344 (program): Numerator of Hermite(n, 26/31).
  • A160345 (program): Numerator of Hermite(n, 27/31).
  • A160346 (program): Numerator of Hermite(n, 28/31).
  • A160347 (program): Numerator of Hermite(n, 29/31).
  • A160349 (program): Numerator of Hermite(n, 30/31).
  • A160361 (program): Numerator of Hermite(n, 1/32).
  • A160362 (program): Numerator of Hermite(n, 3/32).
  • A160363 (program): Numerator of Hermite(n, 5/32).
  • A160372 (program): The 4-tuple (2, ((2*n+1)^2-1)/2, (2*n+3)^2-1)/2, a(n)}, where a(n)=4(3+20n+42n^2+32n^3+8n^4), has Diophantus’ property that the product of any two distinct terms plus one is a square.
  • A160374 (program): Numerator of Hermite(n, 7/32).
  • A160376 (program): Numerator of Hermite(n, 9/32).
  • A160377 (program): Phi-torial of n (A001783) modulo n.
  • A160378 (program): a(n) = n^3 - n*(n+1)/2.
  • A160380 (program): a(0) = 0; for n >= 1, a(n) = number of 0’s in base-4 representation of n.
  • A160381 (program): Number of 1’s in base-4 representation of n.
  • A160382 (program): Number of 2’s in base-4 representation of n.
  • A160383 (program): Number of 3’s in base-4 representation of n.
  • A160384 (program): Number of nonzero digits in the base-3 representation of n.
  • A160385 (program): Number of nonzero digits in base-4 representation of n.
  • A160386 (program): Decimal expansion of Sum_{n>=0}(-1)^n/3^(2^n).
  • A160388 (program): Decimal expansion of (e + 1)/3.
  • A160389 (program): Decimal expansion of 2*cos(Pi/7).
  • A160390 (program): Decimal expansion of sqrt(3) - 1.
  • A160391 (program): Numerator of Hermite(n, 11/32).
  • A160393 (program): Square root of A003462, rounded up.
  • A160396 (program): Numerator of Hermite(n, 13/32).
  • A160397 (program): Numerator of Hermite(n, 15/32).
  • A160398 (program): Numerator of Hermite(n, 17/32).
  • A160399 (program): a(n) = Sum_{k=1..n} binomial(n,k) * d(k), where d(k) = the number of positive divisors of k.
  • A160400 (program): a(n) is the smallest positive integer such that a(n)*n = j^k, for some j (j>=1) and k (k>=2).
  • A160401 (program): Table read by antidiagonals: a(m,n) = the smallest composite multiple of both m and n.
  • A160406 (program): Toothpick sequence starting at the vertex of an infinite 90-degree wedge.
  • A160407 (program): First differences of toothpick numbers A160406.
  • A160408 (program): Toothpick pyramid (see Comments lines for definition).
  • A160409 (program): First differences of toothpick numbers A160408.
  • A160410 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
  • A160411 (program): Number of cells turned “ON” at n-th stage of A160117.
  • A160412 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (see Comments for precise definition).
  • A160413 (program): a(n) = A160411(n+1)/4.
  • A160414 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton (same as A160410, but a(1) = 1, not 4).
  • A160415 (program): First differences of A160118.
  • A160417 (program): a(n) = A160415(n+1)/4.
  • A160418 (program): a(n) = A160407(n+2)/2.
  • A160424 (program): Partial sums of A139250.
  • A160428 (program): Number of ON cells at n-th stage of three-dimensional version of the cellular automaton A160410, using cubes.
  • A160429 (program): First differences of A160428.
  • A160431 (program): Numerator of Hermite(n, 19/32).
  • A160435 (program): Numerator of Hermite(n, 21/32).
  • A160436 (program): Numerator of Hermite(n, 23/32).
  • A160437 (program): Numerator of Hermite(n, 25/32).
  • A160441 (program): Numerator of Hermite(n, 27/32).
  • A160442 (program): Numerator of Hermite(n, 29/32).
  • A160443 (program): Numerator of Hermite(n, 31/32).
  • A160444 (program): G.f.: x^2*(-1-x+x^2)/(-1+2*x^2+2*x^4).
  • A160445 (program): Numerator of Hermite(n, 20/21).
  • A160451 (program): (4/3)u(u^3+6*u^2+8u-3) where u=Floor[{3n+5)/2].
  • A160455 (program): Number of triangles that can be built from rods with lengths 1,2,…,n by using and concatenating all rods.
  • A160457 (program): a(n) = n^2 - 2*n + 2.
  • A160458 (program): Coefficients in the expansion of C^2/B^10, in Watson’s notation of page 106.
  • A160459 (program): Omit first term of A160458 and divide by 5.
  • A160467 (program): a(n) = 1 if n is odd; otherwise, a(n) = 2^(k-1) where 2^k is the largest power of 2 that divides n.
  • A160469 (program): The left hand column of the triangle A160468.
  • A160473 (program): The p(n) sequence that is associated with the Eta triangle A160464.
  • A160481 (program): Row sums of the Beta triangle A160480.
  • A160483 (program): Second right hand column of the Beta triangle A160480
  • A160491 (program): First differences of A062481.
  • A160501 (program): (n+1)^prime(n+1) + n^prime(n).
  • A160505 (program): a(1)=1, a(n) = p*a(n-1), where p is the smallest prime satisfying gcd(n,p)=1.
  • A160511 (program): Number of weighings needed to find lighter coins among n coins.
  • A160517 (program): A walk of 10-divisible “less regular” figurate cuboctahedra, from sequence A160249.
  • A160522 (program): The n-th odd composite number minus the n-th even composite number.
  • A160529 (program): a(1) = 1; for n>1, a(n) = a(n-1) + d1 + d2 where d1 = 4 if n is even. d1 = 1 if n is odd, d2 = 15 if n mod 4 = 0, d2 = 0 if n mod 4 != 0.
  • A160530 (program): Positive integers that contain only odd-length runs of 0’s and 1’s in their binary expansion.
  • A160532 (program): Those positive integers n that contain runs of 0’s and 1’s that are each a power of 2 in length when n is represented in binary.
  • A160536 (program): a(n) = Fibonacci(n) + n^2.
  • A160538 (program): a(n) = 4*(n^4-n^3).
  • A160541 (program): Number of odd-then-even runs to reach 1 under the modified `3x+1’ map: n -> n/2 if n is even, n -> (3n+1)/2 if n is odd.
  • A160542 (program): Not divisible by 11
  • A160543 (program): Not divisible by 17
  • A160544 (program): Not divisible by 19.
  • A160545 (program): Numbers coprime to 21.
  • A160546 (program): Not divisible by 29.
  • A160547 (program): Not divisible by 31.
  • A160550 (program): a(n) = A001065(n) mod A000005(n).
  • A160551 (program): Number of unordered ways of making change for n dollars using coins of denominations 1, 5, 10, and 25.
  • A160552 (program): a(0)=0, a(1)=1; a(2^i+j) = 2*a(j) + a(j+1) for 0 <= j < 2^i.
  • A160554 (program): Numerator of Laguerre(n, -12).
  • A160555 (program): Denominator of Laguerre(n, -12).
  • A160565 (program): Diagonal sums of number triangle [k<=n]*C(n,2n-2k)2^(n-k)A000108(n-k).
  • A160566 (program): Numerator of Laguerre(n, -11).
  • A160567 (program): a(n)=4*(a(n-1)a(n-3)-a(n-2)^2)/a(n-4), a(1)=a(2)=a(3)=1, a(4)=-4.
  • A160568 (program): Diagonal sums of number triangle [k<=n]*C(n,2n-2k)3^(n-k)A000108(n-k).
  • A160569 (program): a(n)=9*(a(n-1)a(n-3)-a(n-2)^2)/a(n-4), a(1)=a(2)=a(3)=1, a(4)=-9.
  • A160572 (program): Elements of A160444, pairs of consecutive entries swapped.
  • A160573 (program): G.f.: Product_{ k >= 0} (1 + x^(2^k-1) + x^(2^k)).
  • A160575 (program): Decimal expansion of (363+130*sqrt(2))/313.
  • A160578 (program): Decimal expansion of (473+168*sqrt(2))/409.
  • A160581 (program): Decimal expansion of (601+276*sqrt(2))/457.
  • A160584 (program): Decimal expansion of (537 +92*sqrt(2))/521.
  • A160586 (program): Denominator of Laguerre(n, -11).
  • A160587 (program): Numerator of Laguerre(n, -10).
  • A160588 (program): Interleaving of A053645 and A000027.
  • A160589 (program): Denominator of Laguerre(n, -10).
  • A160590 (program): Next-to-least significant digit of 2^n.
  • A160591 (program): Indices of primes congruent to 5 modulo 12.
  • A160592 (program): Indices of primes congruent to 7 modulo 12.
  • A160593 (program): Indices of primes congruent to 11 modulo 12.
  • A160594 (program): Indices of primes congruent to 1 modulo 12.
  • A160595 (program): Numerator of resilience R(n) = phi(n)/(n-1), with a(1) = 1 by convention.
  • A160596 (program): Denominator of resilience R(n) = phi(n)/(n-1).
  • A160597 (program): Denominator of coresilience C(n) = (n - phi(n))/(n-1).
  • A160598 (program): Numerator of coresilience C(n) = (n - phi(n))/(n-1).
  • A160601 (program): Numerator of Laguerre(n, -9).
  • A160602 (program): Denominator of Laguerre(n, -9).
  • A160603 (program): Numerator of Laguerre(n, -8).
  • A160604 (program): Denominator of Laguerre(n, -8).
  • A160605 (program): Numerator of Laguerre(n, -7).
  • A160606 (program): Denominator of Laguerre(n, -7).
  • A160607 (program): Numerator of Laguerre(n, -6).
  • A160608 (program): Denominator of Laguerre(n, -6).
  • A160609 (program): Numerator of Laguerre(n, -5).
  • A160610 (program): Denominator of Laguerre(n, -5).
  • A160611 (program): Numerator of Laguerre(n, -4).
  • A160612 (program): Denominator of Laguerre(n, -4).
  • A160613 (program): Numerator of Laguerre(n, -3).
  • A160614 (program): Denominator of Laguerre(n, -3).
  • A160615 (program): Numerator of Laguerre(n, -2).
  • A160616 (program): Denominator of Laguerre(n, -2).
  • A160617 (program): Numerator of Laguerre(n, -1).
  • A160618 (program): Denominator of Laguerre(n, -1).
  • A160619 (program): a(n) = Sum_{d|n} phi(n/d)*2^(d+1), with a(0) = 0.
  • A160621 (program): Numerator of Laguerre(n, 1).
  • A160622 (program): Denominator of Laguerre(n, 1).
  • A160623 (program): Numerator of Laguerre(n, 2).
  • A160624 (program): Denominator of Laguerre(n, 2).
  • A160625 (program): Numerator of Laguerre(n, 3).
  • A160626 (program): Denominator of Laguerre(n, 3).
  • A160627 (program): Numerator of Laguerre(n, 4).
  • A160628 (program): Denominator of Laguerre(n, 4).
  • A160629 (program): Numerator of Laguerre(n, 5).
  • A160630 (program): Denominator of Laguerre(n, 5).
  • A160631 (program): Numerator of Laguerre(n, 6).
  • A160632 (program): Denominator of Laguerre(n, 6).
  • A160633 (program): Numerator of Laguerre(n, 7).
  • A160634 (program): Denominator of Laguerre(n, 7).
  • A160635 (program): Numerator of Laguerre(n, 8).
  • A160637 (program): Hankel transform of A114464(n+1).
  • A160638 (program): Bit-reversed 8-bit binary numbers.
  • A160639 (program): Denominator of Laguerre(n, 8).
  • A160640 (program): Numerator of Laguerre(n, 9).
  • A160641 (program): Denominator of Laguerre(n, 9).
  • A160644 (program): First of two sequences bisecting the second differences of the partition numbers (see A053445).
  • A160649 (program): a(1)=2. a(n) = a(n-1) + A001222(a(n-1)); where A001222(m) is the sum of prime-factorization exponents of m (or, A001222(m) is the number of primes dividing m, with multiplicity).
  • A160650 (program): a(n) = A001222(A160649(n)) = A160649(n+1) - A160649(n); where A001222(m) is the sum of prime-factorization exponents of m (or, A001222(m) is the number of primes dividing m, counted with multiplicity).
  • A160651 (program): a(n) is the number of triangular nonnegative integers that are each equal to n(n+1)/2 - m(m+1)/2, for some m’s where 0 <= m <= n.
  • A160653 (program): Numerator of Laguerre(n, 10).
  • A160654 (program): Denominator of Laguerre(n, 10).
  • A160655 (program): Numerator of Laguerre(n, 11).
  • A160656 (program): The odd prime numbers together with 0: p - (-1)^p - 1 where p = n-th prime.
  • A160664 (program): a(n) = a(n-1) + A000203(n), a(0)=1.
  • A160666 (program): Numbers whose distance to the closest prime number is a prime number.
  • A160667 (program): Denominator of Laguerre(n, 11).
  • A160668 (program): Distance between prime(n) and the next higher power of 10.
  • A160670 (program): Primes in A160668 in order of appearance.
  • A160671 (program): Numerator of Laguerre(n, 12).
  • A160672 (program): Denominator of Laguerre(n, 12).
  • A160674 (program): A bisection of A063522.
  • A160675 (program): Duplication root: the maximal number of distinct squarefree words that a word of length n can be reduced to by iterated application of string-rewriting rules uu->u.
  • A160682 (program): The list of the A values in the common solutions to 13*k+1 = A^2 and 17*k+1 = B^2.
  • A160692 (program): Iteration of (k terms=k, followed by 2^k-k terms=0), beginning with k=0.
  • A160695 (program): Integers m such that 3*m+1 and 7*m+1 are both perfect squares.
  • A160696 (program): Largest k such that k^2 divides prime(n)+1.
  • A160697 (program): Record values in A160696.
  • A160699 (program): A bisection of A063522.
  • A160703 (program): Generalized Somos-4 Hankel determinant recurrence sequence.
  • A160704 (program): Jacobsthal sequence A001045 convolved with A139251 (first differences of toothpick numbers).
  • A160706 (program): Hankel transform of A052702(n+1).
  • A160713 (program): 3 times numbers of Gould’s sequence: a(n) = A001316(n)*3.
  • A160718 (program): a(n) = A160406(n+2)/2.
  • A160719 (program): a(n) = A160406(n+2)/2 - 1.
  • A160720 (program): Number of “ON” cells at n-th stage in 2-dimensional cellular automaton (see Comments for precise definition).
  • A160721 (program): First differences of A160720.
  • A160722 (program): Number of “ON” cells at n-th stage in a certain 2-dimensional cellular automaton based on Sierpinski triangles (see Comments for precise definition).
  • A160723 (program): First differences of A160722.
  • A160727 (program): a(n) = A161415(n+1)/4.
  • A160728 (program): Toothpick cube: a(n) = A160408(n)*6.
  • A160729 (program): First differences of A160728.
  • A160734 (program): a(n) = (A160158(n+2)-4)/4.
  • A160735 (program): First differences of A160734.
  • A160736 (program): Toothpick sequence starting from a right angle formed by 2 toothpicks: a(n)=A160406(n)*2.
  • A160737 (program): 4*P_5(n), 4 times the Legendre Polynomial of order 5 at n.
  • A160738 (program): Toothpick sequence starting from a T formed by 3 toothpicks: a(n)=A160406(n)*3.
  • A160739 (program): 16*P_6(n), 16 times the Legendre Polynomial of order 6 at n.
  • A160740 (program): Toothpick sequence starting from a cross formed by 4 toothpicks.
  • A160741 (program): Numerator of P_6(2n), the Legendre polynomial of order 6 at 2n.
  • A160742 (program): a(n) = A151566(n)*2.
  • A160743 (program): 8*P_7(n), 8 times the Legendre Polynomial of order 7 at n.
  • A160744 (program): a(n) = A151566(n)*3.
  • A160745 (program): First differences of A160744.
  • A160746 (program): a(n) = A151566(n)*4.
  • A160747 (program): Expansion of (1+10*x+20*x^2+10*x^3+x^4)/(1-x)^5.
  • A160749 (program): a(n) = (11*n^2 + 19*n + 10)/2.
  • A160755 (program): Number of correct digits of the MRB constant derived from the sequence of partial sums up to m=10^n terms as defined by S[n]= Sum[(-1)^k*(k^(1/k)-1),{k,m}].
  • A160760 (program): Triangle read by rows, binomial transform of an infinite lower triangular Toeplitz matrix with A078008 in every column.
  • A160762 (program): Convolved with the toothpick sequence A139250 = (2*n - 1): (1, 3, 5, 7, …).
  • A160765 (program): Expansion of (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.
  • A160767 (program): Expansion of (1+12*x+28*x^2+12*x^3+x^4)/(1-x)^5.
  • A160772 (program): Number of nodes (or order) of a graph model obtained using an automata scheme on sets of order prime(n) >= 5 and in which all not halt states are linked by arcs (edges).
  • A160785 (program): Even squarefree numbers plus 1.
  • A160790 (program): Vertex number of a rectangular spiral. The first differences (A160791) are the edge lengths of the spiral. The distances between two nearest edges, that are parallel to the initial edge, are the natural numbers.
  • A160791 (program): First differences of A160790.
  • A160792 (program): Vertex number of a rectangular spiral related to prime numbers. The distances between nearest edges of the spiral that are parallel to the initial edge are the prime numbers, while the distances between nearest edges perpendicular to the initial edge are all one.
  • A160793 (program): Natural numbers and the sum of first n primes interleaved.
  • A160796 (program): Total number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton which is the “corner” structure corresponding to A160118.
  • A160797 (program): First differences of A160796.
  • A160798 (program): a(n) = A160797(n+2)/3.
  • A160799 (program): Partial sums of A160410.
  • A160804 (program): Consider a permutation K = (k(1),k(2),…k(A000005(n))) of the positive divisors of n. Consider the partial sums S= sum{j=1 to m} k(j), 1<=m<=A000005(n). Then, a(n) = the minimum number, for any permutation K, of partial sums S that are coprime to n.
  • A160805 (program): a(n) = (2*n^3 + 9*n^2 + n + 24) / 6.
  • A160807 (program): a(n) = A160799(n)/4.
  • A160810 (program): Numbers k such that the number of partitions of k into prime divisors of k exceeds the number of distinct transpositions of prime factors of k.
  • A160811 (program): Numbers not dividing 24.
  • A160812 (program): a(n) = A161205(n)-A000005(n).
  • A160813 (program): a(n) = n-th squarefree number plus n-th cubefree number.
  • A160823 (program): A transform of the large Schroeder numbers.
  • A160827 (program): a(n) = 3*n^4 + 12*n^3 + 30*n^2 + 36*n + 17.
  • A160828 (program): a(n) = 4*n^4 + 24*n^3 + 84*n^2 + 144*n + 98.
  • A160830 (program): Integer part of the product of two consecutive primes divided by their sum.
  • A160832 (program): Expansion of eta(q)*eta(q^2)*eta(q^4), where eta(q) = Product((1-q^m), m=1..oo).
  • A160842 (program): Number of lines through at least 2 points of a 2 X n grid of points.
  • A160843 (program): Number of lines through at least 2 points of a 3 X n grid of points.
  • A160864 (program): 64*P_9(n), 64 times the Legendre polynomial of order 9 at n.
  • A160865 (program): 128*P_11(n), 128 times the Legendre polynomial of order 11 at n.
  • A160866 (program): 512*P_11(n), 512 times the Legendre polynomial of order 13 at n.
  • A160867 (program): 1024*P_15(n), 1024 times the Legendre polynomial of order 15 at n.
  • A160868 (program): 16384*P_17(n), 16384 times the Legendre polynomial of order 17 at n.
  • A160869 (program): a(n) = sigma(6^(n-1)).
  • A160873 (program): Number of isomorphism classes of connected (D_4)-fold coverings of a connected graph with circuit rank n.
  • A160889 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4.
  • A160890 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 3.
  • A160891 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 5.
  • A160892 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 4.
  • A160893 (program): a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n).
  • A160894 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 5.
  • A160895 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7.
  • A160896 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 6.
  • A160897 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8.
  • A160898 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 7.
  • A160900 (program): a(n) = the smallest positive multiple of n that has exactly a prime number of (non-leading) 0’s in its binary representation.
  • A160902 (program): Square array read by antidiagonals: a(m,n) = the smallest prime >= m*n.
  • A160903 (program): Square array read by antidiagonals: a(m,n) = the largest noncomposite <= m*n.
  • A160904 (program): Row sums of A159881.
  • A160906 (program): Row sums of A159841.
  • A160908 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 9.
  • A160909 (program): Row sums of triangle defined in A096539.
  • A160910 (program): Decimal expansion of c = sum over twin primes (p, p+2) of (1/p^2 + 1/(p+2)^2).
  • A160912 (program): [1, 3, 5, 7, …] convolved with [1, 4, 0, 0, 0, …].
  • A160913 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 8.
  • A160914 (program): Extended s-block elements for Janet table.
  • A160924 (program): a(n)= n + reversal(n+1)
  • A160925 (program): a(n)= n - reversal(n+1)
  • A160926 (program): a(n)= n * reversal(n+1)
  • A160927 (program): a(n) = n + reversal(n-1).
  • A160928 (program): a(n) = n - reversal(n-1)
  • A160929 (program): a(n)= n * reversal(n-1)
  • A160930 (program): a(n)= n + reversal(n-1) + reversal(n+1)
  • A160931 (program): a(n)= n + digital sum(n+1)
  • A160933 (program): a(n)= n - reversal(n-1) - reversal(n+1)
  • A160936 (program): a(n)= n * reversal(n-1) * reversal(n+1).
  • A160938 (program): a(n)= n * digital sum(n+1)
  • A160939 (program): a(n) = n + digital sum (n-1).
  • A160941 (program): a(n)= n - digital sum(n-1)
  • A160942 (program): a(n)= n * digital sum(n-1)
  • A160943 (program): a(n) = n + digital sum(n-1) + digital sum(n+1).
  • A160944 (program): a(n)= n * digital sum(n-1) * digital sum(n+1)
  • A160947 (program): Numbers k that are multiples of the digital sum of k+1.
  • A160948 (program): Numbers n that are multiples of the digital sum of n-1.
  • A160949 (program): a(n) = n - digital sum(n+1)
  • A160950 (program): Primes p such that 2p + 105 is prime.
  • A160953 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10.
  • A160956 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 9.
  • A160957 (program): a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 11.
  • A160958 (program): a(n) = (9^n - (-7)^n)/(9 - (-7)).
  • A160959 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 10.
  • A160964 (program): a(n) = ((2^b-1)/phi(n))*Sum_{d|n} Moebius(n/d)*d^(b-1) for b = 11.
  • A160967 (program): Numbers of the form (4^k - 1)/3 or 2^k.
  • A160970 (program): Indices of square numbers that are also 18-gonal numbers.
  • A160973 (program): a(n) is the number of positive integers of the form (n-3k)/(2k+1), 1 <= k <= (n-1)/5.
  • A160993 (program): The number of ordered ways to achieve a score of n in American football.
  • A160997 (program): Antidiagonal sums of the Wythoff array A035513
  • A161003 (program): A list of the composite numbers divided by their largest prime factors.
  • A161007 (program): a(n+1) = 2*a(n) + 16*a(n-1), a(0)=0, a(1)=1.
  • A161011 (program): Decimal expansion of tan(1/2).
  • A161021 (program): Collatz (or 3x+1) trajectory starting at 703.
  • A161051 (program): Number of partitions of 2n into powers of two where every part appears at least twice.
  • A161116 (program): a(n) is the number of nontrivial positive divisors of 2n+3.
  • A161120 (program): Number of cycles with entries of opposite parities in all fixed-point-free involutions of {1,2,…,2n}.
  • A161122 (program): Number of cycles with entries of the same parity in all fixed-point-free involutions of {1,2,…,2n}.
  • A161124 (program): Number of inversions in all fixed-point-free involutions of {1,2,…,2n}.
  • A161125 (program): Number of descents in all involutions of {1,2,…,n}.
  • A161128 (program): a(n) = n!*(1/1 + 1/2 + … + 1/n) - (1! + 2! + … + n!).
  • A161129 (program): Triangle read by rows: T(n,k) is the number of non-derangements of {1,2,…,n} for which the difference between the largest and smallest fixed points is k (n>=1; 0 <= k <= n-1).
  • A161130 (program): Sum of the differences between the largest and the smallest fixed points over all non-derangement permutations of {1,2,…,n}.
  • A161131 (program): Number of permutations of {1,2,…,n} that have no odd fixed points.
  • A161132 (program): Number of permutations of {1,2,…,n} that have no even fixed points.
  • A161149 (program): a(n) = (2*n)!*(2*n+1)!/n! = n!*A000909(n), n=0,1…
  • A161150 (program): a(n) = (largest odd divisor of n)*(largest power of 2 dividing (n+1)).
  • A161151 (program): a(n) = (largest odd divisor of (n+1))*(largest power of 2 dividing n).
  • A161152 (program): Positive integers n such that {the number of (non-leading) 0’s in the binary representation of n} is coprime to n.
  • A161153 (program): Positive integers that are coprime to their number of digits in binary representation.
  • A161154 (program): Positive integers n such that both {the number of (non-leading) 0’s in the binary representation of n} is coprime to n and {the number of 1’s in the binary representation of n} is coprime to n.
  • A161158 (program): a(n) = A003696(n+1)/A001353(n+1).
  • A161159 (program): a(n) = A003739(n)/(5*A001906(n)*A006238(n)).
  • A161163 (program): Indices of the isolated primes in the prime sequence, if indices are odd.
  • A161165 (program): The n-th twin prime plus the n-th isolated prime.
  • A161168 (program): a(n) = 2^n + 4^n.
  • A161175 (program): Triangle read by rows, modified Thue-Morse sequence (A010060 with offset 1): change 0 to 2, else 1.
  • A161176 (program): a(n) = 4n^2 - 10n + 107.
  • A161178 (program): Sum of the double factorials of the digits of n.
  • A161179 (program): A double interspersion, R(n,k), by antidiagonals.
  • A161182 (program): Successive differences between positions of squares in list of nonprimes.
  • A161187 (program): Let S = A089237\{0} = union of primes and nonzero squares; sequence gives indices of squares.
  • A161188 (program): Let S = A089237\{0} = union of primes and nonzero squares; sequence gives indices of primes.
  • A161199 (program): Numerators in expansion of (1-x)^(-5/2).
  • A161200 (program): Numerators in expansion of (1-x)^(3/2).
  • A161201 (program): Numerators in expansion of (1-x)^(-7/2)
  • A161202 (program): Numerators in expansion of (1-x)^(5/2)
  • A161203 (program): n-th square plus n-th squarefree number.
  • A161204 (program): a(0)=2. a(n+1) = 2*a(n) + period 4: repeat -5,1,3,1.
  • A161205 (program): Triangle read by rows in which row n lists 2n-1 followed by 2n numbers 2n.
  • A161219 (program): a(n) = (1/n) * Sum_{d|n} phi(n/d)*2^(d+1).
  • A161220 (program): The n-th member of a twin prime pair minus 2*n.
  • A161221 (program): Consider necklaces with n beads, each black or white, where the n segments of cord between the beads are each colored red or green; a(n) is the number of different necklaces under the action of the dihedral group D_{2n}.
  • A161225 (program): a(n) = number of distinct integers that can be constructed by removing one or more 0’s from the binary representation of n, and concatenating while leaving the remaining digits in their same order.
  • A161226 (program): a(0)=0. a(n) = the smallest integer of the form k^j, j>=2, such that a(n) >= a(n-1) + n.
  • A161321 (program): Decimal expansion of (sqrt(35)-5)/10.
  • A161325 (program): Partial sums of A160414.
  • A161339 (program): Partial sums of A161205.
  • A161342 (program): Number of “ON” cubic cells at n-th stage in simple 3-dimensional cellular automaton: a(n) = A160428(n)/8.
  • A161343 (program): a(n) = 7^A000120(n).
  • A161344 (program): Numbers k with A033676(k)=2, where A033676 is the largest divisor <= sqrt(k).
  • A161345 (program): Numbers k whose largest divisor <= sqrt(k) is 3.
  • A161346 (program): a(n) = A161345(n)/3.
  • A161351 (program): a(n) = n + sum_of_digits(n) + product_of_digits(n).
  • A161365 (program): a(n) = 3/2 + 5*n - 5*(-1)^n/2.
  • A161367 (program): Primes such that p(n)-p(n-1)+1 is not prime
  • A161370 (program): a(n) = 2*A010844(n) + 1.
  • A161380 (program): Triangle read by rows: T(n,k) = 2*k*T(n-1,n-1) + 1 (n >= 0, 0 <= k <= n), with T(0,0) = 1.
  • A161381 (program): Triangle read by rows: T(n,k) = n!*2^k/(n-k)! (n >= 0, 0 <= k <= n).
  • A161382 (program): (0,1)-sequence where n-th run has length n^2.
  • A161385 (program): (1,2)-sequence where n-th run has length n^2.
  • A161400 (program): Positive integers that are palindromes (of even length) in binary, each made by concatenating two identical binary palindromes.
  • A161411 (program): First differences of A160410.
  • A161415 (program): First differences of A160414.
  • A161416 (program): Partial sums of A056737.
  • A161418 (program): Number of triangles in the Y-toothpick structure after n rounds.
  • A161422 (program): a(n) = A161418(n)/6.
  • A161424 (program): Numbers k whose largest divisor <= sqrt(k) equals 4.
  • A161425 (program): a(n) = A161424(n)/2.
  • A161426 (program): Y-toothpick sequence starting at the outside corner of an infinite triangle-shaped polygon as the sieve of A160120 after 2^k rounds.
  • A161427 (program): First differences of A161426.
  • A161428 (program): a(n) = A161424(n)/4.
  • A161434 (program): Number of 6-compositions.
  • A161435 (program): Number of reduced words of length n in the Weyl group A_3 (or D_3).
  • A161436 (program): Number of reduced words of length n in the Weyl group A_4.
  • A161440 (program): Numbers m such that A160700(m) = 0.
  • A161441 (program): Numbers n such that A160700(n) = 1.
  • A161442 (program): Numbers n such that A160700(n) = 2.
  • A161443 (program): Numbers m such that A160700(m) = 3.
  • A161444 (program): Numbers n such that A160700(n) = 4.
  • A161445 (program): Numbers n such that A160700(n) = 5.
  • A161446 (program): Numbers n such that A160700(n) = 6.
  • A161447 (program): Numbers n such that A160700(n) = 7.
  • A161448 (program): Numbers n such that A160700(n) = 8.
  • A161449 (program): Numbers n such that A160700(n) = 9.
  • A161450 (program): Numbers n such that A160700(n) = 10.
  • A161451 (program): Numbers n such that A160700(n) = 11.
  • A161452 (program): Numbers m such that A160700(m) = 12.
  • A161453 (program): Numbers n such that A160700(n) = 13.
  • A161454 (program): Numbers n such that A160700(n) = 14.
  • A161455 (program): Numbers n such that A160700(n) = 15.
  • A161462 (program): Final digit of the sum of all the integers from n to 2*n-1.
  • A161463 (program): Sum of all primes from n-th prime to (2*n-1)-th prime.
  • A161464 (program): Sum of all digits of primes from n-th prime to (2*n-1)-th prime.
  • A161474 (program): Triple factorials n!!!: a(n) = n*a(n-3).
  • A161480 (program): Decimal expansion of (129 +44*sqrt(2))/113.
  • A161484 (program): Decimal expansion of (187 + 78*sqrt(2))/151.
  • A161488 (program): Decimal expansion of (209+60*sqrt(2))/191.
  • A161495 (program): Expansion of x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4).
  • A161498 (program): Expansion of x*(1-x)*(1+x)/(1-13*x+36*x^2-13*x^3+x^4).
  • A161504 (program): Primes congruent to {1, 2, 10, 11, 19, 20} mod 21.
  • A161511 (program): Number of 1…0 pairs in the binary representation of 2n.
  • A161513 (program): Number of reduced words of length n in the Weyl group A_20.
  • A161517 (program): Sum of remainders of c mod k where k = 1, 2, 3, …, c and c is the n-th composite number.
  • A161518 (program): Number of reduced words of length n in the Weyl group A_21.
  • A161521 (program): Number of reduced words of length n in the Weyl group A_22.
  • A161522 (program): prime(n)*( prime(n)-n ).
  • A161523 (program): Number of reduced words of length n in the Weyl group A_23.
  • A161524 (program): Number of reduced words of length n in the Weyl group A_24.
  • A161525 (program): Number of reduced words of length n in the Weyl group A_25.
  • A161526 (program): Number of reduced words of length n in the Weyl group A_26.
  • A161527 (program): Numerators of cumulative sums of rational sequence A038110(k)/A038111(k).
  • A161528 (program): Expansion of the q-series Sum_{n >= 0} (-1)^nq^(n(n+1)/2)(1-q)(1-q^2)…(1-q^n)/((1-q^(n+1))(1-q^(n+2))…(1-q^(2n+1))).
  • A161530 (program): Number of reduced words of length n in the Weyl group A_27.
  • A161532 (program): a(n) = 2n^2 + 8n + 1.
  • A161537 (program): a(n) = n-th composite + n.
  • A161538 (program): Numbers n such that composite (n) + n is a prime, where composite (n) denotes the n-th composite number.
  • A161539 (program): Numbers n such that composite (n) + n is a composite, where composite (n) denotes the n-th composite number.
  • A161540 (program): Primes which are the sum of a smaller n and its composite(n) subscript. A002808 + a(n) (= prime)
  • A161541 (program): Composite which are the sum of a smaller n and its composite(n) subscript A002808 + a(n) (= composite)
  • A161542 (program): m-th composite composite(m) is included iff composite(m) + m is prime.
  • A161543 (program): The m-th composite number composite(m) is a term iff composite(m) + m is composite.
  • A161549 (program): a(n) = 2n^2 + 14n + 1.
  • A161550 (program): Largest prime <= n^2+n.
  • A161552 (program): E.g.f. satisfies: A(x,y) = exp(x*y*exp(x*A(x,y))).
  • A161556 (program): Exponential Riordan array [1 + (sqrt(Pi)/2)*x*exp(x^2/4)*erf(x/2), x].
  • A161560 (program): a(n) = floor(A000069(n)/2-1/2).
  • A161561 (program): The smallest number larger than n with digital sum equal to n.
  • A161565 (program): E.g.f. satisfies: A(x) = exp(x*exp(2*x*A(x))).
  • A161569 (program): Sum of first n nonprimes minus their indices.
  • A161570 (program): Sum of all numbers from n up to A018252(n).
  • A161571 (program): Number of reduced words of length n in the Weyl group A_28.
  • A161572 (program): Number of reduced words of length n in the Weyl group A_29.
  • A161573 (program): Number of reduced words of length n in the Weyl group A_30.
  • A161579 (program): Positions n such that A010060(n) = A010060(n+3).
  • A161580 (program): Positions n such that A010060(n) + A010060(n+3) = 1.
  • A161581 (program): a(n) = (3n)!/(n!(n+1)!(n+2)!).
  • A161582 (program): The list of the k values in the common solutions to the 2 equations 5*k+1=A^2, 9*k+1=B^2.
  • A161583 (program): The list of the k values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2.
  • A161584 (program): The list of the k values in the common solutions to the 2 equations 13*k+1=A^2, 17*k+1=B^2.
  • A161585 (program): The list of the k values in the common solutions to the 2 equations 7*k+1=A^2, 11*k+1=B^2.
  • A161586 (program): The list of the k values in the common solutions to the 2 equations 9*k+1=A^2, 13*k+1=B^2.
  • A161587 (program): a(n) = 13n^2 + 10n + 1.
  • A161588 (program): The list of the k values in the common solutions to the 2 equations 11*k+1=A^2, 15*k+1=B^2.
  • A161591 (program): The list of the B values in the common solutions to the 2 equations 13*k + 1 = A^2, 17*k + 1 = B^2.
  • A161595 (program): The list of the A values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2.
  • A161599 (program): The list of the B values in the common solutions to the 2 equations 15*k + 1 = A^2, 19*k + 1 = B^2.
  • A161601 (program): Positive integers k that are less than the value of the reversal of k’s representation in binary.
  • A161602 (program): Positive integers k that are greater than the value of the reversal of k’s binary representation.
  • A161603 (program): Odd elements of sequence A161602.
  • A161604 (program): A positive integer k is included if the value of (the reversal of k’s representation in binary) divides k.
  • A161606 (program): a(n) = gcd(A008472(n), A001222(n)).
  • A161607 (program): Positive integers k that are coprime to the value of the reversal of k’s representation in binary.
  • A161617 (program): 8*n^2+20*n+1.
  • A161621 (program): Numerator of (b(n+1) - b(n))/(b(n+2) - b(n)), where b(n) = A038107(n) is the number of primes up to n^2.
  • A161622 (program): Denominators of the ratios (in lowest terms) of numbers of primes in one square interval to that of the interval and its successor.
  • A161624 (program): Sum of all numbers from n to n-th prime.
  • A161625 (program): Sum of all numbers from 1 up to the final digit of prime(n).
  • A161626 (program): Sum of all numbers from 2*n-1 up to prime(n).
  • A161627 (program): Positions n such that A010060(n)=A010060(n+4).
  • A161628 (program): E.g.f.: A(x,y) = LambertW(x*y*exp(x))/(x*y*exp(x)), as a triangle of coefficients T(n,k) = [x^n*y^k/n! ] A(x,y), read by rows.
  • A161629 (program): E.g.f. satisfies: A(x) = exp( x*Catalan(x*A(x)) ), where Catalan(x) = (1-sqrt(1-4*x))/(2*x) is the g.f. of A000108.
  • A161630 (program): E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x)) ).
  • A161631 (program): E.g.f. satisfies: A(x) = 1 + x*exp(x*A(x)).
  • A161632 (program): E.g.f. satisfies: A(x) = (1 + x*exp(x*A(x)))^2.
  • A161633 (program): E.g.f. satisfies: A(x) = 1/(1 - x*exp(x*A(x))).
  • A161634 (program): G.f. satisfies: A(x) = 1/(1 - x*(1 + x*A(x))^2).
  • A161635 (program): E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x))^2 ).
  • A161636 (program): Number of reduced words of length n in the Weyl group A_31.
  • A161639 (program): Positions n such that A010060(n) = A010060(n+8).
  • A161640 (program): Number of reduced words of length n in the Weyl group A_32.
  • A161641 (program): Positions n such that A010060(n) + A010060(n+4) = 1.
  • A161642 (program): Triangle (by rows): T(n,k) = A007318(n,k) / A003989(n+1,k+1).
  • A161646 (program): Number of reduced words of length n in the Weyl group A_33.
  • A161647 (program): Number of reduced words of length n in the Weyl group A_34.
  • A161648 (program): Number of reduced words of length n in the Weyl group A_35.
  • A161649 (program): Number of reduced words of length n in the Weyl group A_36.
  • A161650 (program): Number of reduced words of length n in the Weyl group A_37.
  • A161651 (program): Number of reduced words of length n in the Weyl group A_38.
  • A161652 (program): Number of reduced words of length n in the Weyl group A_39.
  • A161653 (program): Number of reduced words of length n in the Weyl group A_40.
  • A161654 (program): a(n) = the largest multiple of {the number of divisors of n} that is <= n.
  • A161655 (program): a(n) = the smallest multiple of {the number of divisors of n} that is >= n.
  • A161656 (program): The largest multiple of {the sum of the distinct prime divisors of n} that is <=n.
  • A161657 (program): a(n) = the smallest multiple of {the sum of the distinct prime divisors of n} that is >= n.
  • A161658 (program): a(n) = the largest multiple of {the sum of the prime-factorization exponents of n} that is <= n.
  • A161659 (program): a(n) = the smallest multiple of {the sum of the prime-factorization exponents of n} that is >= n.
  • A161662 (program): Number of reduced words of length n in the Weyl group A_41.
  • A161663 (program): Number of reduced words of length n in the Weyl group A_42.
  • A161664 (program): a(n) = Sum_{i=1..n} (i - d(i)), where d(n) is the number of divisors of n (A000005).
  • A161668 (program): Number of reduced words of length n in the Weyl group A_43.
  • A161671 (program): a(n) = prime(n) - A141468(n).
  • A161673 (program): Positions n such that A010060(n) + A010060(n+8) = 1.
  • A161674 (program): Positions n such that A010060(n) + A010060(n+2) = 1.
  • A161679 (program): Number of reduced words of length n in the Weyl group A_44.
  • A161680 (program): a(n) = binomial(n,2): number of size-2 subsets of {0,1,…,n} that contain no consecutive integers.
  • A161690 (program): Number of reduced words of length n in the Weyl group A_45.
  • A161691 (program): Number of reduced words of length n in the Weyl group A_46.
  • A161692 (program): Number of reduced words of length n in the Weyl group A_47.
  • A161693 (program): Number of reduced words of length n in the Weyl group A_48.
  • A161694 (program): Number of reduced words of length n in the Weyl group A_49.
  • A161695 (program): Number of reduced words of length n in the Weyl group A_50.
  • A161696 (program): Number of reduced words of length n in the Weyl group B_3.
  • A161701 (program): a(n) = (n^5 - 5*n^4 + 5*n^3 + 5*n^2 + 114*n + 120)/120.
  • A161702 (program): a(n) = (-n^3 + 9n^2 - 5n + 3)/3.
  • A161703 (program): a(n) = (4*n^3 - 12*n^2 + 14*n + 3)/3.
  • A161704 (program): a(n) = (3*n^5 - 35*n^4 + 145*n^3 - 235*n^2 + 152*n + 30)/30.
  • A161705 (program): a(n) = 18*n + 1.
  • A161707 (program): a(n) = (4*n^3 - 9*n^2 + 11*n + 3)/3.
  • A161708 (program): a(n) = -n^3 + 7*n^2 - 5*n + 1.
  • A161709 (program): a(n) = 22*n + 1.
  • A161711 (program): a(n) = (-4*n^3 + 27*n^2 - 20*n + 3)/3.
  • A161712 (program): a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3.
  • A161713 (program): a(n) = (-n^5 + 15*n^4 - 65*n^3 + 125*n^2 - 34*n + 40)/40.
  • A161714 (program): a(n) = 28*n + 1.
  • A161718 (program): Expansion of (1+3*x^2)/(1+x)^2.
  • A161720 (program): a(n) = (prime(n) - 7)/2.
  • A161722 (program): Generalized Bernoulli numbers B_n(X,0), X a Dirichlet character modulus 8.
  • A161726 (program): a(n) = n^2 - 917*n + 9479.
  • A161727 (program): a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
  • A161728 (program): a(n) = ((3+sqrt(3))*(4+sqrt(3))^n-(3-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
  • A161729 (program): a(n) = ((4+sqrt(3))*(8+2*sqrt(3))^n-(4-sqrt(3))*(8-2*sqrt(3))^n)/(2*sqrt(3)).
  • A161731 (program): Expansion of (1-3*x)/(1-8*x+14*x^2).
  • A161734 (program): a(n) = ((2+sqrt(2))*(5+sqrt(2))^n+(2-sqrt(2))*(5-sqrt(2))^n)/4.
  • A161736 (program): Denominators of the column sums of the BG2 matrix.
  • A161737 (program): Numerators of the column sums of the BG2 matrix.
  • A161738 (program): Sequence related to the column sums of the BG2 matrix
  • A161744 (program): The subfactorial with index prime(n).
  • A161745 (program): The subfactorial with index Fibonacci(n).
  • A161750 (program): Numbers n such that the decimal digits of 123456789*n are all distinct.
  • A161753 (program): Squares of nonprime numbers A141468.
  • A161756 (program): The sum of all numbers from n up to A002808(n)-3.
  • A161757 (program): a(n) = (prime(n))^2 - (nonprime(n))^2.
  • A161758 (program): a(n)=n-p+1 where p is the maximal prime less than n-2.
  • A161762 (program): Sum of all numbers from Fibonacci(n-1) to Fibonacci(n).
  • A161763 (program): Product of the two primes with indices equal to the members of the n-th twin prime pair.
  • A161764 (program): a(n) is the largest multiple of {the number of 1’s in the binary representation of n} that is <= n.
  • A161765 (program): a(n) is the smallest multiple of {the number of 1’s in the binary representation of n} that is >= n.
  • A161769 (program): A positive integer n is included if the greatest common divisor of (the sum of the distinct primes dividing n) and (the sum of the exponents in the prime-factorization of n) is > 1.
  • A161770 (program): n 1’s followed by three 0’s.
  • A161777 (program): n-th nonprime*(n-th nonprime-1)/2
  • A161784 (program): Product of primes on successive square intervals.
  • A161788 (program): a(n) is the largest integer of the form 2^k - 1 that divides n.
  • A161789 (program): a(n) is the largest integer k such that 2^k - 1 divides n.
  • A161790 (program): The positive integer n is included if 1 is the largest integer of the form {2^k - 1} to divide n.
  • A161797 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3).
  • A161798 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^3)^2.
  • A161799 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^2)^3.
  • A161809 (program): G.f.: A(x) = exp( Sum_{n>=1} 3*A038500(n) * x^n/n ), where A038500 is the highest power of 3 dividing n.
  • A161811 (program): Difference between nonprime(n+2) and nonprime(n).
  • A161816 (program): Denominator of fraction in Redheffer type matrix.
  • A161823 (program): Among any n lines on the plane, there exists a pair at an angle not more than a(n)degrees.
  • A161824 (program): Numbers such that A010060(n) = A010060(n+6).
  • A161825 (program): a(n) is the GCD of n and {the number made by reversing the order of the digits of n written in binary}.
  • A161826 (program): Number of maximal vertex-independent sets in the hypergraph with nodes V = {1, 2, …, n} and “edges” consisting of the triples (X,Y,Z) with X<Y<Z and X+Y=Z.
  • A161827 (program): Complement of A006446.
  • A161828 (program): Number of rhombuses in the Y-toothpick structure of A160120 after n rounds.
  • A161830 (program): Y-toothpick triangle (see Comments lines for definition).
  • A161831 (program): First differences of A161830.
  • A161832 (program): a(n) = (A161830(n+1)-1)/2.
  • A161833 (program): First differences of A161832.
  • A161834 (program): a(n) = A161828(n)/3.
  • A161835 (program): Numbers k whose largest divisor <= sqrt(k) is 5.
  • A161836 (program): Number of concave-convex hexagons in the Y-toothpick structure of A160120 after n rounds.
  • A161838 (program): a(n) = A161836(n)/3.
  • A161839 (program): a(n) = A161835(n)/5.
  • A161840 (program): Number of noncentral divisors of n.
  • A161841 (program): Number of factors, with repetition, in all distinct pairs (a <= b) such that a*b = n.
  • A161842 (program): Partial sums of A161841.
  • A161843 (program): a(n) = n-th composite plus n-th nonprime.
  • A161844 (program): Product of the n-th composite by the n-th nonprime.
  • A161845 (program): a(n) = A002808(n)^A141468(n).
  • A161847 (program): Denominator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n).
  • A161849 (program): a(n) = A052369(n) mod A056608(n).
  • A161850 (program): Subsequence of A161986 consisting of all terms that are prime.
  • A161852 (program): Solutions to the simultaneous equations m(n)+1=a(n)^2 and 7*m(n)+1=b(n)^2.
  • A161859 (program): Number of reduced words of length n in the Weyl group B_13.
  • A161862 (program): Number of reduced words of length n in the Weyl group B_14.
  • A161865 (program): Numerators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor.
  • A161867 (program): Denominators of ratio of nonprimes in a square interval to that of nonprimes in that interval and its successor.
  • A161870 (program): Convolution square of A000219.
  • A161877 (program): Number of reduced words of length n in the Weyl group B_17.
  • A161878 (program): Number of reduced words of length n in the Weyl group B_18.
  • A161879 (program): Number of reduced words of length n in the Weyl group B_19.
  • A161880 (program): Number of reduced words of length n in the Weyl group B_20.
  • A161882 (program): Smallest k such that n^2 = a_1^2+…+a_k^2 and all a_i are positive integers less than n.
  • A161886 (program): Number of nonzero elements in the n X n Redheffer matrix.
  • A161891 (program): Primes p with the property that every non-solvable transitive permutation group of degree p is alternating or symmetric.
  • A161899 (program): Number of reduced words of length n in the Weyl group B_21.
  • A161900 (program): Number of reduced words of length n in the Weyl group B_22.
  • A161903 (program): Convert n into a sequence of binary digits, apply one step of the rule 110 cellular automaton, and interpret the results as a binary integer.
  • A161907 (program): Primes of the form n^3+n+91.
  • A161909 (program): Inverse binomial transform of A181586.
  • A161910 (program): Y-toothpick sequence starting at the corner of an infinite hexagon from which protrudes a half toothpick with an angle = Pi/6.
  • A161911 (program): a(n) is the n-th difference between consecutive primes minus the number of divisors of n.
  • A161912 (program): a(n) = A040976(n+1) - A006218(n).
  • A161913 (program): Numbers k such that A001223(k) <> A000005(k).
  • A161916 (program): The smallest k such that A010060(n+k)=A010060(n).
  • A161918 (program): Numbers n such that the sum of the divisors minus the sum of the prime factors (counted with multiplicity) is equal to n+1.
  • A161920 (program): a(n) = A161511(A004760(n)).
  • A161921 (program): The bisection A053445(2n+1).
  • A161930 (program): Number of reduced words of length n in the Weyl group B_23.
  • A161931 (program): Number of reduced words of length n in the Weyl group B_24.
  • A161932 (program): Number of reduced words of length n in the Weyl group B_25.
  • A161933 (program): Number of reduced words of length n in the Weyl group B_26.
  • A161935 (program): 28-gonal numbers: a(n) = n*(13*n - 12).
  • A161936 (program): The number of direct isometries that are derangements of the (n-1)-dimensional facets of an n-cube.
  • A161937 (program): The number of indirect isometries that are derangements of the (n-1)-dimensional facets of an n-cube.
  • A161938 (program): a(n) = ((3+sqrt(2))*(2+sqrt(2))^n + (3-sqrt(2))*(2-sqrt(2))^n)/2.
  • A161939 (program): a(n) = ((3+sqrt(2))*(4+sqrt(2))^n + (3-sqrt(2))*(4-sqrt(2))^n)/2.
  • A161940 (program): a(n) = ((3+sqrt(2))*(5+sqrt(2))^n + (3-sqrt(2))*(5-sqrt(2))^n)/2.
  • A161941 (program): a(n) = ((4+sqrt(2))*(2+sqrt(2))^n + (4-sqrt(2))*(2-sqrt(2))^n)/4.
  • A161942 (program): Odd part of sum of divisors of n.
  • A161944 (program): a(n) = ((4+sqrt(2))*(3+sqrt(2))^n + (4-sqrt(2))*(3-sqrt(2))^n)/4.
  • A161945 (program): Numbers n with property that three consecutive odd numbers {n,n+2,n+4} are all composite.
  • A161946 (program): Odd part of sum of unitary divisors of n.
  • A161947 (program): a(n) = ((4+sqrt(2))*(5+sqrt(2))^n + (4-sqrt(2))*(5-sqrt(2))^n)/4.
  • A161954 (program): Number of reduced words of length n in the Weyl group B_27.
  • A161956 (program): Number of reduced words of length n in the Weyl group B_28.
  • A161964 (program): Prime(n) raised to the nonprime(n)-th power.
  • A161969 (program): Expansion of f(q)^8 in powers of q where f() is a Ramanujan theta function.
  • A161972 (program): Number of reduced words of length n in the Weyl group B_29.
  • A161976 (program): Number of reduced words of length n in the Weyl group B_30.
  • A161977 (program): Number of reduced words of length n in the Weyl group B_31.
  • A161983 (program): Irregular triangle read by rows: the group of 2n + 1 integers starting at A014105(n).
  • A161984 (program): Table read by rows: the number n followed by the odd numbers from n(n-1)+1 to (n-1)(n+2)+1.
  • A161986 (program): a(n) = k+r where k is composite(n) and r is (largest prime divisor of k) mod (smallest prime divisor of k).
  • A161987 (program): Number of reduced words of length n in the Weyl group B_32.
  • A161988 (program): Number of reduced words of length n in the Weyl group B_33.
  • A161989 (program): Numbers having more than 2 or fewer than 2 ones in their binary representation.
  • A161991 (program): Number of reduced words of length n in the Weyl group B_34.
  • A161992 (program): Numbers which squared are a sum of 3 distinct nonzero squares.
  • A161996 (program): A (negated) characteristic function of twin composite odd numbers.
  • A161999 (program): For n even a(n) = a(n-1) + 10*a(n-2), for n odd a(n) = a(n-3) + 10 a(n-2); with a(1) = 0, a(2) = 1.
  • A162004 (program): Primes of the form n+(n+3)^3, n>=0.
  • A162022 (program): Smallest prime factor of n-th odd composite integers A071904.
  • A162023 (program): Exactly 10 consecutive odd integers starting with n are composite.
  • A162024 (program): Number of n X n binary arrays with rows and columns, considered as binary numbers, in nondecreasing order, and all but the outermost row or column zero.
  • A162142 (program): Numbers that are the cube of a product of two distinct primes (p^3*q^3).
  • A162143 (program): a(n) = A007304(n)^2.
  • A162144 (program): Products of cubes of 3 distinct primes.
  • A162147 (program): a(n) = n*(n+1)*(5*n + 4)/6.
  • A162148 (program): a(n) = n*(n+1)*(5*n+7)/6.
  • A162149 (program): Number of reduced words of length n in the Weyl group B_35.
  • A162150 (program): Number of reduced words of length n in the Weyl group B_36.
  • A162153 (program): Differences between the sum of consecutive composites and the prime that precedes them.
  • A162154 (program): Odd-indexed terms are the number of consecutive prime numbers until a composite, even-indexed terms are the number of consecutive composite numbers until a prime.
  • A162165 (program): Number of reduced words of length n in the Weyl group B_37.
  • A162166 (program): Number of reduced words of length n in the Weyl group B_38.
  • A162168 (program): Number of reduced words of length n in the Weyl group B_39.
  • A162169 (program): Exponential series expansion of (cos(x) - sin(x))*cosh(t*x) + sinh(t*x).
  • A162171 (program): Third column of A162170.
  • A162176 (program): Number of reduced words of length n in the Weyl group B_40.
  • A162177 (program): a(n) is the number of composite numbers that are smaller than A008578(n).
  • A162178 (program): Number of reduced words of length n in the Weyl group B_41.
  • A162179 (program): Number of reduced words of length n in the Weyl group B_42.
  • A162181 (program): Number of reduced words of length n in the Weyl group B_43.
  • A162182 (program): Number of reduced words of length n in the Weyl group B_44.
  • A162183 (program): Number of reduced words of length n in the Weyl group B_45.
  • A162186 (program): Number of reduced words of length n in the Weyl group B_46.
  • A162188 (program): Numbers k such that A001223(k) > A000005(k).
  • A162189 (program): Numbers k such that A001223(k) < A000005(k).
  • A162191 (program): Number of reduced words of length n in the Weyl group B_47.
  • A162193 (program): Number of reduced words of length n in the Weyl group B_48.
  • A162194 (program): Sum of divisors of nonprime number A018252(n).
  • A162195 (program): Sum of proper divisors of n-th nonprime number A018252(n).
  • A162196 (program): Sum of proper divisors minus the number of proper divisors of nonprime number A018252(n).
  • A162200 (program): Number on the positive y axis of the n-th horizontal component in the graph of the “mountain path” function for prime numbers.
  • A162201 (program): First differences of A162200.
  • A162204 (program): Number of reduced words of length n in the Weyl group B_49.
  • A162205 (program): Number of reduced words of length n in the Weyl group B_50.
  • A162213 (program): a(n) = the smallest positive multiple of n with exactly n digits when written in binary.
  • A162214 (program): a(n) = the largest positive multiple of n with exactly n digits when written in binary.
  • A162245 (program): Triangle T(n,m) = 6*m*n + 3*m + 3*n + 1 read by rows.
  • A162246 (program): Swinging polynomials, coefficients read by rows.
  • A162251 (program): Sum of digits of product of previous terms, with a(1) = 2.
  • A162254 (program): a(n) = (2*n^3 + 5*n^2 + n)/2.
  • A162255 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 2.
  • A162256 (program): a(n) = (2*n^3 + 5*n^2 - 3*n)/2.
  • A162257 (program): a(n) = (2*n^3 + 5*n^2 - 11*n)/2.
  • A162258 (program): a(n) = (2*n^3 + 5*n^2 - 9*n)/2.
  • A162259 (program): a(n) = (2*n^3 + 5*n^2 - 17*n)/2.
  • A162260 (program): a(n) = (n^3 + 4*n^2 - n)/2.
  • A162261 (program): a(n) = (2*n^3 + 5*n^2 - 7*n)/2.
  • A162262 (program): a(n) = (2*n^3 + 5*n^2 - 13*n)/2.
  • A162263 (program): a(n) = (2*n^3 + 5*n^2 + 11*n)/2.
  • A162264 (program): a(n) = (2*n^3 + 5*n^2 + 7*n)/2.
  • A162265 (program): a(n) = (2*n^3 + 5*n^2 - 5*n)/2.
  • A162266 (program): a(n) = (2*n^3 + 5*n^2 + 21*n)/2.
  • A162267 (program): a(n) = (2*n^3 + 5*n^2 + 5*n)/2.
  • A162268 (program): a(n) = ((5+sqrt(2))*(1+sqrt(2))^n + (5-sqrt(2))*(1-sqrt(2))^n)/2.
  • A162269 (program): a(n) = ((5+sqrt(2))*(2+sqrt(2))^n + (5-sqrt(2))*(2-sqrt(2))^n)/2.
  • A162270 (program): a(n) = ((5+sqrt(2))*(3+sqrt(2))^n + (5-sqrt(2))*(3-sqrt(2))^n)/2.
  • A162271 (program): a(n) = ((5+sqrt(2))*(4+sqrt(2))^n + (5-sqrt(2))*(4-sqrt(2))^n)/2.
  • A162272 (program): a(n) = ((1+sqrt(3))*(5+sqrt(3))^n + (1-sqrt(3))*(5-sqrt(3))^n)/2.
  • A162273 (program): a(n) = ((2+sqrt(3))*(3+sqrt(3))^n + (2-sqrt(3))*(3-sqrt(3))^n)/2.
  • A162274 (program): a(n) = ((2+sqrt(3))*(4+sqrt(3))^n + (2-sqrt(3))*(4-sqrt(3))^n)/2.
  • A162275 (program): a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 2, a(1) = 13.
  • A162285 (program): Periodic length 8 sequence [1, -1, -1, 1, -1, 1, 1, -1, …].
  • A162289 (program): a(n) = 1 if n is relatively prime to 30 else 0.
  • A162291 (program): Primes of the form n^3-n^2-1.
  • A162292 (program): Primes of the form k^3-k^2+1, k>0.
  • A162293 (program): Numbers k such that k^2*(k-1)-1 is prime.
  • A162294 (program): Numbers k such that k^3-k^2-k-1 is prime.
  • A162295 (program): Primes of the form k^3-k^2-k-1.
  • A162296 (program): Sum of divisors of n that have a square factor.
  • A162307 (program): Primes of the form k*(k+2)/3 - 2, k > 0.
  • A162308 (program): Number of twin primes A001097 smaller than the non-twin prime A007510(n).
  • A162309 (program): a(n) is the number of isolated primes up to the smaller component of the n-th twin prime pair.
  • A162310 (program): The count of lesser-twin-primes smaller than the n-th isolated prime.
  • A162312 (program): Triangular array, inverse of 2*P - I, where P is Pascal’s triangle and I is the identity matrix.
  • A162313 (program): Triangular array P*(2*I - P^2)^-1, where P is Pascal’s triangle A007318 and I is the identity matrix.
  • A162314 (program): Row sums of A162313.
  • A162315 (program): Triangular array 2*P - P^-1, where P is Pascal’s triangle A007318.
  • A162316 (program): a(n) = 5n^2 + 20n + 1.
  • A162317 (program): A positive integer k is included if |d(k+1) - d(k)| is a prime, where d(k) is the number of divisors of k.
  • A162318 (program): A positive integer n is included if |d(n+1)-d(n)| = 2, where d(n) is the number of divisors of n.
  • A162319 (program): Array read by antidiagonals: a(n,m) = the number of digits of m is when written in base n. The top row is the number of digits for each m in base 1.
  • A162320 (program): Array read by antidiagonals: a(n,m) = the number of digits of m when written in base n. The top row is the number of digits for each m in base 2.
  • A162322 (program): Take sequence A000005 (where A000005(n) = the number of divisors of n). To get {a(k)}, replace each run of multiple occurrences of the same integer in sequence A000005 with just one occurrence of that integer, such that a(n) never equals a(n+1).
  • A162325 (program): a(n) = the largest divisor of n such that this and every smaller divisor of n are all coprime to each other.
  • A162326 (program): Let a(0) = a(1) = 1, and n*a(n) = 2*(-7+5*n)*a(n-1) + 9*(2-n)*a(n-2) for n >= 2.
  • A162329 (program): Sum of all parts of the partitions of n, minus sigma(n).
  • A162330 (program): Blocks of 4 numbers of the form 2k, 2k-1, 2k, 2k+1, k=1,2,3,4,…
  • A162336 (program): Primes p of the form p = r+(r+1)/2 (where r is a prime number).
  • A162337 (program): Primes p such that floor(p/3) is prime.
  • A162338 (program): Primes q such that q = floor(p/3) for some prime p.
  • A162339 (program): Numbers A161912 such that a(n)<>a(n+1).
  • A162340 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton whose virtual skeleton is a polyedge as the graph of the “mountain path” function for prime numbers.
  • A162341 (program): a(n) = number of grid points P(x,y) that are covered by a polyedge as the graph of the “mountain path” function for prime numbers, where x=n and y=0..oo.
  • A162342 (program): Partial sums of A162200.
  • A162345 (program): Length of n-th edge in the graph of the zig-zag function for prime numbers.
  • A162349 (program): First differences of A160412.
  • A162351 (program): Values x of pairs (x,y) that generate the graph of the “mountain path” function for prime numbers.
  • A162356 (program): a(n) = 8*a(n-1)-14*a(n-2) for n>1; a(0) = 2; a(1) = 9.
  • A162361 (program): Central prime factor of A014612(n).
  • A162364 (program): Number of reduced words of length n in the Weyl group D_22.
  • A162365 (program): Number of reduced words of length n in the Weyl group D_23.
  • A162366 (program): Number of reduced words of length n in the Weyl group D_24.
  • A162367 (program): Number of reduced words of length n in the Weyl group D_25.
  • A162368 (program): Number of reduced words of length n in the Weyl group D_26.
  • A162369 (program): Number of reduced words of length n in the Weyl group D_27.
  • A162370 (program): Number of reduced words of length n in the Weyl group D_28.
  • A162376 (program): Number of reduced words of length n in the Weyl group D_29.
  • A162377 (program): Number of reduced words of length n in the Weyl group D_30.
  • A162378 (program): Number of reduced words of length n in the Weyl group D_31.
  • A162379 (program): Number of reduced words of length n in the Weyl group D_32.
  • A162380 (program): Number of reduced words of length n in the Weyl group D_33.
  • A162381 (program): Number of reduced words of length n in the Weyl group D_34.
  • A162382 (program): Triangle, read by rows, defined by: T(n,k) = 1/((k+1)n-1) binomial((k+1)n-1,n) for n,k>0.
  • A162384 (program): Number of reduced words of length n in the Weyl group D_35.
  • A162388 (program): Number of reduced words of length n in the Weyl group D_36.
  • A162389 (program): Number of reduced words of length n in the Weyl group D_37.
  • A162392 (program): Number of reduced words of length n in the Weyl group D_38.
  • A162395 (program): a(n) = -(-1)^n * n^2.
  • A162396 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 2.
  • A162397 (program): a(n) = n * Kronecker(-3, n).
  • A162399 (program): Number of reduced words of length n in the Weyl group D_39.
  • A162402 (program): Number of reduced words of length n in the Weyl group D_40.
  • A162410 (program): Numbers n such that 10*n + 3 and 10*n + 7 are prime.
  • A162411 (program): Number of reduced words of length n in the Weyl group D_42.
  • A162412 (program): Number of reduced words of length n in the Weyl group D_43.
  • A162413 (program): Number of reduced words of length n in the Weyl group D_44.
  • A162415 (program): L.g.f.: Sum_{n>=1} a(n)*x^n/n = log( Sum_{n>=0} x^(2^n-1) ).
  • A162417 (program): Find max {primes such that p < n^2, n = 2,3,…}, then the gap g(n) between that prime and its successor. This sequence is the sequence of differences {2n - g(n)}.
  • A162418 (program): Number of reduced words of length n in the Weyl group D_45.
  • A162419 (program): a(n) = sigma(n)*|A002129(n)| where sigma(n) = A000203(n).
  • A162420 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)*|A002129(n)|*x^n/n ).
  • A162421 (program): Numbers whose prime factors all have the same number of digits.
  • A162422 (program): Numbers with at least 2 different numbers of digits among their prime factors.
  • A162425 (program): Row 2 of table A162424.
  • A162431 (program): Row 2 of table A162430.
  • A162432 (program): Row 3 of table A162430.
  • A162433 (program): Row 4 of table A162430.
  • A162436 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
  • A162437 (program): a(1)=1, a(2)=2. Take terms a(n-1) and a(n-2), then convert to binary. Concatenate them, with either binary a(n-1) on the left and a(n-2) on the right, or with a(n-1) on the right and a(n-2) on the left such that the value of the resulting binary number is minimized. a(n) = the decimal equivalent of the resulting binary number.
  • A162438 (program): a(1)=1, a(2)=2. Take terms a(n-1) and a(n-2), then convert to binary. Concatenate them, with either binary a(n-1) on the left and a(n-2) on the right, or with a(n-1) on the right and a(n-2) on the left such that the value of the resulting binary number is maximized. a(n) = the decimal equivalent of the resulting binary number.
  • A162439 (program): Write down the binary representation of n. Partition the string which is this binary representation by placing a ‘+’ just left of every 1. Add the resulting base 2 numbers. a(n) = decimal equivalent of this sum.
  • A162440 (program): The pg(n) sequence that is associated with the Eta triangle A160464.
  • A162441 (program): Numerators of the column sums of the EG1 matrix coefficients
  • A162442 (program): Denominators of the column sums of the EG1 matrix coefficients
  • A162445 (program): A sequence related to the Beta function
  • A162452 (program): Number of reduced words of length n in the Weyl group D_46.
  • A162456 (program): Number of reduced words of length n in the Weyl group D_47.
  • A162459 (program): A002321*A000079.
  • A162460 (program): First differences of A161762.
  • A162461 (program): Number of reduced words of length n in the Weyl group D_48.
  • A162462 (program): Sum of all numbers from n to sigma(n).
  • A162466 (program): a(n) = 12*a(n-2) for n > 2; a(1) = 1, a(2) = 8.
  • A162469 (program): Number of reduced words of length n in the Weyl group D_49.
  • A162473 (program): Write n in binary n times and concatenate (see example). a(n) is the decimal equivalent.
  • A162475 (program): Expansion of c(x/(1-x)^4), c(x) the g.f. of A000108.
  • A162476 (program): Expansion of (1/(1-x))*c(x/(1-x)^4), c(x) the g.f. of A000108.
  • A162477 (program): Expansion of (1/(1-x)^2)*c(x/(1-x)^4), c(x) the g.f. of A000108.
  • A162478 (program): Expansion of 1/sqrt(1-4x/(1-x)^4).
  • A162479 (program): Expansion of 1/((1-x)*sqrt(1-4x/(1-x)^4)).
  • A162480 (program): Expansion of 1/((1-x)^2*sqrt(1-4x/(1-x)^4)).
  • A162481 (program): Expansion of (1/(1-x)^3)*c(x/(1-x)^3), c(x) the g.f. of A000108.
  • A162483 (program): a(n) is the number of perfect matchings of an edge-labeled 2 X (2n+1) Mobius grid graph.
  • A162484 (program): a(1) = 2, a(2) = 8; a(n) = 2 a(n - 1) + a(n - 2) - 4*(n mod 2).
  • A162485 (program): a(1)=4, a(2)=6; for n > 2, a(n) = 2*a(n-1) + a(n-2) - 4*((n-1) mod 2).
  • A162492 (program): Number of reduced words of length n in the Weyl group D_50.
  • A162495 (program): Number of reduced words of length n in the icosahedral reflection group [3,5] of order 120.
  • A162500 (program): Expansion of the polynomial (1-x^3) * (1-x^6) * (1-x^9) / (1-x)^3.
  • A162508 (program): A binomial sum of powers related to the Bernoulli numbers, triangular array, read by rows.
  • A162509 (program): Row sums of the absolute values of a triangular array related to the Bernoulli numbers.
  • A162510 (program): Dirichlet inverse of A076479.
  • A162511 (program): Multiplicative function with a(p^e) = (-1)^(e-1).
  • A162512 (program): Dirichlet inverse of A162511.
  • A162514 (program): Triangle of coefficients of polynomials defined by the Binet form P(n,x) = U^n + L^n, where U = (x + d)/2, L = (x - d)/2, d = (4 + x^2)^(1/2). Decreasing powers of x.
  • A162515 (program): Triangle of coefficients of polynomials defined by Binet form: P(n,x) = (U^n - L^n)/d, where U = (x + d)/2, L = (x - d)/2, d = sqrt(x^2 + 4).
  • A162520 (program): Pairs (i,j) of positive integers where j<10.
  • A162526 (program): Numbers k whose largest divisor <= sqrt(k) equals 6.
  • A162527 (program): Numbers k whose largest divisor <= sqrt(k) equals 7.
  • A162528 (program): Numbers k whose largest divisor <= sqrt(k) equals 8.
  • A162529 (program): Numbers k whose largest divisor <= sqrt(k) equals 9.
  • A162530 (program): Numbers k whose largest divisor <= sqrt(k) equals 10.
  • A162531 (program): Numbers k whose largest divisor <= sqrt(k) is 11.
  • A162532 (program): Numbers k such that their largest divisor <= sqrt(k) equals 12.
  • A162533 (program): a(n) = Sum_{k=0..n} binomial(n,2k)*A002426(k).
  • A162535 (program): A positive integer k is included if every length of the runs of 0’s and 1’s in the binary representation of k is coprime to k.
  • A162540 (program): a(n) = (2*n+1)*(2*n+3)*(2*n+5)/3.
  • A162547 (program): Somos-4 variant: if n!=4k+1, then a(n) = (4*a(n-1)*a(n-3) - 4*a(n-2)^2) / a(n-4), otherwise a(n) = 0, with a(-2) = a(-1) = a(0) = 1.
  • A162550 (program): 2n repeated C_n times, where C_n = A000108(n) is a Catalan number.
  • A162551 (program): a(n) = 2 * C(2*n,n-1).
  • A162552 (program): L.g.f.: log( Sum_{n>=1} x^(n^2) ), the log of the characteristic function of the squares.
  • A162557 (program): a(n) = ((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)/6.
  • A162558 (program): a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/6.
  • A162559 (program): a(n) = ((4+sqrt(3))*(1+sqrt(3))^n + (4-sqrt(3))*(1-sqrt(3))^n)/2.
  • A162560 (program): a(n) = (4+sqrt(3))*(3+sqrt(3))^n + (4-sqrt(3))*(3-sqrt(3))^n.
  • A162561 (program): a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2.
  • A162562 (program): a(n) = ((5+sqrt(3))*(1+sqrt(3))^n + (5-sqrt(3))*(1-sqrt(3))^n)/2.
  • A162563 (program): a(n) = ((5+sqrt(3))*(2+sqrt(3))^n + (5-sqrt(3))*(2-sqrt(3))^n)/2.
  • A162581 (program): G.f.: A(x) = exp( 2*Sum_{n>=1} A006519(n)^2 * x^n/n ), where A006519(n) = highest power of 2 dividing n.
  • A162589 (program): G.f.: A(x) = exp( Sum_{n>=1} 2^n*A006519(n) * x^n/n ), where A006519(n) = highest power of 2 dividing n.
  • A162590 (program): Polynomials with e.g.f. exp(x*t)/csch(t), triangle of coefficients read by rows.
  • A162593 (program): Differences of squares: T(n,n) = n^2, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.
  • A162594 (program): Differences of cubes: T(n,n) = n^3, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.
  • A162607 (program): a(n) = n*(n^2 - 4*n + 5)/2.
  • A162608 (program): Triangle read by rows in which row n lists n+1 terms, starting with n!, such that the difference between successive terms is also equal to n!.
  • A162609 (program): Triangle read by rows in which row n lists n terms, starting with 1, with gaps = n-2 between successive terms.
  • A162610 (program): Triangle read by rows in which row n lists n terms, starting with 2n-1, with gaps = n-1 between successive terms.
  • A162611 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^2 - 1.
  • A162612 (program): Triangle read by rows in which row n lists n terms, starting with n^2+n-1, with gaps = n^2-1 between successive terms.
  • A162613 (program): Triangle read by rows in which row n lists n terms, starting with n, with gaps = n^2-1 between successive terms.
  • A162614 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^3 - 1.
  • A162615 (program): Triangle read by rows in which row n lists n terms, starting with n, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).
  • A162616 (program): Triangle read by rows in which row n lists n terms, starting with n^3 + n - 1, such that the difference between successive terms is equal to n^3 - 1 = A068601(n).
  • A162618 (program): Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A008578(n-1) - n + 1.
  • A162619 (program): Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A014689(n) = A000040(n)-n.
  • A162620 (program): Triangle read by rows in which row n lists n consecutive natural numbers A000027, starting with A000040(n)-n+1.
  • A162622 (program): Triangle read by rows in which row n lists n+1 terms, starting with n, such that the difference between successive terms is equal to n^4 - 1.
  • A162623 (program): Triangle read by rows in which row n lists n terms, starting with n, such that the difference between successive terms is equal to n^4 - 1 = A123865(n).
  • A162624 (program): Triangle read by rows in which row n lists n terms, starting with n^4 + n - 1, such that the difference between successive terms is equal to n^4 - 1 = A123865(n).
  • A162626 (program): If 0 <= n <= 3 then a(n) = n(n+1)(n+2)/3, if n >= 4 then a(n) = n(n^2+5)/3.
  • A162630 (program): Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
  • A162641 (program): Number of even exponents in canonical prime factorization of n.
  • A162642 (program): Number of odd exponents in the canonical prime factorization of n.
  • A162643 (program): Numbers whose number of divisors is not a power of 2.
  • A162644 (program): Numbers m such that A162511(m) = +1.
  • A162645 (program): Numbers m such that A162511(m) = -1.
  • A162648 (program): Locations of patterns 1001 or 0110 in the Thue-Morse sequence A010060.
  • A162652 (program): Primes p such that there are positive integers m and n and a prime q such that p = m^2+m-q = n^2+n+q.
  • A162660 (program): Triangle read by rows, the coefficients of the complementary Swiss-Knife polynomials.
  • A162664 (program): a(n) = sigma(n) + tau(n)^2.
  • A162666 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A162667 (program): a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A162668 (program): a(n) = n*(n+1)*(n+2)*(n+3)/3.
  • A162669 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/5.
  • A162670 (program): Expansion of x/(1 - x - 100*x^2).
  • A162671 (program): Generalized Fibonacci numbers
  • A162672 (program): Lunar product 19*n.
  • A162673 (program): Number of different fixed (possibly) disconnected trominoes bounded (not necessarily tightly) by an n*n square
  • A162674 (program): Number of different fixed (possibly) disconnected tetrominoes bounded (not necessarily tightly) by an n X n square.
  • A162677 (program): Number of different fixed (possibly) disconnected polyominoes (of any area) bounded (not necessarily tightly) by an n*n square.
  • A162691 (program): Strictly positive numbers n such that 24*n/(24+n) is an integer.
  • A162693 (program): Strictly positive numbers n such that 30*n/(30+n) are integers.
  • A162694 (program): Strictly positive numbers n such that 36*n/(36+n) are integers.
  • A162695 (program): E.g.f. satisfies: A(x) = exp( x*A(x) * exp(x*A(x)) ).
  • A162698 (program): Numbers n such that the incidence matrix of the grid n X n has -1 as eigenvalue.
  • A162699 (program): Odd numbers not divisible by 7.
  • A162720 (program): A014499 represented in binary.
  • A162723 (program): a(n) = 9 a (n-1)-26 a(n-2) +24 a(n-3) (n >= 3) with a(0) =a(1)=1, a(2)=2.
  • A162725 (program): a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) (n >= 3) with a(0) = a(1) = 1, a(2) = 2.
  • A162728 (program): G.f.: x/(1-x) = Sum_{n>=1} a(n)*log(1+x^n)/n.
  • A162729 (program): a(n) = 5^n*(5^n-1)/2.
  • A162731 (program): a(n) is the n-th triprime (A014612) minus its central prime factor.
  • A162734 (program): An alternating sum of all numbers from the n-th up to the (n+1)st isolated prime.
  • A162735 (program): An alternating sum of all numbers from prime(n) to prime(n+1).
  • A162738 (program): a(n) is the smallest positive multiple of {the n-th composite} that is greater than the n-th prime.
  • A162740 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
  • A162741 (program): Fibonacci-Pascal triangle; same as Pascal triangle, but beginning another Pascal triangle to the right of each row starting at row 2.
  • A162746 (program): Row sums of Fibonacci-Pascal triangle A162745.
  • A162747 (program): A factorial-Pascal matrix.
  • A162748 (program): Row sums of factorial-Pascal matrix A162747.
  • A162750 (program): The a(n)-th (odd) binary palindrome is A162749(n).
  • A162751 (program): Write down in binary the n-th positive (odd) integer that is a palindrome in base 2. Take only the leftmost half of the digits (including the middle digit if there are an odd number of digits). a(n) is the decimal equivalent of the result.
  • A162752 (program): a(1)=2^2. a(n) = the smallest p^q, p and q primes, that is > a(n-1), and where the base (p) of a(n) is the exponent (q) of a(n-1).
  • A162753 (program): a(0)=a(1)=2; a(n) is the smallest prime such that a(n-1)^a(n) > a(n-2)^a(n-1).
  • A162757 (program): a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A162758 (program): a(n) = 14*a(n-1)-46*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
  • A162759 (program): a(n) = 16*a(n-1)-61*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
  • A162761 (program): Minimal total number of floors an elevator must move to transport n people initially waiting at floors i = 1, …, n to their destination floors n-i+1 (= n, …, 1), when the elevator can hold at most one person at a time and starts at floor 1, and no passenger may get off the elevator before reaching his/her destination.
  • A162762 (program): Minimal number of floors an elevator must move to transport n passengers initially waiting at floors i = 1, …, n to their destinations, floor n+1-i (= n, …, 1), if the elevator can transport at most C = 2 persons at a time and starts at floor 1, and no one may get off the elevator before reaching their destination.
  • A162764 (program): Minimal total number of floors that an elevator must move to get n persons waiting, respectively, on floors i = 1, 2, …, n, to their destination floors n-i+1 (= n, n-1, …, 1), if the elevator can hold up to C = 4 persons at a time and starts at floor 1, and no passenger may get off the elevator before reaching his destination.
  • A162766 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 4, a(2) = 3.
  • A162769 (program): a(n) = ((1+sqrt(5))*(4+sqrt(5))^n + (1-sqrt(5))*(4-sqrt(5))^n)/2.
  • A162770 (program): a(n) = ((2+sqrt(5))*(1+sqrt(5))^n + (2-sqrt(5))*(1-sqrt(5))^n)/2.
  • A162771 (program): a(n) = ((2+sqrt(5))*(3+sqrt(5))^n + (2-sqrt(5))*(3-sqrt(5))^n)/2.
  • A162772 (program): a(n) = ((2+sqrt(5))*(4+sqrt(5))^n + (2-sqrt(5))*(4-sqrt(5))^n)/2.
  • A162773 (program): a(n) = ((2+sqrt(5))*(5+sqrt(5))^n + (2-sqrt(5))*(5-sqrt(5))^n)/2.
  • A162775 (program): a(n) = A141042(n+1)/2.
  • A162776 (program): a(n) = A161828(n)*2/3.
  • A162777 (program): a(n) = A153003(n) - A153006(n).
  • A162779 (program): Rows of A162777 when written as a triangle converge to this sequence.
  • A162784 (program): a(n) = (A048883(n)+1)/2.
  • A162786 (program): a(n) = A162526(n)/6.
  • A162787 (program): a(n) = A162527(n)/7.
  • A162788 (program): a(n) = A162528(n)/8.
  • A162789 (program): a(n) = A162529(n)/9.
  • A162790 (program): a(n) = A162530(n)/10.
  • A162792 (program): a(n) = A162532(n)/12.
  • A162793 (program): Number of toothpicks added to the toothpick structure A139250 at the n-th odd round.
  • A162794 (program): Number of toothpicks added to the toothpick structure A139250 at the n-th even round.
  • A162795 (program): Total number of toothpicks in the toothpick structure A139250 that are parallel to the initial toothpick, after n odd rounds.
  • A162796 (program): Number of toothpicks in the toothpick structure A139250 that are orthogonal to the initial toothpick after n even rounds.
  • A162797 (program): a(n) = difference between the number of toothpicks of A139250 that are orthogonal to the initial toothpick and the number of toothpicks that are parallel to the initial toothpick, after n even rounds.
  • A162800 (program): a(n) = n-th grid point that is covered by the zig-zag function for prime numbers such that the grid point is a vertex in the graph of the function.
  • A162801 (program): Bisection of A162800.
  • A162802 (program): Bisection of A162800.
  • A162813 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 5, a(2) = 3.
  • A162814 (program): a(n) = 6*a(n-1)-6*a(n-2) for n > 1; a(0) = 5, a(1) = 18.
  • A162815 (program): a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 5, a(1) = 23.
  • A162816 (program): a(n) = 12*a(n-1)-33*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
  • A162817 (program): Positive numbers n such that 40*n/(40+n) are integers.
  • A162818 (program): Strictly positive numbers n such that (42*n)/(42+n) is an integer.
  • A162819 (program): Positive numbers n such that 48*n/(48+n) are integers.
  • A162820 (program): Positive numbers n such that 60*n/(60+n) are integers.
  • A162826 (program): Positive numbers n such that 2*60*n/(60+n) are integers.
  • A162845 (program): Sum of digits of binomial(3n,n).
  • A162852 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 3, a(2) = -1.
  • A162857 (program): Primes of form 4p-1, p a prime.
  • A162860 (program): Numbers k such that k^2+4*k+1 is prime.
  • A162867 (program): a(n) is the sum of all possible pairs of the first n primes.
  • A162880 (program): Numbers k such that tau(sigma(k)) is not equal to sigma(tau(k)).
  • A162886 (program): Even numbers in an alternating 1-based sum up to some odd nonprime.
  • A162888 (program): An alternating sum of the first n nonprimes.
  • A162897 (program): a(1)=a(2)=2. a(n) = the smallest integer >= 2 such that a(n-1)^a(n) > a(n-2)^a(n-1).
  • A162898 (program): a(n) = A162897(n)^A162897(n+1).
  • A162899 (program): Partial sums of [A052938(n)^2].
  • A162902 (program): An increasing sequence of alternatingly squarefree and nonsquarefree numbers.
  • A162903 (program): a(n) = A162531(n)/11.
  • A162904 (program): Primes 2 less than a tetrahedral number.
  • A162905 (program): Primes of form p^2-6, p also a prime.
  • A162906 (program): a(n) = n - A081707(n).
  • A162907 (program): Sum of all numbers from tau(n) to sigma(n).
  • A162909 (program): Numerators of Bird tree fractions.
  • A162910 (program): Denominators of Bird tree fractions.
  • A162911 (program): Numerators of drib tree fractions, where drib is the bit-reversal permutation tree of the Bird tree.
  • A162912 (program): Denominators of drib tree fractions, where drib is the bit-reversal permutation tree of the Bird tree.
  • A162917 (program): Numbers n which are not in A161983.
  • A162918 (program): Natural numbers n such that there are s and w satisfying 0 < s < w and 2*s + 5*w = n.
  • A162920 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
  • A162921 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
  • A162932 (program): a(n) = A053445(n-2) - A053445(n-4).
  • A162934 (program): Shift sequence A162932 twice then subtract from the original sequence.
  • A162938 (program): A 2-based alternate sum over the numbers from 0 to the n-th nonprime.
  • A162939 (program): A 1-based alternate sum over the numbers from 0 to prime(n).
  • A162940 (program): a(n) = binomial(n+1,2)*6^2.
  • A162942 (program): a(n) = binomial(n + 1, 2)*7^2.
  • A162943 (program): a(n) = 2^(1-A002321(n)).
  • A162944 (program): A162943(A010766).
  • A162947 (program): Numbers k such that the product of all divisors of k equals k^3.
  • A162956 (program): a(0) = 0, a(1) = 1; a(2^i + j) = 3a(j) + a(j + 1) for 0 <= j < 2^i.
  • A162959 (program): The pairs (x,y) such that (x^2 + y^2)/(x*y + 1) is a perfect square, i.e., 4.
  • A162962 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
  • A162963 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 2, a(2) = 5.
  • A162964 (program): a(n) = sigma(sigma(sigma(sigma(sigma(n))))).
  • A162966 (program): Union of 1 and nonsquarefree numbers (A013929).
  • A162968 (program): Number of pairs of consecutive non-fixed points in all permutations of {1,2,…,n}.
  • A162970 (program): Number of 2-cycles in all involutions of {1,2,…,n}.
  • A162973 (program): Number of cycles in all derangement permutations of {1,2,…,n}.
  • A162988 (program): n appears A008578(n) times.
  • A162990 (program): Triangle of polynomial coefficients related to 3F2([1,n+1,n+1],[n+2,n+2],z).
  • A162991 (program): The first right hand column of triangle A162990
  • A162992 (program): The second right hand column of triangle A162990
  • A162993 (program): The second left hand column of triangle A162990
  • A162994 (program): The third left hand column of triangle A162990
  • A162995 (program): A scaled version of triangle A162990.
  • A163000 (program): Count of integers x in [0,n] satisfying A000120(x) + A000120(n-x) = A000120(n) + 1.
  • A163037 (program): Number of nX2 binary arrays with all 1s connected and a path of 1s from left column to right column
  • A163057 (program): An alternating sum from the n-th odd number up to the n-th odd prime.
  • A163058 (program): Primes in A163057.
  • A163059 (program): An alternating sum from 4*n-3 up to the smaller of the n-th twin primes.
  • A163061 (program): Sum of the first n primes plus the first n nonprimes.
  • A163062 (program): a(n) = ((3+sqrt(5))*(1+sqrt(5))^n + (3-sqrt(5))*(1-sqrt(5))^n)/2.
  • A163063 (program): Lucas(3n+2) = Fibonacci(3n+1) + Fibonacci(3n+3).
  • A163064 (program): a(n) = ((3+sqrt(5))*(4+sqrt(5))^n + (3-sqrt(5))*(4-sqrt(5))^n)/2.
  • A163065 (program): a(n) = ((3+sqrt(5))*(5+sqrt(5))^n + (3-sqrt(5))*(5-sqrt(5))^n)/2.
  • A163066 (program): a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 2, a(1) = 17.
  • A163067 (program): a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 2, a(1) = 19.
  • A163068 (program): a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 2, a(1) = 21.
  • A163069 (program): a(n) = ((4+sqrt(5))*(1+sqrt(5))^n + (4-sqrt(5))*(1-sqrt(5))^n)/2.
  • A163070 (program): a(n) = ((4+sqrt(5))*(2+sqrt(5))^n + (4-sqrt(5))*(2-sqrt(5))^n)/2.
  • A163071 (program): a(n) = ((4+sqrt(5))*(3+sqrt(5))^n + (4-sqrt(5))*(3-sqrt(5))^n)/2.
  • A163072 (program): a(n) = ((4+sqrt(5))*(5+sqrt(5))^n + (4-sqrt(5))*(5-sqrt(5))^n)/2.
  • A163073 (program): a(n) = ((5+sqrt(5))*(4+sqrt(5))^n + (5-sqrt(5))*(4-sqrt(5))^n)/10.
  • A163085 (program): Product of first n swinging factorials (A056040).
  • A163086 (program): Product of first n terms of A163085.
  • A163094 (program): a(n) = A162796(n)/2.
  • A163095 (program): a(n) = A000788(n)^2.
  • A163102 (program): a(n) = n^2*(n+1)^2/2.
  • A163103 (program): Decimal expansion of the astronomical unit (measured in meters).
  • A163105 (program): a(n) = tau(sigma(tau(n))), where tau = number of divisors of n (A000005), and sigma = sum of divisors of n (A000203).
  • A163106 (program): a(n) = sigma(sigma(tau(n))), where tau = number of divisors and sigma = sum of divisors.
  • A163107 (program): a(n) = tau(tau(sigma(n))), where tau = A000005, the number of divisors, and sigma = A000203, the sum of divisors of n.
  • A163108 (program): a(n) = sigma(tau(sigma(n))).
  • A163109 (program): a(n) = phi(tau(n)).
  • A163114 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 3, a(2) = 5.
  • A163116 (program): Partial sums of A161671.
  • A163125 (program): Sum of digits of the n-th Self-number (or Colombian number), A003052(n).
  • A163126 (program): a(1)=1. a(n) = the number of integers k, 1 <= k <= n-1, where a(k) is coprime to n-k.
  • A163128 (program): a(n) is the n-th self-number minus n.
  • A163139 (program): First differences of A163128.
  • A163141 (program): a(n) = 5*a(n-2) for n > 2; a(1) = 4, a(2) = 5.
  • A163146 (program): a(n) = 12*a(n-1)-31*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A163147 (program): a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
  • A163148 (program): a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
  • A163162 (program): Numbers k such that sigma(k) is not prime.
  • A163163 (program): a(n) = sigma(n) + tau(n) - n.
  • A163164 (program): Positions n such that A163163(n) is not prime.
  • A163165 (program): a(n) = 20*a(n-1) - 96*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163166 (program): a(n) = 20*a(n-1)-95*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163169 (program): a(n) = minimal number of consecutive integers required which when summed make n.
  • A163173 (program): The n-th product of three primes divided by its central prime factor.
  • A163176 (program): The n-th Minkowski number divided by the n-th factorial: a(n) = A053657(n)/n!.
  • A163180 (program): a(n) = tau(n) + Sum_{k=1..n} (n mod k).
  • A163190 (program): a(n) = Sum_{k=0..n} C(n,k)*sigma(n,k) for n>0 with a(0)=1.
  • A163191 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n,k)*sigma(n,k) for n>0 with a(0)=1.
  • A163192 (program): a(n) = 20*a(n-1)-93*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163194 (program): a(n) = F(n)^2 * L(n+1)^2 * F(n-1) * L(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
  • A163195 (program): a(n) = (1/4)*F(n)^2 * L(n+1)^2 * F(n-1) * L(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
  • A163196 (program): a(n) = L(n)^2 * F(n+1)^2 * L(n-1) * F(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
  • A163197 (program): a(n) = (1/4)* L(n)^2 * F(n+1)^2 * L(n-1) * F(n+2), where F(n) and L(n) are the Fibonacci and Lucas numbers, respectively.
  • A163198 (program): Sum of the cubes of the first n even-indexed Fibonacci numbers.
  • A163199 (program): Sum of the cubes of the first n even-indexed Fibonacci numbers, minus 1.
  • A163200 (program): Sum of the cubes of the first n odd-indexed Fibonacci numbers.
  • A163201 (program): Alternating sum of the cubes of the first n even-indexed Fibonacci numbers.
  • A163202 (program): Alternating sum of the cubes of the first n odd-indexed Fibonacci numbers.
  • A163206 (program): a(n) = 20*a(n-1) - 92*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163210 (program): Swinging Wilson quotients ((p-1)$ +(-1)^floor((p+2)/2))/p, p prime. Here ‘$’ denotes the swinging factorial function (A056040).
  • A163213 (program): Swinging Wilson remainders ((p-1)$ + (-1)^floor((p+2)/2))/p mod p, p prime. Here ‘$’ denotes the swinging factorial function (A056040).
  • A163227 (program): Fibonacci-accumulation sequence.
  • A163241 (program): Simple self-inverse permutation: Write n in base 4, then replace each digit ‘2’ with ‘3’ and vice versa, then convert back to decimal.
  • A163242 (program): Row sums of A163233 and A163235.
  • A163248 (program): Sum of the n-th composite number plus the number of composite numbers less than the n-th noncomposite number.
  • A163249 (program): Sum of prime(n) and number of numbers from this set less than n-th nonprime number (A018252(n)).
  • A163250 (program): The number of nonisomorphic complete simple games with n voters of two different types.
  • A163253 (program): An interspersion: the order array of the odd-numbered columns of the double interspersion at A161179.
  • A163254 (program): Array of the nonsquares; the columns satisfy c(n)=c(n-1)+c(n-2)-c(n-3)+1.
  • A163255 (program): An interspersion: the order array of A163254.
  • A163256 (program): Fractal sequence of the interspersion A163253.
  • A163259 (program): Triangle T(n,k) read by rows: mod(A007318(n,k+1);A007318(n,k)).
  • A163260 (program): Row sums of A163259.
  • A163267 (program): Partial sums of A118977.
  • A163270 (program): First column in matrix inverse of (A047999*A154990).
  • A163271 (program): Numerators of fractions in a ‘zero-transform’ approximation of sqrt(2) by means of a(n) = (a(n-1) + c)/(a(n-1) + 1) with c=2 and a(1)=0.
  • A163274 (program): a(n) = n^4*(n+1)^2/2.
  • A163275 (program): a(n) = n^5*(n+1)^2/2.
  • A163276 (program): a(n) = n^6*(n+1)^2/2.
  • A163277 (program): a(n) = n^7*(n+1)^2/2.
  • A163279 (program): a(n) = (n^6 + 2n^5 + 2n^4 + n^3 + 2n)/2.
  • A163282 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^2 and ending with n^3, such that difference between successive terms is equal to n^2 - n.
  • A163283 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^3 and ending with n^4, such that the difference between successive terms is equal to n^3 - n^2.
  • A163284 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^4 and ending with n^5, such that the difference between successive terms is equal to n^4 - n^3.
  • A163285 (program): Triangle read by rows in which row n lists n+1 terms, starting with n^5 and ending with n^6, such that the difference between successive terms is equal to n^5 - n^4.
  • A163291 (program): Number of digits of n-th prime written in base 4.
  • A163292 (program): a(n) = n-th prime minus (number of digits of n-th prime written in base 4).
  • A163293 (program): a(n) = n-th prime minus (number of bits in binary expansion of n-th prime).
  • A163295 (program): Binary order of n plus number of partitions of n-1.
  • A163296 (program): Absolute value of the Sum_{x=0..A141468(n)} x*(-1)^x.
  • A163297 (program): a(n) = sum of divisors of n plus length of the binary expansion of n.
  • A163298 (program): Sum of divisors of n minus binary order of n.
  • A163299 (program): a(n) = (the number of divisors of n)^(the binary order of n).
  • A163300 (program): Zero together with the even nonprimes.
  • A163301 (program): a(n) = Sum_{x=n-th even nonprime..n-th odd nonprime} -x*(-1)^x.
  • A163303 (program): a(n) = n^3 + 73*n^2 + n + 67.
  • A163305 (program): Numerators of fractions in the approximation of the square root of 5 satisfying: a(n)= (a(n-1)+ c)/(a(n-1)+1); with c=5 and a(1)=0. Also product of the powers of two and five times the Fibonacci numbers.
  • A163306 (program): a(n) = 12*a(n-1) - 31*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A163307 (program): a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
  • A163308 (program): a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
  • A163309 (program): a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163310 (program): a(n) = 20*a(n-1) - 95*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A163314 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
  • A163322 (program): The 3rd Hermite Polynomial evaluated at n: H_3(n) = 8*n^3 - 12*n.
  • A163323 (program): The 4th Hermite Polynomial evaluated at n: H_4(n) = 16n^4 - 48n^2 + 12.
  • A163325 (program): Pick digits at the even distance from the least significant end of the ternary expansion of n, then convert back to decimal.
  • A163326 (program): Pick digits at the odd distance from the least significant end of the ternary expansion of n, then convert back to decimal.
  • A163327 (program): Self-inverse permutation of integers: swap the odd- and even-positioned digits in the ternary expansion of n, then convert back to decimal.
  • A163343 (program): Central diagonal of A163334 and A163336.
  • A163344 (program): Central diagonal of A163334 and A163336 divided by 4.
  • A163346 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A163348 (program): a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A163349 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
  • A163350 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
  • A163366 (program): a(n) = (-1)^floor((prime(n)+2)/2) mod prime(n).
  • A163367 (program): a(n) = phi(tau(sigma(n))).
  • A163368 (program): a(n) = phi(sigma(tau(n))).
  • A163369 (program): a(n) = sigma(sigma(phi(n))).
  • A163370 (program): a(n) = phi(sigma(phi(n))).
  • A163371 (program): a(n) = tau(phi(sigma(n)))
  • A163372 (program): a(n) = sigma(phi(sigma(n))).
  • A163373 (program): a(n) = phi(phi(sigma(n))).
  • A163374 (program): a(n) = tau(tau(phi(n))).
  • A163375 (program): a(n) = sigma(tau(phi(n))).
  • A163376 (program): a(n) = phi(tau(phi(n))).
  • A163377 (program): a(n) = tau(phi(tau(n))).
  • A163378 (program): a(n) = sigma(phi(tau(n))).
  • A163379 (program): a(n) = phi(phi(tau(n))).
  • A163383 (program): a(n) = (n-1)*2^n - 1.
  • A163385 (program): Primes p such that 3(p-3)-1 and 3(p-3)+1 are twin primes.
  • A163388 (program): Primes p such that 6*(p-6) is an average of a twin prime pair.
  • A163394 (program): The odd part of Minkowski(n)/n!
  • A163395 (program): a(n) = (n-th even nonprime)^(n-th even number).
  • A163399 (program): a(n)=(the binary order of n)^sigma(n)
  • A163400 (program): Number of bits in binary expansion of n-th nonprime.
  • A163403 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 2.
  • A163405 (program): a(n) = (n-th nonprime) + (number of bits in binary expansion of n-th nonprime).
  • A163406 (program): Numbers n which are not in A163405
  • A163407 (program): Sum of semiprime divisors of n with repetition.
  • A163408 (program): Positive integers n such that A008475(n) is composite.
  • A163409 (program): Subsequence of composite terms of A008475.
  • A163412 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n>1, a(0)=1, a(1)=10.
  • A163413 (program): a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A163414 (program): a(n) = 16*a(n-1) - 62*a(n-2) for n>1, a(0)=1, a(1)=12.
  • A163415 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n>1, a(0)=1, a(1)=13.
  • A163416 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n>1, a(0)=1, a(1)=14.
  • A163417 (program): a(n) = 2^(floor((n-1)/2)) - n*(n-1)/2.
  • A163418 (program): Primes of the form ((p-1)/2)^2+((p+1)/2), where p is prime.
  • A163419 (program): Primes of the form ((p+1)/2)^2+((p-1)/2), where p is prime.
  • A163420 (program): Primes p such that p+(p^2-1)/4 is also prime.
  • A163433 (program): Number of different fixed (possibly) disconnected trominoes bounded tightly by an n X n square.
  • A163434 (program): Number of different fixed (possibly) disconnected tetrominoes bounded tightly by an n X n square.
  • A163435 (program): Number of different fixed (possibly) disconnected pentominoes bounded tightly by an n X n square.
  • A163444 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
  • A163445 (program): a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
  • A163446 (program): a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163447 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A163448 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
  • A163449 (program): A007582 written in base 2.
  • A163450 (program): A028403 written in base 2.
  • A163455 (program): a(n) = binomial(5*n-1,n).
  • A163456 (program): a(n) = binomial(5*n,n)/5.
  • A163458 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A163459 (program): a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
  • A163460 (program): a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
  • A163461 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A163462 (program): a(n) = 20*a(n-1) - 98*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A163464 (program): Cumulative sum of a repeated shift-and-add operation on the base-7 representation of prime(n).
  • A163466 (program): A permutation of two copies of the prime sequence, one moved to nonprime indices, the other to prime indices.
  • A163467 (program): a(n) = floor(p/2) * floor(floor(p/2)/2) * floor(floor(floor(p/2)/2)/2) * … * 1, where p=prime(n).
  • A163468 (program): Indices k such that half of the k-th nonprime nonnegative integer is prime.
  • A163470 (program): a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 3, a(1) = 15.
  • A163471 (program): a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 3, a(1) = 18.
  • A163472 (program): a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 3, a(1) = 21.
  • A163473 (program): a(n) = 14*a(n-1) - 46*a(n-2) for n > 1; a(0) = 3, a(1) = 24.
  • A163474 (program): a(n) = 16*a(n-1) - 61*a(n-2) for n > 1; a(0) = 3, a(1) = 27.
  • A163475 (program): a(n) = 18*a(n-1) - 78*a(n-2) for n > 1; a(0) = 3, a(1) = 30.
  • A163476 (program): a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 3, a(1) = 33.
  • A163478 (program): Row sums of A163233 and A163235 divided by 3.
  • A163480 (program): Row 0 of A163334 (column 0 of A163336).
  • A163481 (program): Row 0 of A163336 (column 0 of A163334).
  • A163489 (program): Indices n such that composite(n)/3 is prime.
  • A163491 (program): A fractal sequence (if we delete the first occurrence of n we get the sequence itself).
  • A163493 (program): Number of binary strings of length n which have the same number of 00 and 01 substrings.
  • A163495 (program): a(0)=0, a(1)=1, a(2)=2. For n >= 3, a(n) = a(n-1) - min(a(n-2), a(n-3)).
  • A163504 (program): a(n) = abs(n-th prime minus n-th odd nonprime).
  • A163505 (program): a(n) = n-th odd nonprime mod n-th odd number.
  • A163506 (program): a(n) = n-th odd nonprime * n-th odd number.
  • A163508 (program): The sum of the prime factors (with repetition) of the sum of 2 successive primes.
  • A163509 (program): Take n written in binary. Replace the leftmost run of 1’s with just a single 1. a(n) is the decimal equivalent of the result.
  • A163511 (program): a(0)=1. a(n) = p(A000120(n)) * product{m=1 to A000120(n)} p(m)^A163510(n,m), where p(m) is the m-th prime.
  • A163515 (program): If n-th composite is the product of k1-th prime, k2-th prime, …, kr-th prime then set a(n) = k1 + k2 + … + kr.
  • A163517 (program): If m-th composite is the product of k1-th prime, k2-th prime,..,kr-th prime and prime=k1+k2+..+kr then set a(n)=m.
  • A163520 (program): a(n) is the least integer x such that n < x and the product n*x is divisible by an integer y where n < y < x.
  • A163522 (program): a(1)=2; for n>1, a(n) = sum of digits of a(n-1)^2.
  • A163523 (program): a(n) = tau(n) + omega(n).
  • A163528 (program): The X-coordinate of the n-th point in the Peano curve A163334.
  • A163529 (program): The Y-coordinate of the n-th point in the Peano curve A163334.
  • A163532 (program): The change in X-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.
  • A163533 (program): The change in Y-coordinate when moving from the n-1:th to the n-th point in the Peano curve A163334.
  • A163550 (program): a(1)=a(2)=a(3)=1. a(n) = reverseDigits(a(n-1)+a(n-2)+a(n-3)) for n>=4.
  • A163553 (program): First differences of A024816.
  • A163563 (program): n occurs 1+a(n) times starting with a(1)=1.
  • A163569 (program): Numbers of the form p^3*q^2*r where p, q and r are three distinct primes.
  • A163575 (program): Remove all trailing bits equal to (n mod 2) in binary representation of n.
  • A163577 (program): Count of indices x in [0,n] that satisfy the equation A000120(x) + A000120(n-x) = A000120(n) + 2.
  • A163581 (program): Number of zeros of sin(x) in integer intervals starting with (0,1).
  • A163584 (program): Number of singularities of tan(x) in integer intervals starting with (0,1).
  • A163588 (program): Primes which are within 1 of a square number.
  • A163590 (program): Odd part of the swinging factorial A056040.
  • A163595 (program): Numbers k such that prime(k) == 5 (mod 9).
  • A163602 (program): First differences of A161753.
  • A163603 (program): Numbers k such that prime(k) == 5 (mod 7).
  • A163604 (program): a(n) = ((3+2*sqrt(2))*(4+sqrt(2))^n + (3-2*sqrt(2))*(4-sqrt(2))^n)/2.
  • A163605 (program): a(n) = ((3+2*sqrt(2))*(5+sqrt(2))^n + (3-2*sqrt(2))*(5-sqrt(2))^n)/2.
  • A163606 (program): a(n) = ((3 + 2*sqrt(2))*(3 + sqrt(2))^n + (3 - 2*sqrt(2))*(3 - sqrt(2))^n)/2.
  • A163607 (program): a(n) = ((5 + 2*sqrt(2))*(1 + sqrt(2))^n + (5 - 2*sqrt(2))*(1 - sqrt(2))^n)/2.
  • A163608 (program): a(n) = ((5 + 2*sqrt(2))*(2 + sqrt(2))^n + (5 - 2*sqrt(2))*(2 - sqrt(2))^n)/2.
  • A163609 (program): a(n) = ((5 + 2*sqrt(2))*(3 + sqrt(2))^n + (5 - 2*sqrt(2))*(3 - sqrt(2))^n)/2.
  • A163610 (program): a(n) = ((5 + 2*sqrt(2))*(4 + sqrt(2))^n + (5 - 2*sqrt(2))*(4 - sqrt(2))^n)/2.
  • A163611 (program): a(n) = ((5 + 2*sqrt(2))*(5 + sqrt(2))^n + (5 - 2*sqrt(2))*(5 - sqrt(2))^n)/2.
  • A163613 (program): a(n) = ((1 + 3*sqrt(2))*(2 + sqrt(2))^n + (1 - 3*sqrt(2))*(2 - sqrt(2))^n)/2.
  • A163614 (program): a(n) = ((1 + 3*sqrt(2))*(3 + sqrt(2))^n + (1 - 3*sqrt(2))*(3 - sqrt(2))^n)/2.
  • A163615 (program): a(n) = ((1 + 3*sqrt(2))*(4 + sqrt(2))^n + (1 - 3*sqrt(2))*(4 - sqrt(2))^n)/2.
  • A163616 (program): a(n) = ((1 + 3*sqrt(2))*(5 + sqrt(2))^n + (1 - 3*sqrt(2))*(5 - sqrt(2))^n)/2.
  • A163617 (program): a(2*n) = 2*a(n), a(2*n + 1) = 2*a(n) + 2 + (-1)^n, for all n in Z.
  • A163618 (program): a(2*n) = 2 * a(n). a(2*n - 1) = 2 * a(n) - 2 - (-1)^n, for all n in Z.
  • A163621 (program): Square array read by antidiagonals: Write n and m in binary with n on the left. Concatenate. a(n,m) is the decimal equivalent of the result.
  • A163623 (program): Primes of the form 120*k + 1.
  • A163624 (program): Numbers n such that 120n+1 is prime.
  • A163626 (program): Triangle read by rows: The n-th derivative of the logistic function written in terms of y, where y = 1/(1 + exp(-x)).
  • A163627 (program): Numbers n such that 42n + 5 is prime.
  • A163628 (program): Integers such that the two adjacent integers are a prime and three times a prime.
  • A163631 (program): Partial sums of the odd nonprimes, A014076.
  • A163632 (program): Triple and reverse digits.
  • A163634 (program): a(n) = (p*(p+4)+1)/2 where (p,p+4) are the n-th cousin prime pair.
  • A163636 (program): The sum of all odd numbers from 2n-1 up to the n-th odd nonprime.
  • A163637 (program): The sum of all odd numbers from 2n-1 to prime(n).
  • A163639 (program): The count of odd numbers from prime(n) up to the n-th odd nonprime, A014076(n).
  • A163640 (program): The radical of the swinging factorial A056040 for odd indices.
  • A163641 (program): The radical of the swinging factorial A056040.
  • A163644 (program): Product of primes which do not exceed n and do not divide the swinging factorial n$ (A056040).
  • A163650 (program): Subswing - the inverse binomial transform of the swinging factorial (A056040).
  • A163652 (program): Triangle read by rows where T(n,m)=2*m*n + m + n + 6.
  • A163654 (program): The sum of the n-th and (n+1)st isolated prime.
  • A163655 (program): a(n) = n*(2*n^2 + 5*n + 13)/2.
  • A163656 (program): Arithmetic mean of the n-th and (n+1)st twin prime member A001097.
  • A163657 (program): Triangle T(m,n) = 2*m*n + m + n + 8 read by rows.
  • A163658 (program): G.f.: A(x) = exp( Sum_{n>=1} A163659(n)^2*x^n/n ), where x*exp(Sum_{n>=1} A163659(n)*x^n/n) = S(x) is the g.f. of Stern’s diatomic series (A002487).
  • A163659 (program): L.g.f.: Sum_{n>=1} a(n)*x^n/n = log(S(x)/x) where S(x) is the g.f. of Stern’s diatomic series (A002487).
  • A163661 (program): a(n) = n*(2*n^2 + 5*n + 17)/2.
  • A163662 (program): A020988 written in base 2.
  • A163663 (program): a(0) = 0 and A059153(n-1) written in base 2 otherwise.
  • A163664 (program): a(n) = 10^(2*n) + 10^n.
  • A163671 (program): Expansion of Sum_( x^k / (1 - x^(k^2)) ).
  • A163672 (program): Triangle T(n,m) = 2mn + m + n + 7 read by rows.
  • A163673 (program): a(n) = n*(2*n^2 + 5*n + 15)/2.
  • A163674 (program): Triangle T(n,m) = 2*m*n + m + n + 9 read by rows.
  • A163675 (program): a(n) = n*(2*n^2 + 5*n + 19)/2.
  • A163676 (program): Triangle T(n,m) = 4mn + 2m + 2n - 1 read by rows.
  • A163683 (program): a(n) = n^2*(2*n + 5).
  • A163685 (program): Number of nX2 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent
  • A163695 (program): Number of n X 2 binary arrays with all 1s connected, a path of 1s from top row to lower right corner, and no 1 having more than two 1s adjacent.
  • A163704 (program): Number of n X 2 binary arrays with all 1s connected, a path of 1s from left column to lower right corner, and no 1 having more than two 1s adjacent.
  • A163714 (program): Number of n X 2 binary arrays with all 1s connected, a path of 1s from top row to bottom row, and no 1 having more than two 1s adjacent.
  • A163723 (program): Number of nX2 binary arrays with all 1s connected, a path of 1s from left column to right column, and no 1 having more than two 1s adjacent
  • A163733 (program): Number of n X 2 binary arrays with all 1’s connected, all corners 1, and no 1 having more than two 1’s adjacent.
  • A163746 (program): Expansion of (theta_3(q)^2 + 3 * theta_3(q^3)^2) / 4 - 1 in powers of q.
  • A163747 (program): Expansion of e.g.f. 2*exp(x)*(1-exp(x))/(1+exp(2*x)).
  • A163750 (program): a(n) = (n-th even nonprime mod n-th prime).
  • A163751 (program): a(n) = n-th even nonprime minus n-th nonprime.
  • A163755 (program): a(0)=1. For n>=1, write n in binary. Let b(n,m) be the length of the m-th run of 0’s or 1’s, reading right to left. Then a(n) = product{m=1 to M} p(m)^b(n,m), where p(m) is the m-th prime, and M is the number of runs of 0’s and 1’s in binary n.
  • A163756 (program): 14 times triangular numbers.
  • A163758 (program): a(n) = 9*n*(n+1).
  • A163761 (program): a(n) = 10*n*(n+1).
  • A163765 (program): Inverse binomial transform of A048775 (assuming offset zero in both sequences)
  • A163767 (program): a(n) = tau_{n}(n) = number of ordered n-factorizations of n.
  • A163769 (program): Primes p such that 2*p+3 is not prime.
  • A163770 (program): Triangle read by rows interpolating the swinging sub-factorial (A163650) with the swinging factorial (A056040).
  • A163771 (program): Triangle interpolating the swinging factorial (A056040) restricted to even indices with its binomial inverse. Same as interpolating the central trinomial coefficients (A002426) with the central binomial coefficients (A000984).
  • A163772 (program): Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial inverse.
  • A163773 (program): Row sums of the swinging derangement triangle (A163770).
  • A163774 (program): Row sums of the central coefficients triangle (A163771).
  • A163775 (program): Row sums of triangle A163772.
  • A163777 (program): Even terms in the sequence of Queneau numbers A054639.
  • A163778 (program): Odd terms in A054639.
  • A163779 (program): Numbers k of the form 4*j + 1 such that 2*k + 1 is a prime with primitive root 2.
  • A163780 (program): Terms in A054639 equal to 3 mod 4.
  • A163782 (program): a(n) is the n-th J_2-prime (Josephus_2 prime).
  • A163801 (program): a(n)=n-a(a(n-2)) with a(0)=0,a(1)=1
  • A163804 (program): Expansion of (1 - x) * (1 - x^4) / ((1 - x^2) * (1 - x^3)) in powers of x.
  • A163805 (program): Expansion of (1 - x) * (1 - x^6) / ((1 - x^3) * (1 - x^4)) in powers of x.
  • A163806 (program): Expansion of (1 - x^3) * (1 - x^4) / ((1 - x) * (1 - x^6)) in powers of x.
  • A163807 (program): Reverse the order of inner digits (all digits but the first and last) of n written in binary. a(n) = the decimal value of the result.
  • A163808 (program): Write n in binary. Place a 0 right of every 1 without a 0 right of it. a(n) = the decimal value of the result.
  • A163809 (program): Write n in binary. Insert a 0 in the middle of each pair of two consecutive 1’s. a(n) = the decimal value of the result.
  • A163810 (program): Expansion of (1 - x) * (1 - x^2) * (1 - x^3) / (1 - x^6) in powers of x.
  • A163811 (program): Expansion of (1 - x) * (1 - x^10) / ((1 - x^5) * (1 - x^6)) in powers of x.
  • A163812 (program): Expansion of (1 - x^5) * (1 - x^6) / ((1 - x) * (1 - x^10)) in powers of x.
  • A163815 (program): a(n) = n*(2*n^2 + 5*n + 3).
  • A163817 (program): Expansion of (1 - x^2) * (1 - x^5) / ((1 - x) * (1 - x^6)) in powers of x.
  • A163818 (program): Expansion of (1 - x) * (1 - x^6) / ((1 - x^2) * (1 - x^5)) in powers of x.
  • A163822 (program): Number of divisors d of 2n such that gcd(d-1,2n/d-1) = 1.
  • A163823 (program): Number of initial segments of signature sequences of length n.
  • A163826 (program): G.f.: Sum_{n>=1} n * 2^(n^2) * x^n / (1 - 2^n*x)^(n+1).
  • A163827 (program): a(n) = 6n^3 + 1, solution z in Diophantine equation x^3 + y^3 = z^3 - 2. It may be considered a Fermat near miss by 2.
  • A163830 (program): The n-th composite minus the product of the indices of the primes in its prime factorization.
  • A163831 (program): a(n) is the n-th composite minus the sum of the indices of the primes in its prime factorization.
  • A163832 (program): a(n) = n*(2*n^2 + 5*n + 1).
  • A163833 (program): a(n) = n*(6*n^2 + 15*n + 5)/2.
  • A163834 (program): a(n) = (4^n + 5)/3.
  • A163838 (program): a(n) = (n-th composite) * (number of nontrivial divisors of n-th composite).
  • A163839 (program): a(n) = (2^n-1)*4^(2*n-1).
  • A163840 (program): Triangle interpolating the binomial transform of the swinging factorial (A163865) with the swinging factorial (A056040).
  • A163841 (program): Triangle interpolating the swinging factorial (A056040) restricted to even indices with its binomial transform. Same as interpolating bilateral Schroeder paths (A026375) with the central binomial coefficients (A000984).
  • A163842 (program): Triangle interpolating the swinging factorial (A056040) restricted to odd indices with its binomial transform. Same as interpolating the beta numbers 1/beta(n,n) (A002457) with (A163869).
  • A163843 (program): Row sums of triangle A163840.
  • A163844 (program): Row sums of triangle A163841.
  • A163845 (program): Row sums of triangle A163842.
  • A163864 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
  • A163865 (program): The binomial transform of the swinging factorial (A056040).
  • A163866 (program): Partial sums of A007318.
  • A163868 (program): a(n) = (4^n + 11)/3.
  • A163869 (program): Binomial transform of the beta numbers 1/beta(n+1,n+1) (A002457).
  • A163870 (program): Triangle read by rows: row n lists the nontrivial divisors of the n-th composite.
  • A163871 (program): The n-th composite plus the sum of its nontrivial divisors.
  • A163872 (program): Inverse binomial transform of the beta numbers 1/beta(n+1,n+1) (A002457).
  • A163873 (program): a(n) = n - a(a(n-2)) with a(0) = a(1) = 0.
  • A163876 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.
  • A163888 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 4.
  • A163895 (program): Positions where A163894 obtains record values.
  • A163901 (program): The positions i where A163355(i) = i, that is, the fixed points of permutation A163355.
  • A163927 (program): Numerators of the higher order exponential integral constants alpha(k,4).
  • A163929 (program): Denominators of the higher order exponential integral constants alpha(2,n).
  • A163933 (program): Third right hand column of triangle A163932
  • A163935 (program): Third right hand column of triangle A163934
  • A163941 (program): Fourth right hand column of triangle A163940.
  • A163942 (program): Fifth right hand column of triangle A163940.
  • A163943 (program): Third left hand column of triangle A163940.
  • A163944 (program): Fourth left hand column of triangle A163940.
  • A163945 (program): Triangle interpolating between (-1)^n (A033999) and the swinging factorial function (A056040) restricted to odd indices (2n+1)$ (A002457).
  • A163960 (program): Decimal expansion of 2*(sqrt(2) - 1).
  • A163961 (program): First differences of A116533.
  • A163963 (program): First differences of A080735.
  • A163975 (program): n-th nonprime - (-1)^(n-th nonprime).
  • A163976 (program): prime(n) -(-1)^(n-th nonprime).
  • A163978 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 4.
  • A163979 (program): a(n) = n*(n-1) + A144437(n+2).
  • A163980 (program): a(n) = 2*n + (-1)^n.
  • A163982 (program): Real part of the coefficient [x^n] of the expansion of (1+i)/(1-i*exp(x)) - 1 multiplied by 2*n!, where i is the imaginary unit.
  • A163984 (program): First differences of A056737.
  • A163985 (program): Sum of all isolated parts of all partitions of n.
  • A163987 (program): First differences of A160119.
  • A164001 (program): Spiral of triangles around a hexagon.
  • A164004 (program): Zero together with row 4 of the array in A163280.
  • A164005 (program): Zero together with row 5 of the array in A163280.
  • A164006 (program): Zero together with row 6 of the array in A163280.
  • A164013 (program): 3 times centered triangular numbers: 9*n*(n+1)/2 + 3.
  • A164015 (program): 5 times centered pentagonal numbers: 5*(5*n^2 + 5*n + 2)/2.
  • A164016 (program): 6 times centered hexagonal numbers: 18*n*(n+1) + 6.
  • A164018 (program): The index values of the smallest and the largest n-digit Fibonacci numbers.
  • A164019 (program): Table read by rows: row n contains the primes between n and 2n.
  • A164020 (program): Denominators of Bernoulli numbers interleaved with even numbers.
  • A164021 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 3, a(1) = 22.
  • A164028 (program): The n-th composite minus 3.
  • A164029 (program): a(n) = nonprime(n) + (-1)^(nonprime(n)).
  • A164031 (program): a(n) = ((2+3*sqrt(2))*(5+sqrt(2))^n+(2-3*sqrt(2))*(5-sqrt(2))^n)/4.
  • A164032 (program): Number of “ON” cells in a certain 2-dimensional cellular automaton.
  • A164033 (program): a(n) = ((4+3*sqrt(2))*(3+sqrt(2))^n + (4-3*sqrt(2))*(3-sqrt(2))^n)/4.
  • A164034 (program): a(n) = ((4+3*sqrt(2))*(4+sqrt(2))^n + (4-3*sqrt(2))*(4-sqrt(2))^n)/4.
  • A164035 (program): a(n) = ((4+3*sqrt(2))*(5+sqrt(2))^n + (4-3*sqrt(2))*(5-sqrt(2))^n)/4.
  • A164037 (program): Expansion of (5-9*x)/(1-6*x+7*x^2).
  • A164038 (program): Expansion of (5-19*x)/(1-10*x+23*x^2).
  • A164039 (program): a(n+1) = 3*a(n) - n.
  • A164040 (program): 2*alpha^4*e^(Pi/(4*alpha))*(e/2)^(1/4), where alpha is the fine structure constant A003673.
  • A164041 (program): Primes of the form 2*p^2 + 4*p + 1, where p is also prime.
  • A164042 (program): Primes p such that 2*p^2+4*p+1 is also prime.
  • A164044 (program): a(n+1) = 4*a(n) - n.
  • A164045 (program): a(n+1) = 5*a(n) - n.
  • A164046 (program): A001445 written in base 2.
  • A164051 (program): a(n) = 2^(2n) + 2^(n-1).
  • A164053 (program): Partial sums of A162255.
  • A164055 (program): Triangular numbers that are one plus a perfect square.
  • A164056 (program): Triangle of 2^n terms by rows, derived from A088696 as to length of continued fractions, lengths increase = 1, decrease = 0. A088696 can be generated using the following algorithm: Rows 0 and 1 begin 1; 1,2; then for all further rows, bring down current row then append to the right: (1 added to each term in current row). Row 2 (1, 2, 3, 2) then becomes: (1, 2, 3, 2, 3, 4, 3, 2).
  • A164057 (program): Complement to A164056, change A164056 bits (0->1; 1->0). Provides a coding template for Petoukhov matrices, relating to DNA codons.
  • A164072 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A164073 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 1, a(2) = 3.
  • A164080 (program): Perfect squares one less than a triangular number.
  • A164086 (program): Beatty sequence for 4*Pi/3 = 4.1887902… .
  • A164087 (program): Beatty sequence for 4*Pi/(4*Pi-3) = 1.3135986… .
  • A164089 (program): For n >=4, a(n) = the numerical value of the substring of binary n containing all digits but the first and last. a(1) = a(2) = a(3) = 0.
  • A164090 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 2, a(2) = 3.
  • A164092 (program): Triangle by 2^n term rows, codes used for generating Petoukhov matrices in a Gray code format.
  • A164093 (program): 9*4^n+2.
  • A164094 (program): a(n) = 3*2^n + 2.
  • A164095 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 6.
  • A164096 (program): Partial sums of A164095.
  • A164097 (program): Numbers n such that 6n + 7 is a perfect square.
  • A164102 (program): Decimal expansion of 2*Pi^2.
  • A164103 (program): Decimal expansion of 8*Pi^2/15.
  • A164104 (program): Decimal expansion of 8*Pi^2/3.
  • A164105 (program): Decimal expansion of Pi^3/6.
  • A164106 (program): Decimal expansion of 16*Pi^3/105.
  • A164107 (program): Decimal expansion of 16*Pi^3/15.
  • A164108 (program): Decimal expansion of Pi^4/24.
  • A164109 (program): Decimal expansion of Pi^4/3.
  • A164110 (program): a(n) = 12*a(n-1) - 34*a(n-2) for n > 1; a(0) = 5, a(1) = 36.
  • A164111 (program): Expansion of (1-x)/(1+4*x^2).
  • A164114 (program): Numbers k such that Chowla(k) + phi(k) is prime.
  • A164115 (program): Expansion of (1 - x^5) / ((1 - x) * (1 - x^4)) in powers of x.
  • A164116 (program): Expansion of (1 - x) * (1 - x^4) / (1 - x^5) in powers of x.
  • A164117 (program): Expansion of (1 - x) * (1 - x^10) / ((1 - x^2) * (1 - x^4) * (1 - x^5)) in powers of x.
  • A164118 (program): Expansion of (1 - x^2) * (1 - x^4) * (1 - x^5) / ((1 - x) * (1 - x^10)) in powers of x.
  • A164120 (program): Partial sums of A162396.
  • A164123 (program): Partial sums of A162436.
  • A164126 (program): First differences of A006995.
  • A164131 (program): Numbers k such that k^2 == 2 (mod 31).
  • A164135 (program): Numbers k such that k^2 == 2 (mod 47).
  • A164136 (program): a(n) = 11*n*(n+1).
  • A164141 (program): Number of binary strings of length n with equal numbers of 001 and 010 substrings.
  • A164143 (program): Number of binary strings of length n with equal numbers of 001 and 100 substrings
  • A164158 (program): Number of binary strings of length n with equal numbers of 0001 and 0101 substrings
  • A164161 (program): Number of binary strings of length n with equal numbers of 0001 and 1000 substrings.
  • A164203 (program): Number of binary strings of length n with equal numbers of 00001 and 10000 substrings.
  • A164229 (program): Number of binary strings of length n with equal numbers of 00011 and 00101 substrings
  • A164265 (program): Partial sums of A162766.
  • A164267 (program): A Fibonacci convolution.
  • A164269 (program): Expansion of q * f(q^9)^3 * phi(q) / (f(q^3) * phi(q^3)^3) in powers of q where f(), phi() are Ramanujan theta functions.
  • A164270 (program): Expansion of f(x^3)^3 * phi(x^3) / (f(x) * phi(x)^3) in powers of x where f(), phi() are Ramanujan theta functions.
  • A164271 (program): Expansion of ( f(-q^2) * f(q^3) * f(-q^6) / f(q)^3 )^2 in powers of q where f() is a Ramanujan theta function.
  • A164274 (program): (n-th isolated prime) plus (n-th isolated composite).
  • A164275 (program): The absolute value of (the n-th isolated composite minus the n-th isolated prime).
  • A164276 (program): The non-isolated nonprimes.
  • A164278 (program): a(n) = (6*n + 1)^(2*n) - 1.
  • A164279 (program): Triangle of 2^n terms per row, a Petoukhov sequence generated from (3,2).
  • A164281 (program): Triangle read by rows, a Petoukhov sequence (cf. A164279) generated from (1,2).
  • A164282 (program): Hypotenuses of more than two Pythagorean triangles.
  • A164284 (program): a(n) = 15*n-7.
  • A164285 (program): a(n) = 7*2^n + 3.
  • A164292 (program): Binary sequence identifying the twin primes (characteristic function of twin primes: 1 if n is a twin prime else 0).
  • A164295 (program): Triangle T(n,k) read by rows: sum of the triangles A054521 and A051731.
  • A164296 (program): Let S(n) be the set of all positive integers that are <= n and are coprime to n. a(n) = the number of members of S(n) that are each coprime to every other member of S(n).
  • A164297 (program): Let S(n) be the set of all positive integers that are <= n and are coprime to n. a(n) = the number of members of S(n) that are each non-coprime with at least one other member of S(n).
  • A164298 (program): a(n) = ((1+4*sqrt(2))*(2+sqrt(2))^n + (1-4*sqrt(2))*(2-sqrt(2))^n)/2.
  • A164299 (program): a(n) = ((1+4*sqrt(2))*(3+sqrt(2))^n + (1-4*sqrt(2))*(3-sqrt(2))^n)/2.
  • A164300 (program): a(n) = ((1+4*sqrt(2))*(4+sqrt(2))^n + (1-4*sqrt(2))*(4-sqrt(2))^n)/2.
  • A164301 (program): a(n) = ((1+4*sqrt(2))*(5+sqrt(2))^n + (1-4*sqrt(2))*(5-sqrt(2))^n)/2.
  • A164302 (program): a(n) = 2* (the n-th positive (odd) integer that is a palindrome when written in base 2).
  • A164303 (program): a(n) = 2*a(n-1) + a(n-2) for n > 1; a(0) = 3, a(1) = 11.
  • A164304 (program): a(n) = 4*a(n-1) - 2*a(n-2) for n > 1; a(0) = 3, a(1) = 14.
  • A164305 (program): a(n) = 6*a(n-1) - 7*a(n-2) for n > 1; a(0) = 3, a(1) = 17.
  • A164306 (program): Triangle read by rows: T(n, k) = k / gcd(k, n), 1 <= k <= n.
  • A164308 (program): Triangle read by rows, binomial distribution of the terms (1, 3, 9, 27, …).
  • A164309 (program): Triangle read by rows, generated from the binomial expansion of (5x + 2).
  • A164310 (program): a(n) = 6*a(n-1) - 6*a(n-2) for n > 1; a(0) = 4, a(1) = 15.
  • A164311 (program): a(n) = 12*a(n-1) - 33*a(n-2) for n > 1; a(0) = 4, a(1) = 27.
  • A164313 (program): LCM of all differences of odd primes up to prime(n).
  • A164314 (program): Largest prime factor of n^2 - 2.
  • A164315 (program): Number of binary strings of length n with no substrings equal to 000 or 011.
  • A164316 (program): Number of binary strings of length n with no substrings equal to 000, 001, or 010.
  • A164317 (program): Number of binary strings of length n with no substrings equal to 000, 010, or 111.
  • A164318 (program): Primes p such that the sum of divisors of p-1 is larger than 2*p.
  • A164343 (program): A positive integer is included if it is a square that contains the same number of 0’s as 1’s when represented in binary.
  • A164344 (program): Positive integers whose square contains the same number of 0’s as 1’s when represented in binary.
  • A164346 (program): a(n) = 3 * 4^n.
  • A164349 (program): The limit of the string “0, 1” under the operation ‘repeat string twice and remove last symbol’.
  • A164355 (program): Expansion of (1 - x^2)^4 * (1 - x^5) / ((1 - x)^5 * (1 - x^4)^2) in powers of x.
  • A164356 (program): Expansion of (1 - x^2)^4 / ((1 - x)^4 * (1 - x^4)) in powers of x.
  • A164357 (program): Expansion of (1 - x^2)^5 / ((1 - x)^4 * (1 - x^6)) in powers of x.
  • A164358 (program): Expansion of (1 - x^2)^2 * (1 - x^3) / ((1 - x)^3 * (1 - x^4)) in powers of x.
  • A164359 (program): Expansion of (1 - x^2)^3 / ((1 - x)^3 * (1 - x^3)) in powers of x.
  • A164360 (program): Period 3: repeat [5, 4, 3].
  • A164362 (program): The number of 0’s in the n-th stage of A164349.
  • A164363 (program): The number of 1’s in the n-th stage of A164349
  • A164364 (program): a(n) = A164349(2^n).
  • A164367 (program): a(n) = A164051(n) in base 2.
  • A164370 (program): Sequence A005418 written in base 2.
  • A164376 (program): Nonprime numbers that are not a sum of 2 primes.
  • A164383 (program): Composite numbers of the form 4 + some prime.
  • A164384 (program): Positive nonprimes of the form p-4 where p is prime.
  • A164385 (program): Composite numbers n such that n+4 and n-4 are both prime.
  • A164386 (program): Numbers which are not 1 larger than a nonzero square.
  • A164387 (program): Number of binary strings of length n with no substrings equal to 0000 or 0010.
  • A164388 (program): Number of binary strings of length n with no substrings equal to 0000 or 0011.
  • A164389 (program): Number of binary strings of length n with no substrings equal to 0000 or 0101.
  • A164390 (program): Number of binary strings of length n with no substrings equal to 0000 or 0110.
  • A164391 (program): Number of binary strings of length n with no substrings equal to 0000 or 0111.
  • A164392 (program): Number of binary strings of length n with no substrings equal to 0001 or 0010.
  • A164393 (program): Number of binary strings of length n with no substrings equal to 0001 or 0011.
  • A164394 (program): Number of binary strings of length n with no substrings equal to 0001 or 0100.
  • A164395 (program): Number of binary strings of length n with no substrings equal to 0001 or 0101.
  • A164396 (program): Number of binary strings of length n with no substrings equal to 0001 or 0110.
  • A164397 (program): Number of binary strings of length n with no substrings equal to 0001 or 0111.
  • A164398 (program): Number of binary strings of length n with no substrings equal to 0001 or 1000.
  • A164399 (program): Number of binary strings of length n with no substrings equal to 0001 or 1010
  • A164400 (program): Number of binary strings of length n with no substrings equal to 0001 or 1100.
  • A164401 (program): Number of binary strings of length n with no substrings equal to 0010 or 0101.
  • A164402 (program): Number of binary strings of length n with no substrings equal to 0010 or 0110.
  • A164403 (program): Number of binary strings of length n with no substrings equal to 0010 or 1001
  • A164404 (program): Number of binary strings of length n with no substrings equal to 0010 or 1011
  • A164405 (program): Number of binary strings of length n with no substrings equal to 0010 or 1100.
  • A164406 (program): Number of binary strings of length n with no substrings equal to 0011 or 0101.
  • A164407 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0010
  • A164408 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0011.
  • A164409 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0100
  • A164410 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0101
  • A164411 (program): Number of binary strings of length n with no substrings equal to 0000, 0001, or 0110.
  • A164412 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 0111.
  • A164413 (program): Number of binary strings of length n with no substrings equal to 0000, 0001 or 1001.
  • A164414 (program): Number of binary strings of length n with no substrings equal to 0000, 0001, or 1010.
  • A164415 (program): Number of binary strings of length n with no substrings equal to 0000, 0001, or 1100.
  • A164416 (program): Number of binary strings of length n with no substrings equal to 0000 0001 or 1111
  • A164417 (program): Number of binary strings of length n with no substrings equal to 0000, 0010, or 0100.
  • A164418 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 0101
  • A164419 (program): Number of binary strings of length n with no substrings equal to 0000, 0010, or 0110.
  • A164420 (program): Number of binary strings of length n with no substrings equal to 0000, 0010, or 0111.
  • A164421 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1001
  • A164422 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1010
  • A164423 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1100
  • A164424 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1101
  • A164425 (program): Number of binary strings of length n with no substrings equal to 0000 0010 or 1111
  • A164427 (program): Number of binary strings of length n with no substrings equal to 0000 0011 or 0110
  • A164428 (program): Number of binary strings of length n with no substrings equal to 0000, 0011, or 1001.
  • A164429 (program): Number of binary strings of length n with no substrings equal to 0000, 0011, or 1011.
  • A164431 (program): Number of binary strings of length n with no substrings equal to 0000 0011 or 1101
  • A164432 (program): Number of binary strings of length n with no substrings equal to 0000 0101 or 0110
  • A164433 (program): Number of binary strings of length n with no substrings equal to 0000 0101 or 0111
  • A164436 (program): Number of binary strings of length n with no substrings equal to 0000 0101 or 1110.
  • A164438 (program): Number of binary strings of length n with no substrings equal to 0000 0110 or 0111
  • A164439 (program): Number of binary strings of length n with no substrings equal to 0000 0110 or 1001
  • A164440 (program): Number of binary strings of length n with no substrings equal to 0000 0110 or 1011
  • A164442 (program): Number of binary strings of length n with no substrings equal to 0000 0111 or 1001
  • A164443 (program): Number of binary strings of length n with no substrings equal to 0000 0111 or 1110
  • A164444 (program): Number of binary strings of length n with no substrings equal to 0000 1001 or 1011
  • A164445 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0100
  • A164446 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0101
  • A164447 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0110
  • A164448 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 0111
  • A164449 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1010
  • A164450 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1011
  • A164451 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1100
  • A164452 (program): Number of binary strings of length n with no substrings equal to 0001 0010 or 1101.
  • A164453 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 0100
  • A164454 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 0101
  • A164455 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 0111
  • A164456 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1000
  • A164457 (program): Number of binary strings of length n with no substrings equal to 0001, 0011, or 1010.
  • A164458 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1011
  • A164460 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1101
  • A164461 (program): Number of binary strings of length n with no substrings equal to 0001 0011 or 1110
  • A164462 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 0101
  • A164463 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 0110
  • A164464 (program): Number of binary strings of length n with no substrings equal to 0001, 0100, or 0111.
  • A164465 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 1010
  • A164466 (program): Number of binary strings of length n with no substrings equal to 0001, 0100, or 1011.
  • A164467 (program): Number of binary strings of length n with no substrings equal to 0001 0100 or 1101
  • A164468 (program): Number of binary strings of length n with no substrings equal to 0001, 0100, or 1110.
  • A164469 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 0110
  • A164470 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 0111
  • A164471 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1000
  • A164472 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1010
  • A164473 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1011
  • A164474 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1100
  • A164475 (program): Number of binary strings of length n with no substrings equal to 0001 0101 or 1110
  • A164476 (program): Number of binary strings of length n with no substrings equal to 0001, 0110, or 0111.
  • A164477 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1000.
  • A164478 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1010
  • A164479 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1011
  • A164480 (program): Number of binary strings of length n with no substrings equal to 0001, 0110 or 1100.
  • A164481 (program): Number of binary strings of length n with no substrings equal to 0001 0110 or 1101.
  • A164482 (program): Number of binary strings of length n with no substrings equal to 0001, 0110, or 1110.
  • A164483 (program): Number of binary strings of length n with no substrings equal to 0001 0111 or 1010.
  • A164484 (program): Number of binary strings of length n with no substrings equal to 0001 0111 or 1100
  • A164485 (program): Number of binary strings of length n with no substrings equal to 0001, 1000 or 1001.
  • A164487 (program): Number of binary strings of length n with no substrings equal to 0001, 1010, or 1100.
  • A164488 (program): Number of binary strings of length n with no substrings equal to 0001 1010 or 1101
  • A164489 (program): Number of binary strings of length n with no substrings equal to 0001 1011 or 1100
  • A164490 (program): Number of binary strings of length n with no substrings equal to 0010 0011 or 0110
  • A164491 (program): Number of binary strings of length n with no substrings equal to 0010 0100 or 1001
  • A164492 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 0110
  • A164493 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 1001
  • A164494 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 1010
  • A164495 (program): Number of binary strings of length n with no substrings equal to 0010 0101 or 1011
  • A164497 (program): Number of binary strings of length n with no substrings equal to 0010 0110 or 1011
  • A164498 (program): Number of binary strings of length n with no substrings equal to 0010 0110 or 1100
  • A164499 (program): Number of binary strings of length n with no substrings equal to 0010 0110 or 1101
  • A164500 (program): Number of binary strings of length n with no substrings equal to 0010 1001 or 1010
  • A164501 (program): Number of binary strings of length n with no substrings equal to 0010 1001 or 1100
  • A164503 (program): Number of binary strings of length n with no substrings equal to 0011 0101 or 0110
  • A164504 (program): Number of binary strings of length n with no substrings equal to 0011 0101 or 1010
  • A164505 (program): Number of binary strings of length n with no substrings equal to 0011 0101 or 1100
  • A164506 (program): Number of binary strings of length n with no substrings equal to 0011 0110 or 1001
  • A164508 (program): Number of binary strings of length n with no substrings equal to 0101, 0110, or 1001.
  • A164509 (program): Number of binary strings of length n with no substrings equal to 0101, 0110, or 1010.
  • A164510 (program): First differences of A071904 (Odd composite numbers).
  • A164513 (program): Primes with gap to the next prime no less than 20.
  • A164514 (program): 1 followed by numbers that are not squares.
  • A164515 (program): Positive numbers not of the form n^2+2.
  • A164532 (program): a(n) = 6*a(n-2) for n > 2; a(1) = 1, a(2) = 4.
  • A164533 (program): a(n) = sigma(sigma(n))*sigma(n).
  • A164534 (program): (n-th isolated prime) -(-1)^(n-th isolated prime).
  • A164535 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.
  • A164536 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 23.
  • A164537 (program): a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 5, a(1) = 28.
  • A164538 (program): a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
  • A164539 (program): a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
  • A164540 (program): a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 14.
  • A164541 (program): a(n) = 6*a(n-1) - a(n-2) for n > 1; a(0) = 1, a(1) = 15.
  • A164542 (program): a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 16.
  • A164543 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
  • A164544 (program): a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A164545 (program): a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
  • A164546 (program): a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A164547 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A164549 (program): a(n) = 4*a(n-1) + 2*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
  • A164550 (program): a(n) = 6*a(n-1) - 3*a(n-2) for n > 1; a(0) = 1, a(1) = 7.
  • A164551 (program): a(n) = 10*a(n-1)-19*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
  • A164552 (program): a(n) = 12*a(n-1)-30*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A164553 (program): a(n) = 14*a(n-1)-43*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
  • A164555 (program): Numerators of the “original” Bernoulli numbers; also the numerators of the Bernoulli polynomials at x=1.
  • A164559 (program): a(n) = 6^n/3 - 1.
  • A164560 (program): Partial sums of A164532.
  • A164561 (program): Triangle with elements A120070(m,n)/A120072(m,n) read by rows, m>=2, 1<=n<m.
  • A164569 (program): Primes p such that 11*p+8 are prime numbers.
  • A164575 (program): a(n) = n! * [x^n] 2*(tan(x))^2*(sec(x) + tan(x)).
  • A164576 (program): Integer averages of the set of the first positive squares up to some n^2.
  • A164577 (program): Integer averages of the first perfect cubes up to some n^3.
  • A164578 (program): Integers of the form (k+1)*(2k+1)/12.
  • A164579 (program): Integer averages of halves of first cubes of natural numbers (n^3)/2 for some n.
  • A164581 (program): a(n) = 5*a(n - 1) + a(n - 2), with a(0)=1, a(1)=2.
  • A164582 (program): a(n) = 5*a(n - 1) - a(n - 2), with n>2, a(1)=2, a(2)=3.
  • A164583 (program): a(n)=4^n*(2n + 1)^2.
  • A164584 (program): Expansion of (1 + 6*x - 12*x^2 - 8*x^3)/(1 - 24*x^2 + 16*x^4).
  • A164587 (program): a(n) = 2*a(n - 2) for n > 2; a(1) = 1, a(2) = 8.
  • A164588 (program): a(n) = ((3 + sqrt(18))*(5 + sqrt(8))^n + (3 - sqrt(18))*(5 - sqrt(8))^n)/6.
  • A164589 (program): a(n) = ((4 + 3*sqrt(2))*(1 + 2*sqrt(2))^n + (4 - 3*sqrt(2))*(1 - 2*sqrt(2))^n)/8.
  • A164591 (program): a(n) = ((4 + sqrt(18))*(4 + sqrt(8))^n + (4 - sqrt(18))*(4 - sqrt(8))^n)/8 .
  • A164592 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 8.
  • A164593 (program): a(n) = ((5 + sqrt(18))*(2 + sqrt(8))^n + (5 - sqrt(18))*(2 - sqrt(8))^n)/2.
  • A164594 (program): a(n) = ((5 + sqrt(18))*(4 + sqrt(8))^n + (5 - sqrt(18))*(4 - sqrt(8))^n)/2.
  • A164595 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 5, a(1) = 37.
  • A164597 (program): a(n) = the largest integer such that {the n-th prime} + k(k + 1) is prime for all k where 0 <= k <= a(n).
  • A164598 (program): a(n) = 12*a(n-1) - 34*a(n-2), for n > 1, with a(0) = 1, a(1) = 14.
  • A164599 (program): a(n) = 14*a(n-1) - 47*a(n-2), for n > 1, with a(0) = 1, a(1) = 15.
  • A164600 (program): a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 17.
  • A164602 (program): a(n) = ((1+4*sqrt(2))*(1+2*sqrt(2))^n + (1-4*sqrt(2))*(1-2*sqrt(2))^n)/2.
  • A164603 (program): a(n) = ((1+4*sqrt(2))*(2+2*sqrt(2))^n + (1-4*sqrt(2))*(2-2*sqrt(2))^n)/2.
  • A164604 (program): a(n) = ((1+4*sqrt(2))*(3+2*sqrt(2))^n + (1-4*sqrt(2))*(3-2*sqrt(2))^n)/2.
  • A164605 (program): a(n) = ((1+4*sqrt(2))*(4+2*sqrt(2))^n + (1-4*sqrt(2))*(4-2*sqrt(2))^n)/2.
  • A164606 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 21.
  • A164607 (program): a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
  • A164608 (program): Expansion of (1+4*x)/(1-8*x+8*x^2).
  • A164609 (program): a(n) = 10*a(n-1) - 17*a(n-2) for n > 1; a(0) = 1, a(1) = 13.
  • A164611 (program): Expansion of (1 + x + 2*x^2 - x^3)/(1 - 2*x + 3*x^2 - 2*x^3 + x^4).
  • A164614 (program): Expansion of (chi(q) / chi^3(q^3))^2 in powers of q where chi() is a Ramanujan theta function.
  • A164616 (program): Expansion of c(-q) * c(-q^3) / c(q^2)^2 in powers of q where c() is a cubic AGM theta function.
  • A164617 (program): Expansion of (phi^3(q^3) / phi(q)) * (psi(-q^3) / psi^3(-q)) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A164619 (program): Integers of the form A164577(k)/3.
  • A164629 (program): Expansion of phi (golden ratio) in base 5.
  • A164632 (program): a(1)=1 followed by 2^k appearing 2^(2*k-1) times for k>0.
  • A164640 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
  • A164651 (program): Number of permutations of length n that avoid both 1243 and 2134.
  • A164653 (program): a(1) = 1, for n>=2: a(n) = sum of two consecutive noncomposite numbers A008578.
  • A164654 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 3, a(2) = 8.
  • A164655 (program): Numerators of partial sums of Theta(3) = sum(1/(2*j-1)^3, j=1..infinity).
  • A164656 (program): Numerators of partial sums of Theta(5) = sum( 1/(2*j-1)^5, j=1..infinity ).
  • A164657 (program): Denominators of partial sums of Theta(5) = sum(1/(2*j-1)^5, j=1..infinity).
  • A164658 (program): Numerators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).
  • A164659 (program): Denominators of coefficients of integrated Chebyshev polynomials T(n,x) (in increasing order of powers of x).
  • A164660 (program): Numerators of row sums of triangle of rationals A164658/A164659. Definite integral of Chebyshev polynomials of the first kind: Integral_{x=0..1} T(n,x).
  • A164661 (program): Denominators of row sums of triangle of rationals A164658/A164659. Definite integral of Chebyshev polynomials of the first kind: Integral_{x=0..1} T(n,x).
  • A164662 (program): Row sums of triangle A164658 (numerators of coefficients from Integral_{x} T(n,x), with T(n,x) Chebyshev polynomials of the first kind).
  • A164663 (program): Row sums of triangle A164659 (denominators of coefficients from int(T(n,x),x), with T(n,x) Chebyshev polynomials of the first kind).
  • A164675 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 12.
  • A164677 (program): For a binary reflected Gray code, the (Hamming/Euclidean) distance between 2 subsequent points x and y is 1, say in coordinate k. If y has a 1 in coordinate k and x has a 0, than (x,y) is indicated by k, if it is the other way around, (x,y) is indicated by -k. The sequence has a fractal character such that G(d+1) = G(d) d+1 R(G(d)) where R(G(d)) alters d –> -d and leaves all other numbers invariant.
  • A164680 (program): Expansion of x/((1-x)^3*(1-x^2)^3*(1-x^3)).
  • A164682 (program): a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 8.
  • A164683 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 8.
  • A164689 (program): If p and q are (odd) twin primes and q > p then p*q^2+(p+q)+1 is divisible by 3; a(n) = (p*q^2+(p+q)+1)/3.
  • A164703 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 1, a(2) = 16.
  • A164705 (program): T(n,k)=Binomial(2n-k,n)*2^(k-1) for n>=1,0<=k<=n
  • A164711 (program): Those positive integers missing from sequence A164710. Those positive integers that, when written in binary, contain at least two runs of 0’s that are of differing lengths.
  • A164737 (program): a(n) = 8*a(n-2) for n > 2; a(1) = 5, a(2) = 12.
  • A164738 (program): Triangle read by rows. Row 0 = {2}; left half of row n+1 = row n, right half = row n reversed with each term replaced by the next prime.
  • A164740 (program): (2^p-(p+2))/p as p runs through the primes.
  • A164743 (program): Digital root of 3*A000045(n).
  • A164754 (program): Number of n X 2 1..4 arrays with all 1’s connected, all 2’s connected, all 3’s connected, all 4’s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
  • A164765 (program): Partial sums of [A080782^2].
  • A164768 (program): First differences of A003592.
  • A164783 (program): 7^n-6.
  • A164784 (program): a(n) = 6^n-5.
  • A164785 (program): a(n) = 5^n - 4.
  • A164786 (program): a(n) = 8^n-7.
  • A164826 (program): Sequences A087800 and A077416 interleaved.
  • A164827 (program): Generalized Lucas numbers: a(n) = a(n-1) + 10 a(n-2); with a(1)=2 a(2)=1
  • A164844 (program): Generalized Pascal Triangle - satisfying the same recurrence as Pascal’s triangle, but with a(n,0)=1 and a(n,n)=10^n (instead of both being 1).
  • A164845 (program): a(n) = (6 + 10*n + 5*n^2 + n^3)/2.
  • A164847 (program): (100^n,1) Pascal triangle
  • A164848 (program): a(n) = A026741(n)/A051712(n+1).
  • A164849 (program): Diagonal sum of (100^n,1) Pascal Triangle
  • A164851 (program): Generalized Lucas-Pascal triangle; (11*10^n, 1).
  • A164852 (program): Diagonal sum of generalized Lucas-Pascal triangle;(11*10^n,1)
  • A164854 (program): Diagonal sum of generalized Pascal triangle; (10^n,1).
  • A164855 (program): Generalized Lucas-Pascal triangle: (101*100^n,1)
  • A164856 (program): Row sums of generalized Lucas-Pascal triangle: A164855
  • A164861 (program): Odd positive integers that are not palindromes when written in binary.
  • A164866 (program): (101^n,1)-Pascal triangle
  • A164869 (program): n*A027642(n).
  • A164870 (program): The number of permutations of length n that can be sorted by 2 pop stacks in parallel.
  • A164874 (program): Triangle read by rows: T(1,1)=2; T(n,k)=2*T(n-1,k)+1, 1<=k<n; T(n,n)=2*(T(n-1,n-1)+1).
  • A164877 (program): First bisection of A164869.
  • A164881 (program): Inverse of A164844
  • A164884 (program): a(n) = image of n under the base-2 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order).
  • A164894 (program): Base-10 representation of the binary string formed by appending 10, 100, 1000, 10000, …, etc., to 1.
  • A164897 (program): a(n) = 4*n*(n+1) + 3.
  • A164898 (program): First differences of numbers having only odd digits in their decimal representation.
  • A164899 (program): Binomial matrix (1,10^n) read by antidiagonals.
  • A164900 (program): a(2n) = 4*n*(n+1) + 3; a(2n+1) = 2*n*(n+2) + 3.
  • A164901 (program): a(1)=1, a(2) = 2. For n >=3, a(n) = the smallest integer > a(n-1) that is coprime to every sum of any two distinct earlier terms of this sequence.
  • A164907 (program): a(n) = (3*3^n-(-1)^n)/2.
  • A164908 (program): a(n) = (3*4^n - 0^n)/2.
  • A164910 (program): Partial sums of A088748
  • A164913 (program): Expansion of x/(1-9*x-11*x^2+10*x^3).
  • A164915 (program): Inverse of binomial matrix (10^n,1 )A164899. (Subtraction instead of addition)
  • A164921 (program): a(1)=0, a(2)=1. For n >=3, a(n) = the smallest integer > a(n-1) that is coprime to every sum of any two distinct earlier terms of this sequence.
  • A164925 (program): Array binomial(j-i,j) read by rising antidiagonals.
  • A164931 (program): n times the n-th noncomposite.
  • A164938 (program): a(n) = (n^5 - n)/10, which is always an integer.
  • A164940 (program): Partial sums of A138202.
  • A164942 (program): Triangle, read by rows, T(n,k) = (-1)^k*binomial(n, k)*3^(n-k).
  • A164943 (program): Decimal value of the concatenation of first n odd numbers in binary.
  • A164944 (program): Decimal value of the concatenation of first n even numbers in binary.
  • A164945 (program): Decimal value of the concatenation of first n multiples of 3 in binary.
  • A164948 (program): Fibonacci matrix read by antidiagonals. (Inverse of A136158.)
  • A164950 (program): 1 if there is a winning strategy for misère Sprouts with n initial points, else 0.
  • A164955 (program): Sequence obtained from Fibonacci numbers by taking the factorials of each digit and summing.
  • A164961 (program): Triangle read by rows: T[n,m] = quadruple factorials A001813(n) * binomials A007318(n,m)
  • A164965 (program): Cumulative sums of A010892.
  • A164977 (program): Numbers m such that the set {1..m} has only one nontrivial decomposition into subsets with equal element sum.
  • A164978 (program): Number of divisors of n*(n+1)/2 that are >= n.
  • A164981 (program): A triangle with Pell numbers in the first column.
  • A164984 (program): Odd (Jacobsthal) triangle
  • A164985 (program): Denominators of ternary BBP-type series for log(5)
  • A164990 (program): Number of square involutions of n.
  • A164991 (program): Number of triangular involutions of n. A triangular involution is a square involution with at most three faces.
  • A164993 (program): a(n) = image of n under the base-3 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order)
  • A164994 (program): A164993(n)/2
  • A165020 (program): Length of cycle mentioned in A165019
  • A165024 (program): Length of cycle mentioned in A165023
  • A165027 (program): Number of n-digit fixed points under the base-4 Kaprekar map A165012
  • A165051 (program): a(n) = image of n under the base-6 Kaprekar map n -> (n with digits sorted into descending order) - (n with digits sorted into ascending order)
  • A165052 (program): A165051(n)/5
  • A165063 (program): Length of cycle mentioned in A165062
  • A165130 (program): a(n) = (2^(n+4)-1)*(2^n-1).
  • A165133 (program): a(n) = (2^(n+4)-1)*(2^n+1).
  • A165145 (program): Partial sums of A058183.
  • A165147 (program): a(n) = (3*7^n-3^n)/2.
  • A165148 (program): a(n) = (3*8^n-4^n)/2.
  • A165149 (program): a(n) = (3*9^n-5^n)/2.
  • A165150 (program): a(n) = (3*10^n-6^n)/2.
  • A165151 (program): a(n) = (3*11^n-7^n)/2.
  • A165152 (program): a(n) = (3*12^n-8^n)/2.
  • A165154 (program): a(n) = 100*a(n-1) +/- 9^(n-1) for n>0, a(0)=0.
  • A165155 (program): a(n) = 100*a(n-1)+ 11^(n-1) for n>0, a(0)=0.
  • A165156 (program): n^(2*n-1)-(2*n-1)^n.
  • A165157 (program): Zero followed by partial sums of A133622.
  • A165162 (program): Triangle T(n,m) with 2n-1 entries per row, read by rows: the first n entries count down from n to 1, the remaining n-1 entries down from n-1 to 1.
  • A165163 (program): Sequence is obtained from Catalan numbers (A000108) by taking the factorial of each digit and adding them up.
  • A165186 (program): a(n) = Sum_{k=1..n} (k*(n-k) mod n).
  • A165187 (program): a(n) = n^3*(n+1)^2*(n+2)/12.
  • A165188 (program): Interleaving of A014125 and zero followed by A014125.
  • A165189 (program): Partial sums of partial sums of (A001840 interleaved with zeros).
  • A165190 (program): G.f.: 1/((1-x^4)*(1-x^5)).
  • A165191 (program): Irregular triangle B(n,i) = i-th significant bit of Gray code of n.
  • A165192 (program): a(0) = 1, a(1) = 2, a(3) = 3, a(n) = a(n-1) - a(n-3).
  • A165195 (program): Rows of triangle A165194 tend to this sequence; generated from A000110.
  • A165198 (program): Primes from integers by taking the factorial of each digit and adding them up.
  • A165199 (program): a(n) is obtained by flipping every second bit in the binary representation of n starting at the second-most significant bit and on downwards.
  • A165201 (program): Expansion of 1/(1-x*c(x)^3), c(x) the g.f. of A000108.
  • A165202 (program): Expansion of (1+x)/(1 - x + x^2)^2.
  • A165203 (program): Expansion of (1+x)*c(x)^3/(1-x*c(x)^3), c(x) the g.f. of A000108.
  • A165204 (program): Hankel transform of A165203.
  • A165205 (program): a(n) = C(2n-1,n) + C(2n+1,n+1) - C(0,n).
  • A165206 (program): a(n) = (3-4*n)*F(2*n-2) + (4-7*n)*F(2*n-1).
  • A165207 (program): Period 4: repeat [2, 2, 4, 4].
  • A165211 (program): Period 8: repeat [0,1,0,1,1,0,1,0].
  • A165220 (program): Numbers n such that 8*n+1 is a cube.
  • A165221 (program): The Padovan sequence analog of the Fibonacci “rabbit” constant binary expansion. Starting with 0 and using the transitions 0->1,1->10,10->01 the subsequences 0,1,10,01,110,1001,01110,1101001,100101110,011101101001… are formed where each subsequence has P sub n ones and length P sub (n-1) binary digits, where P sub n is the n-th Padovan number. This sequence is the concatenation of all the subsequences. Also note that the n-th subsequence is the concatenation of the n-th-3 and n-th-2 subsequences.
  • A165222 (program): a(n) = (2^(n+4)+1)*(2^n+1).
  • A165224 (program): a(0)=1, a(1)=9, a(n) = 18*a(n-1) - 49*a(n-2) for n > 1.
  • A165225 (program): a(0)=1, a(1)=5, a(n) = 10*a(n-1) - 5*a(n-2) for n > 1.
  • A165226 (program): Numerator of 1 - A164555(n)/A027642(n).
  • A165229 (program): a(n) = 12*a(n-1) - 6*a(n-2), with a(0)=1, a(1)=6.
  • A165230 (program): a(0)=1, a(1)=7, a(n)=14*a(n-1)-7*a(n-2) for n>1 .
  • A165231 (program): a(0)=1, a(1)=8, a(n)=16*a(n-1)-8*a(n-2) for n>1 .
  • A165232 (program): a(0)=1, a(1)=9, a(n)=18*a(n-1)-9*a(n-2) for n>1 .
  • A165233 (program): Signed denominators of terms in series expansion of cos(x)+sin(x).
  • A165240 (program): Integers of the form (a+b+c+..+z)/z where (a,b,c,..,z) is a list of 2 or more distinct consecutive nonprimes.
  • A165241 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,1,0,0,0,0,0,0,0,…] DELTA [1,0,1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A165242 (program): The larger member of the n-th twin prime pair, modulo 8.
  • A165244 (program): The numbers commonly displayed with 7 segments in electric clocks, in ascending order of number of segments lit.
  • A165246 (program): a(n) = (10^n + 53)/9
  • A165247 (program): a(n) = (10^n + 71)/9.
  • A165248 (program): Quintisection A061037(5*n+2).
  • A165253 (program): Triangle T(n,k), read by rows given by [1,0,1,0,0,0,0,0,0,…] DELTA [0,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A165254 (program): a(n) = 9 + n^17.
  • A165256 (program): Numbers whose number of distinct prime factors equals the number of digits in the number.
  • A165257 (program): Triangle in which n-th row is binomial(n+k-1,k), for column k=1..n.
  • A165259 (program): Sum of odd powers of 4 and 9 divided by 13
  • A165263 (program): A sequence similar to the Fibonacci rabbit sequence for the Padovan sequence
  • A165280 (program): If p and q are twin primes then pq + 1 is always divisible by 3, except for (p,q)=(3,5). Sequence gives values of (pq + 1)/3.
  • A165281 (program): a(n) = (n+1)*(6*n^4 - 51*n^3 + 161*n^2 - 251*n + 251).
  • A165283 (program): a(n) = (2*n + 1)*16^n.
  • A165293 (program): Inverse of A038303, and generalization of A130595.
  • A165294 (program): The larger member of a prime pair (p, p+100).
  • A165295 (program): The larger member of a prime pair (p,p + 1000).
  • A165310 (program): a(0)=1, a(1)=3, a(n) = 7*a(n-1) - 9*a(n-2) for n > 1.
  • A165311 (program): a(0)=1, a(1)=4, a(n)=9*a(n-1)-16*a(n-2) for n>1.
  • A165312 (program): a(0)=1, a(1)=5, a(n)=11*a(n-1)-25*a(n-2) for n>1.
  • A165313 (program): Triangle T(n,k) = A091137(k-1) read by rows.
  • A165314 (program): a(0)=1, a(1)=6, a(n)=13*a(n-1)-36*a(n-2) for n>1.
  • A165316 (program): a(n) = the number of digits in the binary representation of n that each either precede and/or follow a similarly valued digit.
  • A165317 (program): a(n) = the number of digits in the binary representation of n that each do not precede or follow a similarly valued digit.
  • A165322 (program): a(0)=1, a(1)=7, a(n)=15*a(n-1)-49*a(n-2) for n>1.
  • A165323 (program): a(0)=1, a(1)=8, a(n)=17*a(n-1)-64*a(n-2) for n>1.
  • A165324 (program): a(0)=1, a(1)=9, a(n)= 19*a(n-1)-81*a(n-2) for n>1.
  • A165326 (program): a(0)=a(1)=1, a(n) = -a(n-1) for n > 1.
  • A165327 (program): E.g.f: Sum_{n>=0} 2^(n(n-1)) * exp(2^n*x) * x^n/n!.
  • A165342 (program): a(n) = A061037(n+2)/A000265(n+4).
  • A165349 (program): Primes p such that (p^2-1)/4-p is also prime.
  • A165351 (program): Numerator of 3*n/2.
  • A165352 (program): Primes of the form p + (p^2 - 1)/8, where p is also prime.
  • A165353 (program): Primes p such that p+(p^2-1)/8 is a prime number.
  • A165355 (program): a(n) = 3n + 1 if n is even, or a(n) = (3n + 1)/2 if n is odd.
  • A165367 (program): Trisection a(n) = A026741(3n + 2).
  • A165372 (program): Number of slanted n X 3 (i=1..n) X (j=i..3+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, and 4 in the lower right corner.
  • A165378 (program): Number of slanted n X 4 (i=1..n) X (j=i..4+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
  • A165392 (program): Number of slanted 2 X n (i=1..2) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 2 neighbors with the same value.
  • A165394 (program): Number of slanted 2 X n (i=1..2) X (j=i..n+i-1) 1..4 arrays with all 1s connected, all 2s connected, all 3s connected, all 4s connected, 1 in the upper left corner, 2 in the upper right corner, 3 in the lower left corner, 4 in the lower right corner, and with no element having more than 3 neighbors with the same value.
  • A165402 (program): a(n) = (10^n*2 - 11)/9.
  • A165403 (program): The positions of zeros in A163898 and A163899.
  • A165404 (program): The positions of zeros in the top row of A163898 (and A163899).
  • A165405 (program): a(0)=1, a(1)=3,a(n)=6*a(n-2)-a(n-1).
  • A165406 (program): Sequence A165404 shown in binary, or equivalently, sequence A163901 in quaternary base.
  • A165407 (program): Expansion of 1/(1-x-x^3*c(x^3)), c(x) the g.f. of A000108.
  • A165410 (program): Hankel transform of the transform of 2^n given by A165409.
  • A165412 (program): Divisors of 2520.
  • A165413 (program): a(n) is the number of distinct lengths of runs in the binary representation of n.
  • A165415 (program): a(n) = the smallest positive integer that contains more digits written in binary than n has written in binary, and which does not contain binary n as a substring in its binary representation.
  • A165420 (program): a(1) = 1, a(2) = 2, a(n) = product of the previous terms for n >= 3.
  • A165421 (program): a(1) = 1, a(2) = 3, a(n) = product of the previous terms for n >= 3.
  • A165422 (program): a(1) = 1, a(2) = 4, a(n) = product of the previous terms for n >= 3.
  • A165431 (program): A transform of the central binomial coefficients.
  • A165433 (program): A transform of the double factorial numbers A001147.
  • A165443 (program): a(n) = ( 16^(2*n+1) + 81^(2*n+1) )/97.
  • A165447 (program): T(n,k) = n^4 - 2*k^2*n^2 + k^4 = A120070(n, k)^2.
  • A165451 (program): Sum of factorial of digits is prime.
  • A165453 (program): Linear interpolation of the sequence that maps an entry of A002378 to the corresponding entry of A006331.
  • A165457 (program): a(n) = (2*n+1)!*(2*n+3)/3.
  • A165458 (program): a(0)=1, a(1)=4, a(n) = 12*a(n-2) - a(n-1).
  • A165470 (program): a(0)=1, a(1)=5, a(n) = 20*a(n-2) - a(n-1).
  • A165478 (program): Positions of zeros in A165477.
  • A165479 (program): a(n) = Least i in range [A165478(n),A165478(n+1)] for which abs(A165477(i)) gets the maximum value in that range.
  • A165491 (program): a(0)=1, a(1)=6, a(n) = 30*a(n-2) - a(n-1).
  • A165505 (program): a(0)=1, a(1)=7, a(n) = 42*a(n-2) - a(n-1).
  • A165506 (program): a(0) = 1, a(1) = 8, a(n) = 56*a(n-2) - a(n-1).
  • A165507 (program): Triangle T(n,m) read by rows: numerator of 1/(1+n-m)^2 - 1/m^2.
  • A165510 (program): a(0)=1, a(1)=9, a(n) = 72*a(n-2) - a(n-1).
  • A165511 (program): a(0)=1, a(1)=10, a(n) = 90*a(n-2) - a(n-1).
  • A165513 (program): Trapezoidal numbers.
  • A165516 (program): Perfect squares (A000290) that can be expressed as the sum of three consecutive triangular numbers (A000217).
  • A165517 (program): Indices of the least triangular numbers (A000217) for which three consecutive triangular numbers sum to a perfect square (A000290).
  • A165518 (program): Perfect squares (A000290) that can be expressed as the sum of four consecutive triangular numbers (A000217).
  • A165520 (program): Antidiagonal writing from three rows trio A165351,A165355,A165367 (first,second and third trisections of A026741).
  • A165530 (program): Number of permutations of length n which avoid the patterns 4321 and 3142.
  • A165538 (program): Number of permutations of length n which avoid the patterns 4312 and 3142.
  • A165543 (program): Number of permutations of length n which avoid the patterns 3241 and 4321.
  • A165552 (program): a(1) = 1, and then a(n) is sum of k*a(k) where k<n and k divides n.
  • A165553 (program): a(n) = (3/2)*(1+(-3)^(n-1)).
  • A165556 (program): A symmetric version of the Josephus problem read modulo 2.
  • A165557 (program): Primes of the form (p^2-1)/4-p where p are also primes.
  • A165559 (program): Product of the arithmetic derivatives from 2 to n.
  • A165560 (program): The arithmetic derivative of n, modulo 2.
  • A165562 (program): Numbers n for which n+n’ is prime, n’ being the arithmetic derivative of n.
  • A165563 (program): a(n) = 1 + 2*n + n^2 + 2*n^3 + n^4.
  • A165568 (program): a(n) = -1 - 2*n + n^2 + 2*n^3 + n^4.
  • A165613 (program): Primes of the form 1 + prime(k) + (prime(k+1))^2, any k.
  • A165618 (program): a(n) = binomial(n+8,8) - 1.
  • A165620 (program): Riordan array ((1-x)/(1-x^4),x/(1+x^2)).
  • A165621 (program): Riordan array (c(x^2)*(1+xc(x^2)), xc(x^2)).
  • A165622 (program): a(n)=(-4)*a(n-1)+8 with a(0)=1.
  • A165625 (program): a(n)=(5/3)*(1+2*(-5)^(n-1)).
  • A165634 (program): Start with x=1 and repeat: if x is a prime number then (append i and then x, with x=prime(i)) else (only append x), continue with x:=x+1.
  • A165635 (program): Primes of the form (p^2 - 3)/2 where p is also prime.
  • A165636 (program): a(n) = A091137(n)/2^n.
  • A165638 (program): a(n)=(6/7)*(2+5*(-6)^(n-1)).
  • A165639 (program): a(n)=(7/4)*(1+3*(-7)^(n-1)).
  • A165640 (program): Number of distinct multisets of n integers, each of which is -2, +1, or +3, such that the sum of the members of each multiset is 3.
  • A165641 (program): A091137(n) / A001316(n) .
  • A165652 (program): Number of disconnected 2-regular graphs on n vertices.
  • A165662 (program): Period 5: repeat 4,4,8,6,8.
  • A165663 (program): Decimal expansion of 3 + sqrt(3).
  • A165664 (program): First digit of the decimal expansion of (n^2-2)/7 after the decimal point.
  • A165665 (program): a(n) = (3*2^n - 2) * 2^n.
  • A165669 (program): First digit of the decimal expansion of (n^2+2)/7 after the decimal point.
  • A165674 (program): Triangle generated by the asymptotic expansions of the E(x,m=2,n).
  • A165675 (program): Triangle read by rows. T(n, k) = (n - k + 1)! * H(k, n - k), where H are the hyperharmonic numbers. For 0 <= k <= n.
  • A165676 (program): Fourth right hand column of triangle A165674
  • A165677 (program): Fifth right hand column of triangle A165674
  • A165678 (program): Sixth right hand column of triangle A165674.
  • A165679 (program): Seventh right hand column of triangle A165674
  • A165680 (program): Triangle of the divisors of the coefficients of triangles A138771 and A165675
  • A165682 (program): Primes p such that 3*p*(p-1)+1 is also prime.
  • A165683 (program): Primes of form 3*p*(p-1)+1 with p also a prime.
  • A165684 (program): Dimension of the space of Siegel cusp forms of genus 2 and dimension 2n (associated with full modular group Gamma_2).
  • A165686 (program): Dimension of the space of Siegel cusp forms of genus 2 and weight 2k which are not Saito-Kurokawa lifts of forms of genus 1.
  • A165717 (program): Integers of the form k*(5+k)/4.
  • A165718 (program): Integers of the form k*(k+7)/6.
  • A165719 (program): Integers of the form k*(k+9)/8.
  • A165720 (program): Integers of the form k*(k+11)/10.
  • A165721 (program): Integers of the form k*(k+13)/12.
  • A165722 (program): Positive integers k such that the sum of decimal digits of (16^k - 1) equals 6*k.
  • A165723 (program): The (d+1)th digit after the decimal point in the decimal representation of 1/n, where d is the number of digits of n.
  • A165725 (program): Largest divisor of n coprime to 30. I.e., a(n) = max { k | gcd(n, k) = k and gcd(k, 30) = 1 }.
  • A165728 (program): If we divide the sequence into these subsequences, the pattern is obvious. {{1,1}, {0,1}, {1,1}}, {{0,1,0,1}, {1,1,1,1}, {0,1,0,1}}, {{1,1,1,1,1,1,1,1}, {0,1,0,1,0,1,0,1}, {1,1,1,1,1,1,1,1}}, {{0,1,0,1,0,1,0,1,0,1,0,1,0,1,0}, {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}, {0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1}}, …
  • A165734 (program): Period 2: repeat 6,30.
  • A165735 (program): Surviving integers under the double-count Josephus problem (see A054995), modulo 3.
  • A165743 (program): The greatest common divisor of n and 210.
  • A165746 (program): a(n) = 3 - 2*3^n.
  • A165747 (program): a(n) = 1-2n.
  • A165748 (program): a(n) = (8/9)*(2+7*(-8)^(n-1)).
  • A165749 (program): a(n) = (9/5)*(1+4*(-9)^(n-1)).
  • A165750 (program): a(n) = (10/11)*(2+9*(-10)^(n-1)).
  • A165751 (program): a(n) = 4 - 3*2^n.
  • A165752 (program): a(n) = (8-5*4^n)/3.
  • A165753 (program): Number of trailing zeros in sequence of factorials of Fibonacci numbers.
  • A165754 (program): a(n) = nimsum(n+(n+1)+(n+2)).
  • A165755 (program): a(n) = (5-3*5^n)/2.
  • A165758 (program): a(n) = (12-7*6^n)/5.
  • A165759 (program): a(n) = (7-4*7^n)/3.
  • A165760 (program): a(n) = (16-9*8^n)/7.
  • A165775 (program): n + (least square >= n), i.e., n + A048761(n).
  • A165776 (program): n + (least square > n), i.e., n + A048761(n+1).
  • A165781 (program): a(n) = (2^A002326(n)-1)/(2*n+1).
  • A165783 (program): a(n) = A002326(n-1) + A000120(A165781(n-1)).
  • A165789 (program): a(n) is the smallest positive integer k that when written in binary, and leading 0’s of k are ignored, contains the reversal of the digits of binary n.
  • A165792 (program): a(0)=1, a(n) = n*(a(n-1)+2).
  • A165793 (program): a(0)=1, a(n)=n*(a(n-1)-2).
  • A165795 (program): Array A(n, k) = numerator of 1/n^2 - 1/k^2 with A(0,k) = 1 and A(n,0) = -1, read by antidiagonals.
  • A165797 (program): a(n) = n^( sigma(n) - tau(n) ).
  • A165798 (program): a(n) = 65*n^2.
  • A165800 (program): Powers of 50.
  • A165801 (program): f(n), f(f(n)), … are all prime, where f(n) = (n-1)/2. Stop when f(…f(n)…) is less than 4.
  • A165804 (program): Numbers of the form i*8^j-1 (i=1..7, j >= 0).
  • A165805 (program): Integers that start a trajectory x -> A008619(x) which contains only primes until terminating at 2 or 3.
  • A165806 (program): a(n) = 15n^2 + 3n + 1.
  • A165810 (program): Primes p such that 18*p+1 is also a prime.
  • A165811 (program): Primes of the form 18*p+1, where p is also a prime.
  • A165813 (program): a(n) = n*(a(n-1)+3), a(0)=1.
  • A165814 (program): a(n)=n*(a(n-1)-3), a(0)=1.
  • A165817 (program): Number of compositions (= ordered integer partitions) of n into 2n parts.
  • A165824 (program): Totally multiplicative sequence with a(p) = 3.
  • A165825 (program): Totally multiplicative sequence with a(p) = 4.
  • A165826 (program): Totally multiplicative sequence with a(p) = 5.
  • A165827 (program): Totally multiplicative sequence with a(p) = 6.
  • A165828 (program): Totally multiplicative sequence with a(p) = 7.
  • A165829 (program): Totally multiplicative sequence with a(p) = 8.
  • A165830 (program): Totally multiplicative sequence with a(p) = 9.
  • A165831 (program): Totally multiplicative sequence with a(p) = 10.
  • A165832 (program): Totally multiplicative sequence with a(p) = 11.
  • A165833 (program): Totally multiplicative sequence with a(p) = 12.
  • A165834 (program): Totally multiplicative sequence with a(p) = 13.
  • A165835 (program): Totally multiplicative sequence with a(p) = 14.
  • A165836 (program): Totally multiplicative sequence with a(p) = 15.
  • A165837 (program): Totally multiplicative sequence with a(p) = 16.
  • A165838 (program): Totally multiplicative sequence with a(p) = 17.
  • A165839 (program): Totally multiplicative sequence with a(p) = 18.
  • A165840 (program): Totally multiplicative sequence with a(p) = 19.
  • A165841 (program): Totally multiplicative sequence with a(p) = 20.
  • A165842 (program): Totally multiplicative sequence with a(p) = 21.
  • A165843 (program): Totally multiplicative sequence with a(p) = 22.
  • A165844 (program): Totally multiplicative sequence with a(p) = 23.
  • A165845 (program): Totally multiplicative sequence with a(p) = 24.
  • A165846 (program): Totally multiplicative sequence with a(p) = 25.
  • A165847 (program): Totally multiplicative sequence with a(p) = 26.
  • A165848 (program): Totally multiplicative sequence with a(p) = 27.
  • A165849 (program): Totally multiplicative sequence with a(p) = 28.
  • A165850 (program): Totally multiplicative sequence with a(p) = 29.
  • A165851 (program): Totally multiplicative sequence with a(p) = 30.
  • A165852 (program): Totally multiplicative sequence with a(p) = 31.
  • A165853 (program): Totally multiplicative sequence with a(p) = 32.
  • A165854 (program): Totally multiplicative sequence with a(p) = 33.
  • A165855 (program): Totally multiplicative sequence with a(p) = 34.
  • A165856 (program): Totally multiplicative sequence with a(p) = 35.
  • A165857 (program): Totally multiplicative sequence with a(p) = 36.
  • A165858 (program): Totally multiplicative sequence with a(p) = 37.
  • A165859 (program): Totally multiplicative sequence with a(p) = 38.
  • A165860 (program): Totally multiplicative sequence with a(p) = 39.
  • A165861 (program): Totally multiplicative sequence with a(p) = 40.
  • A165862 (program): Totally multiplicative sequence with a(p) = 41.
  • A165863 (program): Totally multiplicative sequence with a(p) = 42.
  • A165864 (program): Totally multiplicative sequence with a(p) = 43.
  • A165865 (program): Totally multiplicative sequence with a(p) = 44.
  • A165866 (program): Totally multiplicative sequence with a(p) = 45.
  • A165867 (program): Totally multiplicative sequence with a(p) = 46.
  • A165868 (program): Totally multiplicative sequence with a(p) = 47.
  • A165869 (program): Totally multiplicative sequence with a(p) = 48.
  • A165870 (program): Totally multiplicative sequence with a(p) = 49.
  • A165871 (program): Totally multiplicative sequence with a(p) = 50.
  • A165872 (program): Totally multiplicative sequence with a(p) = - 2.
  • A165886 (program): a(n) = A165641(n+1)/A165641(n).
  • A165897 (program): a(n) = a(n-1) + largest proper divisor of a(n-1), a(1)=4.
  • A165900 (program): Values of Fibonacci polynomial n^2 - n - 1.
  • A165901 (program): a(0)=0, a(1)=1, a(n) = a(n-1) + 2^(n-3)*a(n-2).
  • A165902 (program): a(0)=0, a(1)=1, a(n) = a(n-1) + 3^(n-3)*a(n-2).
  • A165903 (program): a(n) = (a(n-1)^2 + a(n-2)^2 + a(n-1)*a(n-2))/a(n-3) with three initial ones.
  • A165904 (program): Somos-4 recurrence with a(i)=2^i for 0<=i<=3.
  • A165905 (program): Somos-4 recurrence with a(0)=1, a(1)=2, a(2)=4, a(3)=16
  • A165907 (program): Minimal m for packing the first n primes in a prime(n) X m rectangle
  • A165922 (program): Decimal expansion of 2*sqrt(3)/(9*Pi).
  • A165928 (program): a(n) = 2^(n^2)*(2^(2n+1)/3 + 1/3).
  • A165930 (program): a(1) = 1, for n > 1: a(n) = tau(sum of the previous terms) where tau(k) = number of the divisors of k.
  • A165933 (program): Least integer, k, whose value is n in A165413.
  • A165935 (program): a(n) = (-1)^(n-1)*n*(4n^2-5)^2.
  • A165937 (program): G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)*x^n/n ).
  • A165938 (program): a(n) = A002203(n^2) for n>=1.
  • A165943 (program): Heptasection A061037(7*n+2).
  • A165944 (program): Primes of the form p^2 +3p + 1, where p is also a prime.
  • A165947 (program): Primes of the form 2q + 3 where q is composite.
  • A165949 (program): a(n) = A027762(n)/A165734(n).
  • A165951 (program): a(n) = (Sum of the quadratic non-residues of prime(n) - Sum of the quadratic residues of prime(n)) / prime(n)
  • A165952 (program): Decimal expansion of 2*sqrt(3)/(3*Pi).
  • A165955 (program): n-th odd nonprime plus n-th even nonprime.
  • A165957 (program): Product of the digits of the n-th nonprime.
  • A165958 (program): The digits on a number pad from lower right to upper left.
  • A165960 (program): Number of permutations of length n without modular 3-sequences.
  • A165961 (program): Number of circular permutations of length n without 3-sequences.
  • A165966 (program): Triangular numbers that are sums of twin prime pairs.
  • A165968 (program): Number of pairings disjoint to a given pairing, and containing a given pair not in the given pairing.
  • A165971 (program): The n-th odd nonprime minus the n-th even nonprime.
  • A165972 (program): Nonprimes k such that the sum of the smallest and largest divisor of k is prime.
  • A165978 (program): Largest prime factor of number formed from a(n-1) with a 1 added at the end, a(1)=2.
  • A165983 (program): Period 16: repeat 1,1,1,2,1,1,1,2,1,1,1,4,1,1,1,4.
  • A165984 (program): Number of ways to put n indistinguishable balls into n^3 distinguishable boxes.
  • A165986 (program): Even semiprimes n such that (the largest prime factor of n) + 4 is prime.
  • A165988 (program): First trisection of A022998.
  • A165993 (program): a(n) = sum_{j=1..prime(n)-1} floor (j^2/prime(n)).
  • A165994 (program): a(n) is the number of nonzero values of floor (j^2/prime(n)), over 1 <= j < prime(n).
  • A165998 (program): Denominators of Taylor series expansion of 1/(3*x)*log((1+x)/(1-x)^2)
  • A166005 (program): Primes p such that 8*p+15 is also a prime.
  • A166006 (program): Distance from the origin using the binary expansion of Pi to walk the number line: Start at the origin; subtract one for each ‘0’ digit, and add one for each ‘1’ digit.
  • A166008 (program): Number of ones in the binary representation of the average of twin prime pairs.
  • A166009 (program): Primes of the form 7 + 2*p, where p is a prime.
  • A166010 (program): a(n) = prime(n)^2-4.
  • A166011 (program): Least common multiple of prime(n)-3 and prime(n)+3.
  • A166012 (program): a(n) = 2*(A000045(n)-(n mod 2)) + 1 + (n mod 2).
  • A166013 (program): Inverse permutation to A138606.
  • A166021 (program): a(n) = 2*A000124(A003056(n-1)) if A002262(n-1)=0, otherwise a(n-1)+1.
  • A166022 (program): a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +3*a(n-4) -2*a(n-5) for n > 4, with initial values as shown.
  • A166023 (program): a(n) = 6*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
  • A166024 (program): Define dsf(n) = A045503(n) = n_1^{n_1}+n_2^{n_2}+n_3^{n_3} + n_m^{n_m}, where {n_1,n_2,n_3,…n_m} is the list of the decimal digits of n. dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.
  • A166025 (program): a(0) = 6, a(1) = 17, a(n+1) = a(n) + a(n-1) for n>0.
  • A166027 (program): a(n) = 6*a(n-2) for n > 2; a(1) = 4, a(2) = 1.
  • A166033 (program): a(n) = 11/4 +11*n/2 + 29*(-1)^n/4.
  • A166035 (program): a(n) = (3^n+6*(-4)^n)/7.
  • A166036 (program): a(n) = (4^n+8*(-5)^n)/9.
  • A166037 (program): Numbers that are the sum of 2 successive nonprimes A141468.
  • A166039 (program): Sums of three consecutive nonprimes A141468.
  • A166060 (program): a(n) = 4*3^n - 3*2^n.
  • A166061 (program): 19-rough numbers: positive integers that have no prime factors less than 19.
  • A166063 (program): 23-rough numbers: positive integers that have no prime factors less than 23.
  • A166065 (program): Triangle, read by rows, given by [0,1,1,0,0,0,0,0,0,0,…] DELTA [2,-1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A166067 (program): Fibonacci sequence beginning 1, 69.
  • A166070 (program): Sorted sequence of primes and multiply perfect numbers.
  • A166074 (program): a(n) = n^2 - [largest Fibonacci number <= n^2].
  • A166077 (program): a(n)=2^(n(3n-1)/2).
  • A166078 (program): Expansion of (3(1-x)-sqrt(1+6x-7x^2))/(2(1-x)(1-2x)).
  • A166079 (program): Given a row of n payphones, all initially unused, how many people can use the payphones, assuming (1) each always chooses one of the most distant payphones from those in use already, (2) the first person takes a phone at the end, and (3) no people use adjacent phones?
  • A166080 (program): Nonprimes of the form (k^2+1)/2.
  • A166081 (program): Natural numbers that not are the sum of two distinct primes.
  • A166101 (program): Integers k such that A166100(k)/A005408(k) is not an integer.
  • A166102 (program): Odd numbers k such that A166100((k-1)/2)/k is not an integer.
  • A166103 (program): Squares of A166104.
  • A166104 (program): Natural numbers whose prime factors are all congruent to 3 or 5 mod 6 (i.e., are in the sequence A045410).
  • A166105 (program): Quadratic recurrence from Sylvester’s sequence, but starting with a(0)=1 and a(1)=2.
  • A166106 (program): a(n) = a(n-1) + a(n-2) + F(n), with a(0) = 0, a(1) = 1, a(2) = a(1) + a(0), a(3) = a(2) + a(1), a(4) = a(3) + a(2) + 2.
  • A166114 (program): a(n) = (6-(-4)^n)/5.
  • A166117 (program): a(0)=0, a(1)=1, a(2)=2 and a(n) = a(n-1) - 2a(n-2) + a(n-3).
  • A166118 (program): Fixed points of the mapping f(x) = (x + 2^x) mod (17 + x).
  • A166119 (program): a(n)=A165966(n)/12.
  • A166120 (program): a(n) = A027642(n-1) / A089026(n).
  • A166122 (program): a(n) = (7-(-5)^n)/6.
  • A166123 (program): If n is prime, a(n) = 1; otherwise, a(n) is gcd(n, d) where d is the denominator of the (n-1)-th Bernoulli number.
  • A166124 (program): Triangle, read by rows, given by [0,1/2,1/2,0,0,0,0,0,0,0,…] DELTA [2,-1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A166125 (program): Decimal expansion of sqrt(229).
  • A166126 (program): Decimal expansion of 1/(imaginary part of (15+2*I)^(1/2))^2.
  • A166127 (program): Minimum value of j such that floor(j^2 / prime(n)) > 0.
  • A166132 (program): a(n) = 1 + (4*9^n - 9*4^n) / 5.
  • A166135 (program): Number of possible paths to each node that lies along the edge of a cut 4-nomial tree, that is rooted one unit from the cut.
  • A166136 (program): a(n) = n*(n+3)/2 + 7.
  • A166137 (program): a(n) = 5*n*(n+1)/2 - 4.
  • A166138 (program): Trisection A022998(3n+1).
  • A166139 (program): Triangle T(n,k) read by rows. A080305(A126988(n,k)) if k|n, 0 otherwise.
  • A166140 (program): Product of the nonzero elements of the n-th row of A166139.
  • A166142 (program): Row products of A166141; Product of such divisors of n that are squarefree and have an even number of prime factors.
  • A166143 (program): a(n) = 3*n^2 + 3*n - 5.
  • A166144 (program): a(n) = (11*n^2 + 11*n - 20)/2.
  • A166146 (program): a(n) = (7*n^2 + 7*n - 12)/2.
  • A166147 (program): a(n) = 4n^2 + 4n - 7.
  • A166148 (program): a(n) = (9*n^2 + 9*n - 16)/2.
  • A166149 (program): a(n) = (5^n + 10*(-6)^n)/11.
  • A166150 (program): a(n) = 5n^2 + 5n - 9.
  • A166151 (program): (5n^2 + 5n - 6)/2.
  • A166152 (program): a(n) = (6^n+12*(-7)^n)/13.
  • A166153 (program): a(n) = (7^n+14*(-8)^n)/15.
  • A166154 (program): 7*n*(n+1)/2 - 5.
  • A166155 (program): Numbers n such that number of divisors of n + number of perfect partitions of (n-1) is prime.
  • A166157 (program): a(n) = (8^n+16*(-9)^n)/17.
  • A166160 (program): a(n) = (n-th odd prime + n-th odd nonprime)/2 - 1.
  • A166168 (program): G.f.: exp( Sum_{n>=1} Lucas(n^2)*x^n/n ) where Lucas(n) = A000204(n).
  • A166169 (program): a(n) = Lucas(n^2) = A000204(n^2) for n >= 1.
  • A166173 (program): Digit sum of n-th twin prime pair.
  • A166189 (program): Number of 3 X 3 X 3 triangular nonnegative integer arrays with all sums of an element and its neighbors <= n.
  • A166213 (program): Number of 5 X 5 X 5 triangular nonnegative integer arrays, symmetric under 120 degree rotation, with all sums of an element and its neighbors <= n.
  • A166226 (program): Bell number n modulo n.
  • A166228 (program): Alternating sum of large Schroeder numbers.
  • A166229 (program): Expansion of (1-2x-sqrt(1-8x+8x^2))/(2x).
  • A166231 (program): a(n) = 2^C(n+1,2)*A006012(n).
  • A166232 (program): a(n) = A166231(n)/4^n.
  • A166236 (program): Absolute value of (n-th odd prime minus n-th odd nonprime)/2.
  • A166237 (program): Differences between consecutive products of two distinct primes: a(n) = A006881(n+1) - A006881(n).
  • A166238 (program): Horizontal para-Narayana sequence: says which column of 3rd-order Zeckendorf array (starting column count at 0) contains n.
  • A166242 (program): Sequence generated from A014577, the dragon curve.
  • A166245 (program): Numbers n such that the Collatz trajectory of n (iterate T(k)=k/2 if k is even, (3k+1)/2 if k is odd, A014682, starting at n and stopping if you reach 1) never exceeds n.
  • A166247 (program): Number of perfect partitions of n-1 plus sum of remainders of n mod k, for k=1,2,3,..,n.
  • A166248 (program): a(n) is the absolute value of n minus sum of all the remainders modulo the numbers below n.
  • A166249 (program): a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3, a(0)=a(1)=1, a(2)=0, a(3)=2.
  • A166250 (program): a(n) = n-1 plus the largest proper divisor of n.
  • A166253 (program): String substitution 0 -> 01110, 1 -> 10001, started with 1.
  • A166257 (program): Odd numbers not of the form prime(k) + phi(prime(k)).
  • A166260 (program): a(n) = A089026(n) - 1.
  • A166265 (program): Numbers of the form 1+x^2+y^2, x, y integers >= 1.
  • A166266 (program): Number of 1’s in binary expansion of A000110(n).
  • A166267 (program): Number of 1’s in the binary representation of A000129(n).
  • A166279 (program): Triangle, read by rows: T(0,0) = 1, T(n,k) = T(n-1,k-1) (mod 2) + T(n-1,k) (mod 2), T(n,k) = 0 if k < 0 or k > n.
  • A166280 (program): Stirling2 triangle mod 2, T(n,k) = A008277(n,k) mod 2.
  • A166281 (program): Number of perfect partitions of the nonprimes A018252.
  • A166282 (program): Matrix inverse of Sierpinski’s triangle (A047999, Pascal’s triangle mod 2).
  • A166287 (program): Number of peak plateaux in all Dyck paths of semilength n with no UUU’s and no DDD’s (U=(1,1), D=(1,-1)).
  • A166289 (program): Number of Dyck paths with no UUU’s and no DDD’s, of semilength n and having no UDUD’s (U=(1,1), D=(1,-1)).
  • A166290 (program): Number of UDUD’s in all Dyck paths of semilength n with no UUU’s and no DDD’s (U=(1,1), D=(1,-1)).
  • A166294 (program): Number of peaks at even level in all Dyck paths of semilength n with no UUU’s and no DDD’s, (U=(1,1), D=(1,-1)). These Dyck paths are counted by the secondary structure numbers (A004148).
  • A166297 (program): Number of UUDUDD’s starting at level 0 in all Dyck paths of semilength n with no UUU’s and no DDD’s (U=(1,1), D=(1,-1)).
  • A166300 (program): Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no UUDD’s starting at level 0.
  • A166304 (program): Third trisection of A022998.
  • A166305 (program): Even semiprimes k such that the largest prime factor + 8 is a prime. Also semiprimes k such that k+16 is semiprime.
  • A166306 (program): Denominator of Bernoulli_n multiplied by the sum of the associated inverse primes in the Staudt-Clausen theorem, n=1, 2, 4, 6, 8, 10,…
  • A166311 (program): Numbers whose sum of digits is 11.
  • A166312 (program): Number of 1’s in binary expansion of A000326(n).
  • A166314 (program): Number of 1’s in binary expansion of A000124(n).
  • A166329 (program): Products of squares of 2 successive primes.
  • A166333 (program): The largest prime that divides A027642(n) (the denominator of the Bernoulli number B_n), or 1 if A027642(n) is 1.
  • A166334 (program): a(n) = (3*n)!/(2^n*n!).
  • A166335 (program): Exponential Riordan array [1+x*sinh(x), x].
  • A166336 (program): Expansion of (1 - 4*x + 7*x^2 - 4*x^3 + x^4)/(1 - 7*x + 17*x^2 - 17*x^3 + 7*x^4 - x^5).
  • A166337 (program): a(n)=(2n+0^n)*C(4n,2n).
  • A166338 (program): a(n) = (4*n)!/n!.
  • A166350 (program): Table T(n,m) = m! read by rows.
  • A166356 (program): Expansion of e.g.f. 1 + x*arctanh(x), even powers only.
  • A166357 (program): Exponential Riordan array [1+x*arctanh(x), x].
  • A166358 (program): Row sums of exponential Riordan array [1+x*arctanh(x), x], A166357.
  • A166359 (program): Diagonal sums of the exponential Riordan array [1+x*arctanh(x), x], A166357.
  • A166360 (program): Triangle of Narayana numbers mod 2, T(n,k) = A001263(n,k) mod 2.
  • A166361 (program): Scale degrees of the roots of chords in a traditional “twelve-bar blues” in Western music.
  • A166362 (program): a(n) = phi(nonprime(n)).
  • A166370 (program): Numbers whose sum of digits is 17.
  • A166373 (program): Triangle read by rows for floor(j^2 / n) with n >= 2 and 1<=j<n.
  • A166375 (program): a(n) = sum (floor (j^2/n)) taken over 1 <= j <= n-1.
  • A166380 (program): Diagonal sums of exponential Riordan array [1+x^2*sec(x),x], A166378.
  • A166381 (program): a(n) = Sum_{j>n} floor(n^2/j).
  • A166387 (program): a(n) = sum (floor (j^2/n), 1 <= j <= n-1) - floor ((n-1)(n-2)/3), n >= 2.
  • A166389 (program): Multiples of 7 whose reversal + 1 is also a multiple of 7.
  • A166390 (program): Multiples of 13 whose reversal + 1 is also a multiple of 13.
  • A166394 (program): Multiples of 7 whose reversal - 1 is also a multiple of 7.
  • A166397 (program): Multiples of 13 whose reversal - 1 is also a multiple of 13.
  • A166401 (program): Positive integers n where (the largest divisor of n that is <= sqrt(n)) divides (the smallest divisor of n that is >= sqrt(n)).
  • A166444 (program): a(0) = 0, a(1) = 1 and for n > 1, a(n) = sum of all previous terms.
  • A166445 (program): Hankel transform of A025276.
  • A166446 (program): Period 12: repeat [1,1,1,1,0,0,-1,-1,-1,-1,0,0].
  • A166447 (program): a(n) = n*round(sqrt(n)).
  • A166448 (program): Sum of first n primes minus next prime.
  • A166450 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 6.
  • A166452 (program): Binomial transform of A166242
  • A166453 (program): Triangle read by rows, square of Sierpinski’s gasket, (A047999)^2
  • A166454 (program): Triangle read by rows: T(n, k) = (1/2)*(A007318(n,k) - A047999(n,k)).
  • A166456 (program): Row sums of triangle A166455.
  • A166457 (program): Numbers n such that n*100+1 is prime.
  • A166458 (program): Numbers k such that 10*k - (-1)^k is prime.
  • A166459 (program): Numbers whose sum of digits is 19.
  • A166460 (program): Numbers k such that k + (-1)^k is not prime.
  • A166464 (program): a(n) = (3+2n+6n^2+4n^3)/3.
  • A166465 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1, a(2) = 5.
  • A166466 (program): Trisection a(n) = A000265(3n).
  • A166469 (program): Number of divisors of n which are not multiples of consecutive primes.
  • A166470 (program): a(n) = 2^F(n+1)*3^F(n), where F(n) is the n-th Fibonacci number, A000045(n).
  • A166474 (program): a(1)=1; a(2)=2; for n>2, a(n)=a(n-1)+A000217(n-1)*a(n-2).
  • A166479 (program): Lesser of twin primes, written in base 6.
  • A166480 (program): Greater of twin primes, written in base 6.
  • A166481 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 7.
  • A166482 (program): a(n) = Sum_{k=0..n} binomial(n+k,2k)*Fibonacci(2k+1).
  • A166486 (program): Periodic sequence [0,1,1,1] of length 4.
  • A166492 (program): Table of numerators of A120070(n,m)/A002260(n,m), 1 <= m < n.
  • A166494 (program): Irregular triangle T(n,k) = greatest common divisor of n-th row terms of A143753.
  • A166496 (program): Prime plus the next composite.
  • A166502 (program): The n-th power of the product prime(n)*prime(n+1) of 2 successive primes.
  • A166514 (program): Zig-zag function for first two columns of a matrix (take numbers in consecutive pairs).
  • A166515 (program): Partial sum of A166514.
  • A166516 (program): A product of consecutive doubled Fibonacci numbers.
  • A166517 (program): a(n) = (3 + 5*(-1)^n + 6*n)/4.
  • A166519 (program): a(n) = 1 + 2*(-1)^n + 2*n.
  • A166520 (program): a(n) = (10*n + 11*(-1)^n + 5)/4.
  • A166521 (program): a(n) = (6*n + 7*(-1)^n + 3)/2.
  • A166522 (program): a(n) = 7*n - a(n-1), with a(1) = 1.
  • A166523 (program): a(n) = 8*n - a(n-1), with n>1, a(1)=1.
  • A166524 (program): a(n) = 9*n - a(n-1), with n>1, a(1)=1.
  • A166525 (program): a(n) = 10*n - a(n-1), with n>1, a(1)=1.
  • A166526 (program): a(n) = 12*n - a(n-1), with n>1, a(1)=1.
  • A166527 (program): Complement of A076537.
  • A166536 (program): A product of consecutive doubled Fibonacci numbers.
  • A166539 (program): a(n) = (10*n + 7*(-1)^n + 5)/4.
  • A166542 (program): a(n) = 6*n - a(n-1), with n>1, a(1)=2.
  • A166544 (program): a(n) = 7*n - a(n-1), with n>1, a(1)=2.
  • A166545 (program): a(n) = 13*n - a(n-1), (with a(1)=13).
  • A166546 (program): Natural numbers n such that d(n) + 1 is prime.
  • A166547 (program): Primes of the form 100*n+7.
  • A166549 (program): The number of halving steps of the Collatz 3x+1 map to reach 1 starting from 2n-1.
  • A166552 (program): a(n) = 3*a(n-2) for n > 2; a(1) = 1; a(2) = 4.
  • A166554 (program): a(0)=1, a(n) = n*(a(n-1)-1) for n>0.
  • A166555 (program): Triangle read by rows, Sierpinski’s gasket, A047999 * (1,2,4,8,…) diagonalized.
  • A166556 (program): Triangle read by rows, A000012 * A047999
  • A166560 (program): Primes of the form 100*n+9.
  • A166563 (program): Numbers n such that 12*n+5 is not prime.
  • A166569 (program): Numbers n such that 12*n+7 is not prime.
  • A166570 (program): Numbers n such that 12*n+11 is not prime.
  • A166574 (program): If p, q are successive primes, and there is a number k with p < k <= q such that r = p+k is a prime, then r is in the sequence.
  • A166575 (program): Primes p>=5 with the property: if Prime(k)<p/2<Prime(k+1), then p>=Prime(k)+ Prime(k+1)
  • A166577 (program): Inverse binomial transform of A166517.
  • A166578 (program): a(n) = a(n-3) + 2^(n-4) with a(1) = 1, a(2) = 2, a(3) = 1.
  • A166586 (program): Totally multiplicative sequence with a(p) = p - 2 for prime p.
  • A166587 (program): A signed variant of the Motzkin numbers.
  • A166588 (program): Partial sums of A097331; binomial transform of A166587.
  • A166589 (program): Totally multiplicative sequence with a(p) = p-3 for prime p.
  • A166590 (program): Totally multiplicative sequence with a(p) = p+2 for prime p.
  • A166591 (program): Totally multiplicative sequence with a(p) = p+3 for prime p.
  • A166592 (program): Hankel transform of A166588(n-1).
  • A166593 (program): Partial sums of A166592.
  • A166594 (program): Maximal prime gap q-p encountered from 0 to least prime > n.
  • A166595 (program): The number of vertices of a hypercube modulo the number of largest-dimensional surface tiles, in the first fourteen cases of the residue being greater than the dimension number.
  • A166597 (program): Let p = largest prime <= n, with p(0)=p(1)=0, and let q = smallest prime > n; then a(n) = q-p.
  • A166598 (program): a(n) = 5*n - a(n-1), with n>1, a(1)=5.
  • A166602 (program): Numbers k such that Sum_{i=1..k} i^2 divides Product_{i=1..k} i^2.
  • A166621 (program): a(n) = 10*n - a(n-1), with n>1, a(1)=5.
  • A166624 (program): Totally multiplicative sequence with a(p) = 3p for prime p.
  • A166625 (program): Totally multiplicative sequence with a(p) = 4p for prime p.
  • A166626 (program): Totally multiplicative sequence with a(p) = 5p for prime p.
  • A166627 (program): Totally multiplicative sequence with a(p) = 6p for prime p.
  • A166628 (program): Totally multiplicative sequence with a(p) = 7p for prime p.
  • A166629 (program): Totally multiplicative sequence with a(p) = 8p for prime p.
  • A166630 (program): Totally multiplicative sequence with a(p) = 9p for prime p.
  • A166631 (program): Totally multiplicative sequence with a(p) = 10p for prime p.
  • A166632 (program): Totally multiplicative sequence with a(p) = 2*(p-1) for prime p.
  • A166633 (program): Totally multiplicative sequence with a(p) = 3*(p-1) for prime p.
  • A166634 (program): Totally multiplicative sequence with a(p) = 4*(p-1) for prime p.
  • A166635 (program): Totally multiplicative sequence with a(p) = 5*(p-1) for prime p.
  • A166636 (program): Totally multiplicative sequence with a(p) = 6*(p-1) for prime p.
  • A166637 (program): Totally multiplicative sequence with a(p) = 7*(p-1) for prime p.
  • A166638 (program): Totally multiplicative sequence with a(p) = 8*(p-1) for prime p.
  • A166639 (program): a(n) = 6*n + 3 + 4*(-1)^n.
  • A166640 (program): Totally multiplicative sequence with a(p) = 9*(p-1) for prime p.
  • A166641 (program): Totally multiplicative sequence with a(p) = 10*(p-1) for prime p.
  • A166642 (program): Totally multiplicative sequence with a(p) = 2*(p+1) for prime p.
  • A166643 (program): Totally multiplicative sequence with a(p) = 3*(p+1) for prime p.
  • A166644 (program): Totally multiplicative sequence with a(p) = 4*(p+1) for prime p.
  • A166645 (program): Totally multiplicative sequence with a(p) = 5*(p+1) for prime p.
  • A166646 (program): Totally multiplicative sequence with a(p) = 6*(p+1) for prime p.
  • A166647 (program): Totally multiplicative sequence with a(p) = 7*(p+1) for prime p.
  • A166648 (program): Totally multiplicative sequence with a(p) = 8*(p+1) for prime p.
  • A166649 (program): Totally multiplicative sequence with a(p) = 9*(p+1) for prime p.
  • A166650 (program): Totally multiplicative sequence with a(p) = 10*(p+1) for prime p.
  • A166651 (program): Totally multiplicative sequence with a(p) = 2p-1 for prime p.
  • A166652 (program): Totally multiplicative sequence with a(p) = 3p-1 for prime p.
  • A166653 (program): Totally multiplicative sequence with a(p) = 4p-1 for prime p.
  • A166654 (program): Totally multiplicative sequence with a(p) = 5p-1 for prime p.
  • A166655 (program): Totally multiplicative sequence with a(p) = 6p-1 for prime p.
  • A166656 (program): Totally multiplicative sequence with a(p) = 7p-1 for prime p.
  • A166657 (program): Totally multiplicative sequence with a(p) = 8p-1 for prime p.
  • A166658 (program): Totally multiplicative sequence with a(p) = 9p-1 for prime p.
  • A166659 (program): Totally multiplicative sequence with a(p) = 10p-1 for prime p.
  • A166660 (program): Totally multiplicative sequence with a(p) = 2p+1 for prime p.
  • A166661 (program): Totally multiplicative sequence with a(p) = 3p+1 for prime p.
  • A166662 (program): Totally multiplicative sequence with a(p) = 4p+1 for prime p.
  • A166663 (program): Totally multiplicative sequence with a(p) = 5p+1 for prime p.
  • A166664 (program): Totally multiplicative sequence with a(p) = 6p+1 for prime p.
  • A166665 (program): Totally multiplicative sequence with a(p) = 7p+1 for prime p.
  • A166666 (program): Totally multiplicative sequence with a(p) = 8p+1 for prime p.
  • A166667 (program): Totally multiplicative sequence with a(p) = 9p+1 for prime p.
  • A166668 (program): Totally multiplicative sequence with a(p) = 10p+1 for prime p.
  • A166669 (program): Totally multiplicative sequence with a(p) = 3p-2 for prime p.
  • A166670 (program): Totally multiplicative sequence with a(p) = 5p-2 for prime p.
  • A166671 (program): Totally multiplicative sequence with a(p) = 7p-2 for prime p.
  • A166672 (program): Totally multiplicative sequence with a(p) = 9p-2 for prime p.
  • A166673 (program): Totally multiplicative sequence with a(p) = 3p+2 for prime p.
  • A166674 (program): Totally multiplicative sequence with a(p) = 5p+2 for prime p.
  • A166675 (program): Totally multiplicative sequence with a(p) = 7p+2 for prime p.
  • A166676 (program): Totally multiplicative sequence with a(p) = 9p+2 for prime p.
  • A166677 (program): a(n)= n*(a(n-1)+4), a(0)=1.
  • A166680 (program): a(n) = n*(a(n-1)-4), a(0) = 1.
  • A166684 (program): Numbers n such that d(n)<4.
  • A166685 (program): Odd numbers that are the sum of two consecutive nonprimes.
  • A166687 (program): Numbers of the form x^2 + y^2 + 1, x, y integers.
  • A166692 (program): Triangle T(n,k) read by rows: T(n,k) = 2^(k-1), k>0. T(n,0) = (n+1) mod 2.
  • A166694 (program): A transform of the large Schroeder numbers, A006318.
  • A166695 (program): Alternating smallest odd/even number not in list followed by that number of consecutive odd/even numbers, sequence commencing with 1.
  • A166696 (program): A transform of A103210.
  • A166697 (program): A “Morgan Voyce” transform of A103210.
  • A166698 (program): Totally multiplicative sequence with a(p) = a(p-1) - 1 for prime p.
  • A166711 (program): Permutation of the integers: two positives, one negative.
  • A166720 (program): Trisection A165342(3n).
  • A166724 (program): a(n) = PrimePi(A166546(n)).
  • A166725 (program): a(n) = (2*n+1)*25^n.
  • A166726 (program): Nonnegative integers with English names ending in “o”.
  • A166727 (program): Positive integers with English names ending in “r”.
  • A166728 (program): Positive integers with English names ending in “x”.
  • A166729 (program): Positive integers with English names ending in “t”.
  • A166730 (program): Positive integers with English names ending in “y”.
  • A166731 (program): Positive integers with English names ending in “d”.
  • A166733 (program): Numbers n with the property that the concatenation of the trivial divisors of n (i.e., 1 and n) is a prime.
  • A166741 (program): E.g.f.: exp(2*arcsin(x)).
  • A166743 (program): a(n) = (2^p - p^2 - 1)/6 where p = prime(n).
  • A166748 (program): E.g.f.: exp(6*arcsin(x)).
  • A166750 (program): a(n) = (A001147(n))^3 = 2^(3*n)*GAMMA(n+1/2)^3/Pi^(3/2).
  • A166752 (program): Interleave A007583 and A000012.
  • A166753 (program): Partial sums of A166752.
  • A166754 (program): a(n) = 4*A061547(n+1) - 3*A166753(n).
  • A166756 (program): Number of nX2 1..3 arrays containing at least one of each value, and all equal values connected.
  • A166761 (program): Number of nX3 1..2 arrays containing at least one of each value, and all equal values connected.
  • A166776 (program): Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.
  • A166781 (program): Number of nX3 1..2 arrays containing at least one of each value, all equal values connected, and rows considered as a single number in nondecreasing order.
  • A166796 (program): Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
  • A166805 (program): Number of n X 4 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
  • A166808 (program): Number of n X 5 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
  • A166810 (program): Number of n X 6 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
  • A166812 (program): Number of n X 7 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
  • A166813 (program): Number of n X 8 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nondecreasing order.
  • A166814 (program): Number of nX2 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in increasing order.
  • A166830 (program): Number of n X 3 1..2 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in nonincreasing order.
  • A166842 (program): Number of n X 3 1..3 arrays containing at least one of each value, all equal values connected, rows considered as a single number in nondecreasing order, and columns considered as a single number in decreasing order.
  • A166849 (program): Primes with digital root 1, 2, 4 or 8.
  • A166863 (program): a(1)= 1; a(2)= 5; thereafter a(n)= a(n-1) + a(n-2) + 5.
  • A166864 (program): Primes p that divide n! - 1 for some n > 1 other than p-2.
  • A166866 (program): Mixed fractal sequence mf(n). Mix fractals A158405, A002260.
  • A166867 (program): a(n) = Pell(n+3) - Jacobsthal(n+4).
  • A166868 (program): Convolution of Jacobsthal(n+2) and Pell(n+1).
  • A166871 (program): Permutation of the integers: 3 positives, 2 negatives.
  • A166873 (program): a(n) = a(n-1) + 12*n for n > 1; a(1) = 1.
  • A166876 (program): a(n) = a(n-1) + Fibonacci(n), a(1)=1983.
  • A166879 (program): G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)/2*x^n/n ).
  • A166894 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * x^k] * x^n/n ), an integer series in x.
  • A166895 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(n-k)*n/(n-k), n>=1.
  • A166896 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k] * x^n/n ), an integer series in x.
  • A166897 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^3*n/(n-k), n>=1.
  • A166898 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^4 * x^k] * x^n/n ), an integer series in x.
  • A166899 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^4*n/(n-k), n>=1.
  • A166911 (program): a(n) = (9 + 14*n + 12*n^2 + 4*n^3)/3.
  • A166914 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 21, a(1) = 340.
  • A166915 (program): a(n) = 20*a(n-1) - 64*a(n-2) - 45 for n>1; a(0) = 399, a(1) = 5695.
  • A166916 (program): a(n) = 20*a(n-1) - 64*a(n-2) - 15 for n > 1; a(0) = 357, a(1) = 5525.
  • A166917 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 85, a(1) = 1364.
  • A166918 (program): Triangle T(n,k) read by rows: T(n,0) = n mod 2. T(n,k) = 2^(k-1), 0<k<=n.
  • A166920 (program): a(n) = 2^n - (1 + (-1)^n)/2.
  • A166922 (program): E.g.f. exp(-x)*exp(exp(2*x)/2-1/2)/2 + 1/2.
  • A166923 (program): Digital root of prime(n)^2.
  • A166925 (program): Digital root of square of n-th triangular number.
  • A166926 (program): A000004 preceded by 1, 2, 4.
  • A166927 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 18.
  • A166929 (program): Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some coprime integers a, b, c.
  • A166931 (program): Numbers n with property that n mod k is k-1 for all k = 2..9.
  • A166939 (program): Numerators of partial sums (n+1)/n (not sorted).
  • A166941 (program): Product plus sum of four consecutive nonnegative numbers.
  • A166942 (program): One fifth of product plus sum of five consecutive nonnegative numbers.
  • A166943 (program): One third of product plus sum of six consecutive nonnegative numbers.
  • A166944 (program): a(1)=2; a(n) = a(n-1) + gcd(n, a(n-1)) if n is even, a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is odd.
  • A166946 (program): a(n) = 1 if n is a rounded multiple of phi (1.618033989…), the larger golden ratio value; else a(n) = 0.
  • A166948 (program): The count of smallest prime factors in n-th composite.
  • A166949 (program): The count of largest prime factors in n-th composite.
  • A166952 (program): G.f. satisfies: A(x) = theta_3(x*A(x)) where Jacobi theta_3(x) = 1 + 2*Sum_{n>=1} x^(n^2).
  • A166956 (program): a(n) = 2^n +(-1)^n - 2.
  • A166957 (program): a(n) = 841*n^3 + 261*n^2 + 28*n + 1.
  • A166959 (program): Numbers congruent to (12,32) mod 44.
  • A166963 (program): Number of permutations in S_{2n} avoiding 123 and 1432 whose matrices are 180-degree symmetric.
  • A166965 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 19.
  • A166966 (program): Eigensequence of A047999, Sierpinski’s gasket.
  • A166976 (program): Array of A002450 in the top row and higher-order differences in subsequent rows, read by antidiagonals.
  • A166977 (program): Jacobsthal-Lucas numbers A014551, except a(0) = 0.
  • A166978 (program): a(n) = 4*( 1-(-1)^n) -2^n.
  • A166982 (program): Natural numbers with number of perfect partitions equal to a perfect power.
  • A166983 (program): The n-th composite minus the number of its divisors.
  • A166984 (program): a(n) = 20*a(n-1) - 64*a(n-2) for n > 1; a(0) = 1, a(1) = 20.
  • A166985 (program): Primes of the form phi(n)/2.
  • A166986 (program): a(n) = 2*floor((n+2)/log(2)) - 4.
  • A166989 (program): G.f.: A(x) = 1/(1 - 2*x - 7*x^2 - 2*x^3 + x^4).
  • A166990 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A166991 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)*x^n/(2*n) ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A166992 (program): G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/n ) where A005260(n) = Sum_{k=0..n} C(n,k)^4.
  • A166993 (program): G.f.: A(x) = exp( Sum_{n>=1} A005260(n)*x^n/(2*n) ), where A005260(n) = Sum_{k=0..n} C(n,k)^4.
  • A167001 (program): Least possible nonnegative coefficients of x^n in G(x)^(2^n), n>=0, for an integer series G(x) such that G’(0)=G(0)=1; the G(x) that satisfies this condition equals the g.f. of A167000.
  • A167004 (program): Least possible nonnegative coefficients of x^n in G(x)^(3^n), n>=0, such that G(x) is an integer series with G’(0)=G(0)=1; the G(x) that satisfies this condition equals the g.f. of A167003.
  • A167006 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, n*k) ).
  • A167007 (program): G.f.: A(x) = exp( Sum_{n>=1} A167010(n)*x^n/n ) where A167010(n) = Sum_{k=0..n} binomial(n,k)^n.
  • A167008 (program): a(n) = Sum_{k=0..n} C(n,k)^k.
  • A167009 (program): a(n) = Sum_{k=0..n} C(n^2, n*k).
  • A167010 (program): a(n) = Sum_{k=0..n} C(n,k)^n.
  • A167020 (program): a(n) = 1 iff 6n-1 is prime.
  • A167021 (program): a(n) = 1 iff 6n+1 is prime.
  • A167022 (program): Expansion of sqrt(1 - 2*x - 3*x^2) in powers of x.
  • A167024 (program): Triangle read by rows: T(n, m) = binomial(n, m)* Sum_{k=0..m} binomial(n, k) for 0 <= m <= n.
  • A167028 (program): Number of terms in the expansion of the determinant of a skew-symmetric matrix of order n.
  • A167030 (program): a(n) = (2^n - (-1)^n - 3)/3.
  • A167031 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 20.
  • A167032 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 21.
  • A167033 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 1; a(0) = 1, a(1) = 22.
  • A167034 (program): Triangle t(n,m)= (m+1)^n*binomial(n,m) if m <= n/2, otherwise t(n,m) = t(n,n-m).
  • A167040 (program): Triangle T(n, k) = (n-k)^n * binomial(n, n-k) for n < 2*k, k^n * binomial(n, k) for n >= 2*k with T(n, 0) = T(n, n) = 1, read by rows.
  • A167050 (program): Squarefree numbers with as many decimal digits as distinct prime factors.
  • A167051 (program): Start at 1, then add the first term (which is one here) plus 1 for the second term; then add the second term plus 2 for the third term; then add the third term to the sum of the first and second term; this gives the fourth term. Restart the sequence by adding 1 to the fourth term, etc. (From a sixth grade math extra credit assignment)
  • A167055 (program): Numbers n such that 12*n + 5 is prime.
  • A167056 (program): Numbers n such that 12*n + 7 is prime.
  • A167057 (program): Numbers n such that 12*n + 11 is prime.
  • A167060 (program): Number of spanning trees in G X P_n, where G = {{1, 2}, {1, 3}, {1, 4}, {1, 5}, {2, 3}, {2, 4}, {2, 5}}
  • A167120 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 1 for n > 2; a(0) = 1, a(1) = 22, a(2) = 376.
  • A167121 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 2 for n > 2; a(0) = 1, a(1) = 22, a(2) = 377.
  • A167122 (program): a(n) = 20*a(n-1) - 64*a(n-2) + 3 for n > 2; a(0) = 1, a(1) = 22, a(2) = 378.
  • A167129 (program): n^7 mod 21.
  • A167130 (program): Primes of the form A002808(n) + A062502(n+1).
  • A167131 (program): Numbers k such that A002808(k) - A144925(k) is prime.
  • A167132 (program): Gaps between twin prime pairs.
  • A167134 (program): Primes congruent to {2, 3, 5, 7} mod 11.
  • A167135 (program): Primes congruent to {2, 3, 5, 7, 11} mod 12.
  • A167136 (program): a(n) = b(n)-th highest positive integer not equal to any a(k), 1 <= k <= n-1, where b(n) = noncomposite numbers = A008578(n).
  • A167140 (program): Self-convolution of A155200.
  • A167149 (program): 10000-gonal numbers: a(n) = n + 4999 * n * (n-1).
  • A167153 (program): Numbers not appearing in A167152.
  • A167154 (program): Numbers where terms in A167153 change parity: a(n)+1 is in A167153, but a(n)-1 is not.
  • A167155 (program): Exponential primorial constant sum( 1/A140319(k), k>=0 )
  • A167156 (program): Number of n-vertex 4-hedrites.
  • A167166 (program): a(n) = n^7 mod 16.
  • A167167 (program): A001045 with a(0) replaced by -1.
  • A167170 (program): a(6) = 14, for n >= 7, a(n) = a(n-1) + gcd(n, a(n-1)).
  • A167171 (program): Squarefree semiprimes together with primes.
  • A167172 (program): Triangle T(n,k) read by rows: T(n,k) = binomial(n, k) + A140356(n, k) - 1.
  • A167175 (program): Numbers with a nonprime number of prime divisors (counted with multiplicity).
  • A167176 (program): n^3 mod 9.
  • A167179 (program): The number of additional armies one receives in Parker Brothers’ (now part of Hasbro) game of Risk for turning in the n-th set of three different or alike cards.
  • A167180 (program): a(n) = pi(n) plus the number of nonprimes less than prime(n).
  • A167181 (program): Squarefree numbers such that all prime factors are == 3 mod 4.
  • A167182 (program): a(0)=1, a(1)=2; for n>=2, a(n) = 2^A042950(n-2).
  • A167184 (program): Smallest prime power >= n that is not prime.
  • A167185 (program): Largest prime power <= n that is not prime.
  • A167192 (program): Triangle read by rows: T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.
  • A167193 (program): a(n) = (1/3)*(1 - (-2)^n + 3*(-1)^n ) = (-1)^(n+1)*A167030(n).
  • A167194 (program): Triangle read by rows. A130713 in the columns.
  • A167195 (program): a(2)=3, for n>=3, a(n)=a(n-1)+gcd(n, a(n-1)).
  • A167196 (program): Triangle T(n,k) read by rows: matrix inverse of A106246.
  • A167197 (program): a(6) = 7, for n >= 7, a(n) = a(n - 1) + gcd(n, a(n - 1))
  • A167198 (program): Fractal sequence of the interspersion A083047.
  • A167199 (program): First column of A167196.
  • A167204 (program): Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.
  • A167205 (program): a(n) = (3^n+1)/(3-(-1)^n).
  • A167206 (program): Binomial transform of A164555.
  • A167207 (program): Numbers that are not divisible by a smaller number that is a square greater than 1
  • A167208 (program): Append two digits, each increasing by one modulo 10 from the last digit the of the positive integers. 0 -> 12 1 -> 123 2 -> 234 .. 9 -> 901 10 -> 1012.
  • A167211 (program): Numbers n such that number of perfect partitions of n-1 divides n.
  • A167214 (program): a(n) = (sum of first n primes) * n.
  • A167227 (program): Number of 2-self-hedrites with n vertices.
  • A167230 (program): The matrix exponential of Sierpiński’s triangle (A047999) scaled by exp(-1).
  • A167231 (program): Append three digits, each increasing by one modulo 10 from the last digit the of the nonnegative integers. 0 -> 123, 1 -> 1234 2 -> 2345, … , 9 -> 9012, 10 -> 10123, etc.
  • A167237 (program): Lower trim of the Wythoff fractal sequence, A003603.
  • A167238 (program): Number of ways to partition a 2*n X 2 grid into 4 connected equal-area regions
  • A167239 (program): Number of ways to partition a 5*n X 2 grid into 5 connected equal-area regions
  • A167268 (program): Janet’s sequence: Number of elements for each successively filled electronic subshell of an atom.
  • A167269 (program): Triangle read by rows, Pascal’s triangle columns interleaved with 1’s.
  • A167270 (program): a(n) = Fibonacci(n + 2) + floor(n/2).
  • A167274 (program): Triangle read by rows, = 2*A047999 - A047999^(-1); = twice Sierpinski’s gasket minus the inverse of Sierpinski’s gasket.
  • A167275 (program): Row sums of triangle A167274 (a variant of Gould’s sequence A001316).
  • A167277 (program): Largest nonprime<n-th single (or isolated or non-twin) prime.
  • A167278 (program): Smallest prime>n-th single (or isolated or non-twin) prime.
  • A167280 (program): Period length 12: 0,0,1,2,4,7,4,8,7,4,8,5 (and repeat).
  • A167291 (program): a(n) = A137505(2n) + A137505(2n+1).
  • A167294 (program): Totally multiplicative sequence with a(p) = 2*(p-2) for prime p.
  • A167295 (program): Totally multiplicative sequence with a(p) = 3*(p-2) for prime p.
  • A167296 (program): Totally multiplicative sequence with a(p) = 4*(p-2) for prime p.
  • A167297 (program): Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.
  • A167298 (program): Totally multiplicative sequence with a(p) = 6*(p-2) for prime p.
  • A167299 (program): Totally multiplicative sequence with a(p) = 7*(p-2) for prime p.
  • A167300 (program): Totally multiplicative sequence with a(p) = 8*(p-2) for prime p.
  • A167301 (program): Totally multiplicative sequence with a(p) = 9*(p-2) for prime p.
  • A167302 (program): Totally multiplicative sequence with a(p) = 10*(p-2) for prime p.
  • A167303 (program): Totally multiplicative sequence with a(p) = 2*(p+2) for prime p.
  • A167304 (program): Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.
  • A167305 (program): Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.
  • A167306 (program): Totally multiplicative sequence with a(p) = 5*(p+2) for prime p.
  • A167307 (program): Totally multiplicative sequence with a(p) = 6*(p+2) for prime p.
  • A167308 (program): Totally multiplicative sequence with a(p) = 7*(p+2) for prime p.
  • A167309 (program): Totally multiplicative sequence with a(p) = 8*(p+2) for prime p.
  • A167310 (program): Totally multiplicative sequence with a(p) = 9*(p+2) for prime p.
  • A167311 (program): Totally multiplicative sequence with a(p) = 10*(p+2) for prime p.
  • A167312 (program): Totally multiplicative sequence with a(p) = 2*(p-3) for prime p.
  • A167313 (program): Totally multiplicative sequence with a(p) = 3*(p-3) for prime p.
  • A167314 (program): Totally multiplicative sequence with a(p) = 4*(p-3) for prime p.
  • A167315 (program): Totally multiplicative sequence with a(p) = 5*(p-3) for prime p.
  • A167316 (program): Totally multiplicative sequence with a(p) = 6*(p-3) for prime p.
  • A167317 (program): Totally multiplicative sequence with a(p) = 7*(p-3) for prime p.
  • A167318 (program): Totally multiplicative sequence with a(p) = 8*(p-3) for prime p.
  • A167319 (program): Totally multiplicative sequence with a(p) = 9*(p-3) for prime p.
  • A167320 (program): Totally multiplicative sequence with a(p) = 10*(p-3) for prime p.
  • A167321 (program): Totally multiplicative sequence with a(p) = 2*(p+3) for prime p.
  • A167322 (program): Totally multiplicative sequence with a(p) = 3*(p+3) for prime p.
  • A167323 (program): Totally multiplicative sequence with a(p) = 4*(p+3) for prime p.
  • A167324 (program): Totally multiplicative sequence with a(p) = 5*(p+3) for prime p.
  • A167325 (program): Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.
  • A167326 (program): Totally multiplicative sequence with a(p) = 7*(p+3) for prime p.
  • A167327 (program): Totally multiplicative sequence with a(p) = 8*(p+3) for prime p.
  • A167328 (program): Totally multiplicative sequence with a(p) = 9*(p+3) for prime p.
  • A167329 (program): Totally multiplicative sequence with a(p) = 10*(p+3) for prime p.
  • A167330 (program): Totally multiplicative sequence with a(p) = 2*(2p-1) = 4p-2 for prime p.
  • A167331 (program): Totally multiplicative sequence with a(p) = 2*(3p-1) = 6p-2 for prime p.
  • A167332 (program): Totally multiplicative sequence with a(p) = 2*(4p-1) = 8p-2 for prime p.
  • A167333 (program): Totally multiplicative sequence with a(p) = 2*(5p-1) = 10p-2 for prime p.
  • A167334 (program): Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.
  • A167335 (program): Totally multiplicative sequence with a(p) = 2*(3p+1) = 6p+2 for prime p.
  • A167336 (program): Totally multiplicative sequence with a(p) = 2*(4p+1) = 8p+2 for prime p.
  • A167337 (program): Totally multiplicative sequence with a(p) = 2*(5p+1) = 10p+2 for prime p.
  • A167338 (program): Totally multiplicative sequence with a(p) = p*(p+1) = p^2+p for prime p.
  • A167339 (program): Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.
  • A167340 (program): Totally multiplicative sequence with a(p) = p*(p+2) = p^2+2p for prime p.
  • A167341 (program): Totally multiplicative sequence with a(p) = p*(p-3) = p^2-3p for prime p.
  • A167342 (program): Totally multiplicative sequence with a(p) = p*(p+3) = p^2+3p for prime p.
  • A167343 (program): Totally multiplicative sequence with a(p) = (p-1)^2 = p^2-2p+1 for prime p.
  • A167344 (program): Totally multiplicative sequence with a(p) = (p-1)*(p+1) = p^2-1 for prime p.
  • A167345 (program): Totally multiplicative sequence with a(p) = (p-1)*(p-2) = p^2-3p+2 for prime p.
  • A167346 (program): Totally multiplicative sequence with a(p) = (p-1)*(p+2) = p^2+p-2 for prime p.
  • A167347 (program): Totally multiplicative sequence with a(p) = (p-1)*(p-3) = p^2-4p+3 for prime p.
  • A167349 (program): Totally multiplicative sequence with a(p) = (p+1)^2 = p^2+2p+1 for prime p.
  • A167350 (program): Totally multiplicative sequence with a(p) = (p+1)*(p-2) = p^2-p-2 for prime p.
  • A167351 (program): Totally multiplicative sequence with a(p) = (p+1)*(p+2) = p^2+3p+2 for prime p.
  • A167352 (program): Totally multiplicative sequence with a(p) = (p+1)*(p-3) = p^2-2p-3 for prime p.
  • A167353 (program): Totally multiplicative sequence with a(p) = (p+1)*(p+3) = p^2+4p+3 for prime p.
  • A167354 (program): Totally multiplicative sequence with a(p) = (p-2)^2 = p^2-4p+4 for prime p.
  • A167355 (program): Totally multiplicative sequence with a(p) = (p-2)*(p+2) = p^2-4 for prime p.
  • A167356 (program): Totally multiplicative sequence with a(p) = (p-2)*(p-3) = p^2-5p+6 for prime p.
  • A167357 (program): Totally multiplicative sequence with a(p) = (p-2)*(p+3) = p^2+p-6 for prime p.
  • A167358 (program): Totally multiplicative sequence with a(p) = (p+2)^2 = p^2+4p+4 for prime p.
  • A167359 (program): Totally multiplicative sequence with a(p) = (p+2)*(p-3) = p^2-p-6 for prime p.
  • A167360 (program): Totally multiplicative sequence with a(p) = (p+2)*(p+3) = p^2+5p+6 for prime p.
  • A167361 (program): Totally multiplicative sequence with a(p) = (p-3)^2 = p^2-6p+9 for prime p.
  • A167362 (program): Totally multiplicative sequence with a(p) = (p-3)*(p+3) = p^2-9 for prime p.
  • A167363 (program): Totally multiplicative sequence with a(p) = (p+3)^2 = p^2+6p+9 for prime p.
  • A167366 (program): Triangle read by rows, 2*A047999 - A097806 (signed) = twice Sierpinski’s gasket - the signed pair sum operator.
  • A167367 (program): a(n) = sigma(n!!) where n!! is A006882(n).
  • A167371 (program): Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,0,…] DELTA [1,0,-1,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A167373 (program): Expansion of (1+x)*(3*x+1)/(1+x+x^2).
  • A167374 (program): Triangle, read by rows, given by [ -1,1,0,0,0,0,0,0,0,…] DELTA [1,0,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A167375 (program): a(n)=3*a(n-1)-a(n-2) with a(0)=1, a(1)=3, a(2)=11.
  • A167376 (program): Complement of the partition numbers.
  • A167379 (program): Let p and q be twin primes, excluding the pair (3,5). Then p+q is always divisible by 6 and we set a(n) = (p+q)/6.
  • A167380 (program): a(1)=1, a(2)=2, and continued periodically with 4, 5, 1, -4, -5, -1 .
  • A167381 (program): The numbers read down the left-center column of an arrangement of the natural numbers in square blocks.
  • A167385 (program): a(n)= sum_{i=7..n+6} A000931(i).
  • A167386 (program): a(n) = (-1)^n*n*(n+1)*(2*n-5)/6.
  • A167387 (program): a(n) = (-1)^(n+1) * n*(n-1)*(n-4)*(n+1)/12.
  • A167388 (program): Prime numbers ending in the prime number 31.
  • A167389 (program): (arg(exp(-w)) + Im(w)) / (2*Pi), with w = W(n,-log(2)/2)/log(2), where W is the Lambert W function.
  • A167392 (program): Characteristic function of partition numbers.
  • A167393 (program): Characteristic function of the range of A000009.
  • A167394 (program): Largest single or isolated prime < n-th single or isolated composite.
  • A167397 (program): n-th single (or isolated or non-twin) prime minus n.
  • A167398 (program): a(n) = Fibonacci(11*n).
  • A167403 (program): Number of decimal numbers having n or fewer digits and having the sum of their digits equal to n.
  • A167406 (program): Sequence a(n) gives the number of ways to seat 2n people around a circular table so that person i does not sit across from person n+i for any 1 <= i <= n.
  • A167407 (program): T(m,n) is -m if n=0, 1 elsewhere.
  • A167418 (program): G.f.: 1/(1 - 4*x + 5*x^2 - 100*x^3).
  • A167420 (program): 2^n mod 14.
  • A167421 (program): 2^n mod 22.
  • A167422 (program): Expansion of (1+x)*c(x), c(x) the g.f. of A000108.
  • A167423 (program): Hankel transform of a simple Catalan convolution.
  • A167425 (program): 2^n mod 26.
  • A167426 (program): a(n) = 2^n mod 28.
  • A167427 (program): Largest non-isolated nonprime < n-th non-isolated (or twin) prime.
  • A167430 (program): Fractal sequence of the interspersion A163255.
  • A167431 (program): Riordan array (1-4x+4x^2, x(1-2x)).
  • A167432 (program): Riordan array (c(2x)^2,xc(2x)), c(x) the g.f. of A000108.
  • A167433 (program): Row sums of the Riordan array (1-4x+4x^2, x(1-2x)) (A167431).
  • A167434 (program): Diagonal sums of the Riordan array (1-4*x+4*x^2, x*(1-2*x)) (A167431).
  • A167435 (program): Hankel transform of A084076.
  • A167436 (program): 3rd Fibonacci polynomial evaluated at n^n.
  • A167440 (program): 5th GegenbauerC polynomial evaluated at powers of 2 (multiplied by 5).
  • A167441 (program): Prime numbers ending in the prime number 71.
  • A167442 (program): Prime numbers ending in the prime number 11.
  • A167443 (program): Prime numbers ending in the prime number 41.
  • A167444 (program): Fibonacci(n)!!.
  • A167445 (program): Prime numbers ending in the prime number 61.
  • A167449 (program): a(0)=1; a(1)=1; for a>1, a(n)=a(n-1)+((n-1)^3)*a(n-2).
  • A167461 (program): Anagram multiples of 123456789.
  • A167462 (program): Primes p such that 2*p-5 is composite.
  • A167463 (program): a(n) = n mod 15.
  • A167465 (program): n^5 mod 16.
  • A167467 (program): a(n) = 25*n^3 - n*(5*n+1)/2 + 1.
  • A167469 (program): a(n) = 3*n*(5*n-1)/2.
  • A167471 (program): Janet periodic table of the elements and structured hexagonal diamond numbers. a(n) = A166911(2n) + A166911(2n+1).
  • A167477 (program): Expansion of (1-3x+5x^2-x^3)/(1-3x+x^2)^2.
  • A167478 (program): Expansion of (1-2x+6x^2-x^3)/(1-3x+x^2)^2.
  • A167479 (program): Convolution of the Catalan numbers A000108(n) and (-2)^n.
  • A167480 (program): a(n)= primepi(n) if n is prime, otherwise a(n)=prime(n).
  • A167481 (program): Convolution of the central binomial coefficients A000984(n) and (-2)^n.
  • A167482 (program): a(n)=n-1 if n is prime, otherwise a(n)=n+1.
  • A167484 (program): For n people on one side of a river, the number of ways they can all travel to the opposite side following the pattern of 2 sent, 1 returns, 2 sent, 1 returns, …, 2 sent.
  • A167487 (program): a(n) = n*(n + 3)/2 + 8.
  • A167489 (program): Product of run lengths in binary representation of n.
  • A167493 (program): a(1) = 2; thereafter a(n) = a(n-1) + gcd(n, a(n-1)) if n is odd, and a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is even.
  • A167498 (program): a(n) = 6+32*n^2+8*n*(7+8*n^2)/3.
  • A167499 (program): a(n) = n*(n+3)/2 + 6.
  • A167512 (program): Number of Simple Alternating Transit (SAT) mazes with exactly two extreme values.
  • A167515 (program): The sum over the divisors of n, except the maximum-prime-power divisors collected in A008475.
  • A167520 (program): Positions of nonzero digits in this sequence, when all terms are concatenated.
  • A167527 (program): n^5 mod 49.
  • A167528 (program): a(n) = n^5 mod 50.
  • A167531 (program): a(n) = Sum_{d divides n} d*(n/d)^(d-1).
  • A167533 (program): a(n) = 71*n - a(n-1) for n>0, a(0)=12.
  • A167534 (program): a(n) = 79*n - a(n-1) for n>0, a(0)=9.
  • A167539 (program): a(n) = Sum_{k=0..[n/2]} C(n-k,k)^2 * n/(n-k), n>=1.
  • A167541 (program): a(n) = -(n - 4)*(n - 5)*(n - 12)/6.
  • A167542 (program): Natural numbers, swapped in pairs, with decimal digits reversed.
  • A167543 (program): a(n) = (n-5)*(n-6)*(n-7)*(n-16)/24.
  • A167544 (program): a(n) = (n-3)*(n-8)/2.
  • A167545 (program): n^6 mod 16.
  • A167547 (program): The fourth row of the ED1 array A167546.
  • A167548 (program): The fifth row of the ED1 array A167546
  • A167549 (program): The sixth row of the ED1 array A167546.
  • A167550 (program): The a(n,n+1) diagonal of the ED1 array A167546
  • A167554 (program): The second left hand column of triangle A167552.
  • A167555 (program): The third left hand column of triangle A167552.
  • A167557 (program): The lower left triangle of the ED1 array A167546.
  • A167558 (program): The second right hand column of triangle A167557.
  • A167559 (program): The row sums of triangle A167557.
  • A167561 (program): The fourth row of the ED2 array A167560.
  • A167562 (program): The fifth row of the ED2 array A167560.
  • A167566 (program): The third left hand column of triangle A167565.
  • A167569 (program): The lower left triangle of the ED2 array A167560.
  • A167570 (program): The third right hand column of triangle A167569.
  • A167571 (program): The row sums of triangle A167569.
  • A167573 (program): The third row of the ED3 array A167572.
  • A167574 (program): The fourth row of the ED3 array A167572.
  • A167575 (program): The fifth row of the ED3 array A167572.
  • A167576 (program): The first column of the ED3 array A167572.
  • A167577 (program): The second column of the ED3 array A167572.
  • A167578 (program): The third column of the ED3 array A167572.
  • A167581 (program): The second left hand column of triangle A167580.
  • A167585 (program): a(n) = 12*n^2 - 8*n + 9.
  • A167586 (program): The fourth row of the ED4 array A167584.
  • A167588 (program): The second column of the ED4 array A167584.
  • A167589 (program): The third column of the ED4 array A167584.
  • A167592 (program): The second left hand column of triangle A167591.
  • A167596 (program): The number of isolated nonprimes between the nonisolated prime and the isolated prime.
  • A167607 (program): Sum of cousin prime pairs.
  • A167610 (program): Primes that are the sum of three consecutive nonprimes.
  • A167611 (program): Nonprimes that are the sum of two consecutive nonprimes.
  • A167614 (program): a(n) = (n^2 + 3*n + 8)/2.
  • A167616 (program): a(n) = Fibonacci(n) - 5.
  • A167617 (program): G.f.: x^2*(3+3*x+x^2) / ( (2*x+1) * (1+x) * (1+x+x^2) * (x^2-x+1) ) .
  • A167618 (program): Convolution of A010054 with A052343.
  • A167622 (program): n^3 mod n-th prime.
  • A167623 (program): n^3 mod (n-th prime squared).
  • A167624 (program): a(n) = n^6 mod 32.
  • A167626 (program): Prime numbers ending in the prime number 101.
  • A167628 (program): n^11 mod 13.
  • A167632 (program): Smallest m such that A033183(m) = n.
  • A167635 (program): Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at odd level.
  • A167638 (program): Number of Dyck paths of semilength n, having no ascents and no descents of length 1, and having no peaks at even level.
  • A167655 (program): Riordan array (1-u,u) where u=x/(1+x+x^2).
  • A167657 (program): Product of n-th block of identical consecutive values of A000720.
  • A167660 (program): Chocolate dove bar numerator: a(n) = (Sum_{k=0..floor(n/2)} k*binomial(n+k,k)*binomial(n,n-2*k)) + (Sum_{k=0..ceiling(n/2)} k*binomial(n+k-1,k-1)*binomial(n,n-2*k+1)).
  • A167666 (program): Triangle read by rows given by [1,1,-4,2,0,0,0,0,0,0,0,…] DELTA [1,0,0,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A167667 (program): Expansion of (1-x+4*x^2)/(1-2*x)^2.
  • A167679 (program): Replace odd digits with 2 and even digits with 1.
  • A167682 (program): Expansion of (1 - 2*x + 5*x^2) / (1 - 3*x)^2.
  • A167683 (program): Hankel transform of A007325.
  • A167684 (program): Triangle read by rows given by [2,-1,1,-2,0,0,0,0,0,0,0,…] DELTA [1,0,1,-1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A167692 (program): The even nonisolated nonprimes.
  • A167700 (program): Number of partitions of n into distinct odd squares.
  • A167704 (program): a(0)=1, a(1)=0, a(2)=2, a(3)=1, a(n)=a(n-2)+a(n-3)+a(n-4) for n>3.
  • A167705 (program): Composite numbers having four composite nearest neighbors.
  • A167706 (program): The single or isolated numbers. The union of single (or isolated or non-twin) primes and single (or isolated or average of twin prime pairs) nonprimes.
  • A167707 (program): The non-single or nonisolated numbers. The union of non-single (or nonisolated or twin) primes and non-single (or nonisolated) nonprimes.
  • A167710 (program): a(n) = 10*2^n - 3*A083658(n+2).
  • A167711 (program): Numbers such that sum of digits is one more than a prime.
  • A167713 (program): a(n) = 16^n * Sum_{k=0..n} binomial(2*k, k) / 16^k.
  • A167716 (program): Squares that become a prime number when prefixed with a 1.
  • A167717 (program): Squares that becomes a prime number when prefixed with a 2.
  • A167718 (program): Squares that becomes primes when prefixed with a 3.
  • A167719 (program): Squares that become a prime number when prefixed with a 4
  • A167721 (program): Squares that become prime numbers when prefixed with a 6.
  • A167722 (program): Squares that become prime numbers when prefixed with a 7.
  • A167743 (program): Positive differences between distinct positive triangular numbers, with repetition.
  • A167744 (program): Squares that become a prime number when some single digit is inserted in front of its decimal expansion.
  • A167746 (program): Number of prime divisors of A001222 (counted with multiplicity), with a(1) = 1 by convention.
  • A167747 (program): a(n) = phi(6^n).
  • A167752 (program): Hankel transform of A167750.
  • A167758 (program): Numbers n such that d(n)=nonisolated nonprime.
  • A167759 (program): Numbers k such that d(k) is an isolated number (A167706).
  • A167760 (program): The number of permutations w of [n] with no w(i)+1 == w(i+1) (mod n).
  • A167761 (program): a(n) = sqrt(A167657(n).
  • A167762 (program): a(n) = 2*a(n-1)+3*a(n-2)-6*a(n-3) starting a(0)=a(1)=0, a(2)=1.
  • A167770 (program): a(n) = prime(n)^2 modulo prime(n+1).
  • A167772 (program): Riordan array (c(x)/(1+x*c(x)), x*c(x)), c(x) the g.f. of A000108.
  • A167774 (program): Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5*n+1).
  • A167775 (program): Subsequence of A167708 whose indices are congruent to 1 mod 5, i.e., a(n) = A167708(5n+1).
  • A167776 (program): Composite numbers having six composite nearest-neighbors.
  • A167777 (program): Even single (or even isolated) numbers.
  • A167778 (program): Subsequence of A167708 whose indices are 2 mod 5.
  • A167779 (program): Subsequence of A167708 whose indices are congruent to 4 mod 5, i.e., a(n) = A167708(5n+4).
  • A167780 (program): Subsequence of A167708 whose indices are 0 mod 5, that is, a(n) = A167708(5n+5).
  • A167784 (program): a(n) = 2^n - (1 - (-1)^n)*3^((n-1)/2).
  • A167791 (program): Numbers with primitive root 2.
  • A167796 (program): Numbers with primitive root 8.
  • A167808 (program): Numerator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/2.
  • A167816 (program): Numerator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/3; denominator=A167817.
  • A167817 (program): Period 4: repeat [1, 3, 3, 3].
  • A167820 (program): Subsequence of A167709 whose indices are congruent to 0 mod 5, i.e., a(n) = A167709(5*n).
  • A167821 (program): a(n) is the number of n-tosses having a run of 3 or more heads or a run of 3 or more tails for a fair coin (i.e., probability is a(n)/2^n).
  • A167822 (program): Subsequence of A167709 whose indices are congruent to 1 mod 5, i.e., a(n) = A167709(5*n+1).
  • A167823 (program): Subsequence of A167709 whose indices are congruent to 2 mod 5, i.e., a(n) = A167709(5*n+2).
  • A167824 (program): Subsequence of A167709 whose indices are congruent to 3 mod 5, i.e., a(n) = A167709(5*n+3).
  • A167825 (program): Subsequence of A167709 whose indices are congruent to 4 mod 5, i.e., a(n) = A167709(5*n+4).
  • A167826 (program): a(n) is the number of n-tosses having a run of 3 or more heads and a run of 3 or more tails for a fair coin.
  • A167831 (program): Largest m<=n such that no carry occurs when adding m to n in decimal arithmetic.
  • A167832 (program): A167831(n) + n.
  • A167858 (program): A000004 preceded by 3, 14, 36, 36, 12.
  • A167859 (program): a(n) = 4^n * Sum_{k=0..n} binomial(2*k, k)^2 / 4^k.
  • A167865 (program): Number of partitions of n into distinct parts greater than 1, with each part divisible by the next.
  • A167867 (program): a(n) = 2^n * Sum_{k=0..n} binomial(2*k,k)^3 / 2^k.
  • A167868 (program): a(n) = 3^n * Sum_{k=0..n} binomial(2*k,k)^3 / 3^k.
  • A167869 (program): a(n) = 4^n * Sum_{k=0..n} binomial(2*k,k)^3 / 4^k.
  • A167870 (program): a(n) = 16^n * Sum_{k=0..n} binomial(2*k,k)^3 / 16^k.
  • A167871 (program): a(n) = 64^n * Sum_{k=0..n} binomial(2*k,k)^3 / 64^k.
  • A167872 (program): A sequence of moments connected with Feynman numbers (A000698): Half the number of Feynman diagrams of order 2(n+1), for the electron self-energy in quantum electrodynamics (QED), i.e., all proper diagrams including Furry vanishing diagrams (those that vanish in 4-dimensional QED because of Furry theorem).
  • A167873 (program): Period 4: repeat [10, 6, 10, 4].
  • A167875 (program): One third of product plus sum of three consecutive nonnegative integers; a(n)=(n+1)(n^2+2n+3)/3.
  • A167876 (program): A000004 preceded by 1, 3, 4, 2.
  • A167877 (program): Largest m<=n such that no carry occurs when adding m to n in ternary arithmetic.
  • A167878 (program): A167877(n) + n.
  • A167885 (program): n-th single or isolated number*n-th non-single or nonisolated number.
  • A167886 (program): n-th single or isolated number minus n-th non-single or nonisolated number.
  • A167887 (program): n-th single or isolated number plus n-th non-single or nonisolated number.
  • A167888 (program): n-th single or isolated number^n-th non-single or nonisolated number.
  • A167889 (program): a(n) = (-7*3^n+(-3)^n+6*4^n) / 42.
  • A167891 (program): A000004 preceded by 1, 4, 2.
  • A167892 (program): a(n) = Sum_{k=1..n} Catalan(k)^2.
  • A167893 (program): a(n) = Sum_{k=1..n} Catalan(k)^3.
  • A167894 (program): Expansion of g.f.: 1/(Sum_{k >= 0} k!*x^k).
  • A167909 (program): Differences between consecutive single (or isolated) numbers A167706.
  • A167910 (program): a(n) = (4*3^n - 5*2^n + (-2)^n)/20.
  • A167911 (program): Differences between consecutive non-single (or nonisolated) numbers A167707.
  • A167915 (program): Primes which are the sums of two consecutive nonprimes (A141468).
  • A167921 (program): Single or isolated numbers-1.
  • A167925 (program): A triangular sequence of the Matrix Markov type based on the 2x2 matrix: m={{a,1},{-1,1}}; which has determinant equal to trace.
  • A167928 (program): Number of partitions of n that do not contain 1 as a part and whose parts are not the same divisor of n.
  • A167930 (program): Number of partitions of n in which some but not all parts are equal.
  • A167932 (program): Number of partitions of n such that all parts are equal or all parts are distinct.
  • A167934 (program): a(n) = A000041(n) - A032741(n).
  • A167936 (program): 2^n - A108411(n).
  • A167948 (program): Triangle read by rows, A101688 * (an infinite lower triangular matrix with A002083 as the main diagonal and the rest zeros).
  • A167963 (program): a(n) = n*(n^5 + 1)/2.
  • A167968 (program): Signature sequence of phi^4 = 0.14589803375032…, where phi is the golden ratio minus 1 (0.61803398874989…).
  • A167972 (program): Signature sequence of Phi^4 = 6.8541019662497…, where Phi is the golden ratio 1.6180339887499… .
  • A167987 (program): Number of (undirected) cycles in the graph of the n-orthoplex, n>=2.
  • A167990 (program): Elements in A126988 (by row) that are not 1.
  • A167991 (program): Blocks of size 2n, each with 2n-1 replicas of 2n followed by 2n+1; n=1, 2, 3, …
  • A167993 (program): Expansion of x^2/((3*x-1)*(3*x^2-1)).
  • A167998 (program): Numbers n with property that first digit of 5*n = last digit of n.
  • A168007 (program): Jumping divisor sequence (see Comments lines for definition).
  • A168008 (program): First differences of A168007.
  • A168009 (program): Numbers of A168007, in sorted order.
  • A168010 (program): a(n) = Sum of all numbers of divisors of all numbers k such that n^2 <= k < (n+1)^2.
  • A168011 (program): a(n) = Sum of all numbers of divisors of all numbers < (n+1)^2.
  • A168012 (program): a(n) = sum of all divisors of all numbers k such that n^2 <= k < (n+1)^2.
  • A168013 (program): a(n) = Sum of all divisors of all numbers < (n+1)^2.
  • A168014 (program): Sum of all parts of all partitions of n into equal parts that do not contain 1 as a part.
  • A168015 (program): a(n) = A000041(n) + n*A032741(n).
  • A168016 (program): Triangle T(n,k) read by rows in which row n list the number of partitions of n into parts divisible by k for k=n,n-1,…,1.
  • A168017 (program): Triangle read by rows in which row n lists the number of partitions of n into parts divisible by d, where d is a divisor of n listed in decreasing order.
  • A168018 (program): Triangle read by rows in which row n lists the number of partitions of n into parts divisible by d, where d is a divisor of n.
  • A168020 (program): Square array read by antidiagonals in which row n lists the number of partitions of n into parts divisible by k.
  • A168021 (program): Triangle T(n,k) read by rows in which row n lists the number of partitions of n into parts divisible by k.
  • A168022 (program): Noncomposite numbers in the eastern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
  • A168023 (program): Noncomposite numbers in the northern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
  • A168024 (program): Noncomposite numbers in the northwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
  • A168025 (program): Noncomposite numbers in the western ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
  • A168026 (program): Noncomposite numbers in the southwestern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
  • A168027 (program): Noncomposite numbers in the southern ray of the Ulam spiral as oriented on the March 1964 cover of Scientific American.
  • A168029 (program): n*(n^6+1)/2.
  • A168036 (program): Difference between n’ and n, where n’ is the arithmetic derivative of n (A003415).
  • A168037 (program): Period length 18: repeat 0,1,2,0,8,7,0,4,5,0,5,4,0,7,8,0,2,1.
  • A168038 (program): Squares closest to 2*n.
  • A168039 (program): Squares closest to 3*n.
  • A168043 (program): Let S(1)={1} and, for n>1 let S(n) be the smallest set containing x+1, x+2, and 2*x for each element x in S(n-1). a(n) is the number of elements in S(n).
  • A168044 (program): Half of the even nonisolated nonprimes A167692.
  • A168045 (program): a(n) = A167707(n) + n.
  • A168046 (program): Characteristic function of zerofree numbers in decimal representation.
  • A168048 (program): a(n) = C(n)*Pi(n) where C(n) = number of nonprimes <= n, Pi(n) = number of primes <= n.
  • A168049 (program): Expansion of (3 -x -sqrt(1-2*x-3*x^2))/2.
  • A168050 (program): Hankel transform of A168049.
  • A168051 (program): Expansion of (1+x+sqrt(1-2x-3x^2))/2.
  • A168052 (program): Hankel transform of a Motzkin variant.
  • A168053 (program): Expansion of (1-2*x^2-3*x^3)/((1-x)^2*(1+x+x^2)).
  • A168054 (program): Expansion of (1-8x^2-24x^3)/((1-2x)^2*(1+2x+4x^2)).
  • A168055 (program): Expansion of 2 - x - sqrt(1-2x-3x^2).
  • A168056 (program): Expansion of (1+2*x^2+x^3)/((1-x)^2*(1+x+x^2)).
  • A168057 (program): Expansion of (1+8x^2+8x^3)/((1-2x)^2*(1+2x+4x^2)).
  • A168058 (program): Expansion of x + sqrt(1-2x-3x^2).
  • A168059 (program): Denominator of (n+2)/(n*(n+1)).
  • A168061 (program): Denominator of (n+3) / ((n+2) * (n+1) * n).
  • A168065 (program): If n = Product p(k)^e(k) then a(n) = {Product (p(k)+1)^e(k) + Product (p(k)-1)^e(k)}/2, a(1) = 1.
  • A168066 (program): If n = Product p(k)^e(k) then a(n) = {Product (p(k)+1)^e(k) - Product (p(k)-1)^e(k)}/2, a(1) = 0.
  • A168067 (program): n*(n^7+1)/2.
  • A168068 (program): Array T(n,k) read by antidiagonals: T(n,2k+1) = 2k+1. T(n,2k) = 2^n*k.
  • A168071 (program): Expansion of (1-3*x^2-4*x^3)/((1-x)^2*(1+x+x^2)).
  • A168072 (program): Expansion of (1-27x^2-108x^3)/((1-3x)^2*(1+3x+9x^2)).
  • A168073 (program): Expansion of 1 + 3*(1-x-sqrt(1-2*x-3*x^2))/2.
  • A168075 (program): Expansion of (1+27x^2-54x^3)/((1+3x)^2*(1-3x+9 x^2)).
  • A168076 (program): Expansion of 1 - 3*(1-x-sqrt(1-2*x-3*x^2))/2.
  • A168077 (program): a(2n) = A129194(2n)/2; a(2n+1) = A129194(2n+1).
  • A168081 (program): Lucas sequence U_n(x,1) over the field GF(2).
  • A168088 (program): a(n) = 2^tetranacci(n).
  • A168089 (program): a(n) = 2^pentanacci(n).
  • A168090 (program): a(n) = (1 - (n mod 3) mod 2)*2^(floor(n/3) + (n mod 3)/2 ).
  • A168092 (program): a(n) = number of natural numbers m such that n - 2 <= m <= n + 2.
  • A168093 (program): a(n) = number of natural numbers m such that n - 3 <= m <= n + 3.
  • A168094 (program): a(n) = number of natural numbers m such that n - 4 <= m <= n + 4.
  • A168095 (program): a(n) = number of natural numbers m such that n - 5 <= m <= n + 5.
  • A168096 (program): a(n) = number of natural numbers m such that n - 6 <= m <= n + 6.
  • A168097 (program): a(n) = number of natural numbers m such that n - 7 <= m <= n + 7.
  • A168098 (program): a(n) = number of natural numbers m such that n - 8 <= m <= n + 8.
  • A168099 (program): a(n) = number of natural numbers m such that n - 9 <= m <= n + 9.
  • A168100 (program): a(n) = number of natural numbers m such that n - 10 <= m <= n + 10.
  • A168101 (program): a(n) = sum of natural numbers m such that n - 2 <= m <= n + 2.
  • A168102 (program): a(n) = sum of natural numbers m such that n - 3 <= m <= n + 3.
  • A168103 (program): a(n) = sum of natural numbers m such that n - 4 <= m <= n + 4.
  • A168104 (program): a(n) = sum of natural numbers m such that n - 5 <= m <= n + 5.
  • A168105 (program): a(n) = sum of natural numbers m such that n - 6 <= m <= n + 6.
  • A168106 (program): a(n) = sum of natural numbers m such that n - 7 <= m <= n + 7.
  • A168107 (program): a(n) = sum of natural numbers m such that n - 8 <= m <= n + 8.
  • A168108 (program): a(n) = sum of natural numbers m such that n - 9 <= m <= n + 9.
  • A168109 (program): a(n) = sum of natural numbers m such that n - 10 <= m <= n + 10.
  • A168111 (program): Sum of the partition numbers of the proper divisors of n, with a(1) = 0.
  • A168114 (program): If A168113 is regarded as a triangle then the rows converge to this sequence.
  • A168116 (program): a(n) = n*(n^8+1)/2.
  • A168118 (program): n*(n^9+1)/2.
  • A168119 (program): n*(n^10+1)/2.
  • A168120 (program): Square array T(n,k) read by antidiagonals in which column k lists each number A000009 followed by k-1 zeros, for k>0.
  • A168121 (program): Triangle T(n,k) read by rows in which column k lists each number A000009 followed by k-1 zeros, for k>0.
  • A168122 (program): n^2*(n^4+1)/2.
  • A168123 (program): a(n) = n^2*(n^5+1)/2.
  • A168124 (program): a(n) = n^2*(n^6+1)/2.
  • A168125 (program): a(n) = n^2*(n^7+1)/2.
  • A168126 (program): a(n) = n^2*(n^8+1)/2.
  • A168134 (program): Numbers not of the form 7*k+11*m (with nonnegative k, m).
  • A168135 (program): Numbers expressible as 7*k+11*m (with nonnegative k, m) exactly in one way.
  • A168136 (program): a(n) = Bernoulli(2n)*(2n+1)!/n!.
  • A168138 (program): a(n) = Fibonacci(n+1)^tau(n).
  • A168141 (program): a(n) = pi(n + 1) - pi(n - 2), where pi is the prime counting function.
  • A168142 (program): Count downwards from 2, then from 8, then from 18, then from … 2*k^2, k>=1.
  • A168143 (program): a(17)=37; for n>=17, a(n)=3n-14 if gcd(n,a(n-1))>1 and all prime divisors of n more than 17; a(n)=a(n-1)+1, otherwise
  • A168145 (program): Numbers n such that to abs(phi(n) - pi(n)) = 1.
  • A168146 (program): Numbers n such that phi(n) > pi(n).
  • A168147 (program): Primes of the form 10*n^3 + 1.
  • A168150 (program): Inverse binomial transform of A026741.
  • A168152 (program): a(n) = prime(prime(n)) - prime(n).
  • A168153 (program): a(n) = n^2*(n^9 + 1)/2.
  • A168160 (program): Number of 0’s in the matrix whose lines are the binary expansion of the numbers 1,…,n.
  • A168175 (program): Expansion of 1/(1 - 4*x + 7*x^2).
  • A168176 (program): a(n) = n^2*(n^10 + 1)/2.
  • A168178 (program): a(n) = n^3*(n^2 + 1)/2.
  • A168179 (program): a(n) = n^3*(n^4 + 1)/2.
  • A168180 (program): a(n) = n^3*(n^5 + 1)/2.
  • A168181 (program): Characteristic function of numbers that are not multiples of 8.
  • A168182 (program): Characteristic function of numbers that are not multiples of 9.
  • A168183 (program): Numbers that are not multiples of 9.
  • A168184 (program): Characteristic function of numbers that are not multiples of 10.
  • A168185 (program): Characteristic function of numbers that are not multiples of 12.
  • A168186 (program): Positive numbers that are not multiples of 12.
  • A168187 (program): a(n) = n^3*(n^6 + 1)/2.
  • A168188 (program): a(n) = n^3*(n^7 + 1)/2.
  • A168189 (program): a(n) = n^3*(n^8 + 1)/2.
  • A168190 (program): a(n) = n^3*(n^9 + 1)/2.
  • A168191 (program): a(n) = n^3*(n^10 + 1)/2.
  • A168192 (program): a(n) = n^4*(n^2 + 1)/2.
  • A168193 (program): a(n) = a(n-1) + a(n-2) + 4, with a(0)=0, a(1)=2.
  • A168194 (program): a(n) = n^4*(n^3 + 1)/2.
  • A168195 (program): a(n) = 2*n - a(n-1) + 1 with n>1, a(1)=5.
  • A168196 (program): a(n) = n^4*(n^5 + 1)/2.
  • A168197 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=0.
  • A168198 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=1.
  • A168199 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=2.
  • A168200 (program): a(n) = 3*n - a(n-1) + 1, with a(1)=4.
  • A168201 (program): Number of representations of n in the form 7*k+11*m (with nonnegative k, m).
  • A168202 (program): a(n) = 3*n - a(n-1) + 1 with n > 1, a(1)=5.
  • A168203 (program): a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=0.
  • A168204 (program): a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=1.
  • A168205 (program): a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=2.
  • A168206 (program): a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=0.
  • A168207 (program): a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=2.
  • A168209 (program): a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=3.
  • A168210 (program): a(n) = 6*n - a(n-1) + 1 with n>1, a(1)=0.
  • A168211 (program): a(n) = (9 + 14*n + 23*(-1)^n)/4.
  • A168212 (program): a(n) = 7*n - a(n-1) + 1 with n>1, a(1)=4.
  • A168213 (program): a(n) = (11 + 18*n + 9*(-1)^n)/4.
  • A168216 (program): Riordan array (1/(1-x),xc(x)/(1-xc(x))) where c(x)is the g.f. of A000108.It factorizes as A007318*A106566.
  • A168219 (program): Naturals n for which 1 + 10*n^3 (A168147) is prime.
  • A168220 (program): a(n) = n^4*(n^6 + 1)/2.
  • A168221 (program): a(n) = A006368(A006368(n)).
  • A168222 (program): a(n) = A006369(A006369(n)).
  • A168224 (program): Where record values occur in A168223.
  • A168225 (program): a(n) = n^4*(n^7 + 1)/2.
  • A168227 (program): a(n) = n^4*(n^8 + 1)/2.
  • A168230 (program): a(n) = n + 2 - a(n-1) for n>1; a(1) = 0.
  • A168232 (program): a(n) = (2*n - 3*(-1)^n - 1)/2.
  • A168233 (program): a(n) = 3*n - a(n-1) - 1 for n>0, a(1)=1.
  • A168235 (program): 1+5*n+7*n^2.
  • A168236 (program): a(n) = (6*n - 3*(-1)^n - 1)/4.
  • A168237 (program): a(n) = (6*n + 3*(-1)^n - 3)/4.
  • A168240 (program): 1+7*n+13*n^2.
  • A168241 (program): n-th squarefree number plus n-th non-single or nonisolated number.
  • A168243 (program): Expansion of e.g.f. Product_{i>=1} (1 + x^i)^(1/i).
  • A168244 (program): a(n) = 1 + 3*n - 2*n^2.
  • A168245 (program): prime(prime(n+1))-2*prime(n).
  • A168249 (program): n-th single or isolated number minus n-th squarefree number.
  • A168251 (program): a(n) = n^2 if n is odd, n^2*2^(n-2) if n is even.
  • A168255 (program): n appears n-th nonprime number times.
  • A168256 (program): Triangle read by rows: Catalan number C(n) repeated n+1 times.
  • A168258 (program): Triangle read by rows, A101688 * A000012 as infinite lower triangular matrices.
  • A168259 (program): Eigensequence of triangle A168258.
  • A168265 (program): a(n) = A003557(A060735(n)).
  • A168269 (program): a(n) = 2*n - (-1)^n.
  • A168273 (program): a(n) = 2*n + (-1)^n - 1.
  • A168276 (program): a(n) = 2*n - (-1)^n - 1.
  • A168277 (program): a(n) = 2*n - (-1)^n - 2.
  • A168278 (program): (10*n + 5*(-1)^n + 3)/4.
  • A168279 (program): (n+1)-th prime nonprime minus (n+1)-th prime.
  • A168280 (program): (1 - 5*(-1)^n + 10*n)/4.
  • A168281 (program): Triangle T(n,m) = 2*(min(n - m + 1, m))^2 read by rows.
  • A168282 (program): (10*n + 5*(-1)^n - 1)/4.
  • A168283 (program): a(n) = (10*n - 5*(-1)^n - 3)/4.
  • A168284 (program): a(n) = (10*n + 5*(-1)^n - 5)/4.
  • A168285 (program): a(n) = ((n-th nonprime)-th prime) - (n-th nonprime).
  • A168286 (program): a(n) = (6*n + 3*(-1)^n + 1)/2.
  • A168297 (program): a(n) = n^3 + (1-n)^2.
  • A168298 (program): a(n) = 1 - n^2*2^n.
  • A168299 (program): a(n) = 1 + 3^n * n^3.
  • A168300 (program): a(n) = 6*n - a(n-1) - 2 with a(1)=5.
  • A168301 (program): a(n) = (6*n + 3*(-1)^n - 1)/2.
  • A168309 (program): Period 2: repeat 4,-3.
  • A168313 (program): Triangle read by rows, retain 1’s as rightmost diagonal of A101688 and replace all other 1’s with 2’s.
  • A168314 (program): Eigensequence of triangle A168313
  • A168316 (program): Triangle read by rows, square of triangle A101688.
  • A168319 (program): a(-1)=0. a(n)=a(n-1)^2-2^n.
  • A168321 (program): a(n) = n +6 - a(n-1), with a(1) = 0.
  • A168324 (program): Number of distinct permutations of the list of prime factors of n (with multiplicity), where a(1)=0.
  • A168326 (program): a(n) = (6*n - 3*(-1)^n - 1)/2.
  • A168328 (program): a(n) = 6 * floor( n/2 ).
  • A168329 (program): a(n) = (3/2)*(2*n - (-1)^n - 1).
  • A168330 (program): Period 2: repeat [3, -2].
  • A168331 (program): a(n) = (5 + 14*n + 7*(-1)^n)/4.
  • A168332 (program): a(n) = 6 + 7 * floor((n-1)/2).
  • A168333 (program): a(n) = (14*n + 7*(-1)^n + 1)/4.
  • A168336 (program): a(n) = 5 + 7*floor((n-1)/2).
  • A168337 (program): a(n) = 1 + 7*floor(n/2).
  • A168338 (program): Sum of the largest digit of the divisors of n.
  • A168343 (program): n-th single or isolated number minus n.
  • A168345 (program): a(n) = n^4*(n^9 + 1)/2.
  • A168346 (program): a(n) = n^4*(n^10 + 1)/2.
  • A168350 (program): Sum of first n non-single or nonisolated numbers.
  • A168351 (program): a(n) = n^5*(n+1)/2.
  • A168356 (program): A000796(n-2) - A000796(n)
  • A168358 (program): Self-convolution square of A001246, which is the squares of Catalan numbers.
  • A168360 (program): n-b(n), where b(n) = A079777(n) = (b(n-1)+b(n-2) mod n); b(0)=0, b(1)=1.
  • A168361 (program): Period 2: repeat 2, -1.
  • A168364 (program): a(n) = n^5*(n^2 + 1)/2.
  • A168371 (program): a(n) = n^5*(n^3 + 1)/2.
  • A168372 (program): a(n) = n^5*(n^4 + 1)/2.
  • A168373 (program): a(n) = 7*n - a(n-1) - 6 with n>1, a(1)=4.
  • A168374 (program): a(n) = 7 * floor(n/2).
  • A168376 (program): a(n) = (14*n - 7*(-1)^n - 9)/4.
  • A168377 (program): Riordan array (1/(1 + x), x*c(x)), where c(x) is the o.g.f. of Catalan numbers A000108.
  • A168378 (program): a(n) = 3 + 8*floor(n/2).
  • A168379 (program): a(n) = 4*n - 2*(-1)^n + 1.
  • A168380 (program): Row sums of A168281.
  • A168381 (program): a(n) = 4*n + 2*(-1)^n.
  • A168384 (program): a(n) = 4*n - 2*(-1)^n.
  • A168386 (program): Arithmetic derivative of the double factorial of n.
  • A168388 (program): First number in the n-th row of A172002.
  • A168389 (program): a(n) = PrimePi(A147819(n)).
  • A168390 (program): a(n) = 1 + 8*floor(n/2).
  • A168392 (program): a(n) = 5 + 8*floor((n-1)/2).
  • A168393 (program): Moebius function of interprimes (A024675).
  • A168394 (program): Moebius function of even interprimes (A072568).
  • A168395 (program): Moebius function of odd interprimes (A072569).
  • A168397 (program): a(n) = 8 * floor(n/2).
  • A168398 (program): a(n) = 4 + 8*floor((n-1)/2).
  • A168399 (program): a(n) = 3^n mod 13.
  • A168400 (program): 3^n mod 15.
  • A168401 (program): 4 + 9*floor(n/2).
  • A168409 (program): a(n) = 8 + 9*floor((n-1)/2).
  • A168410 (program): a(n) = 3 + 9*floor(n/2).
  • A168411 (program): a(n) = 7 + 9*floor((n-1)/2).
  • A168412 (program): a(n) = n^5*(n^6 + 1)/2.
  • A168413 (program): a(n) = 9*n - a(n-1) - 5, with a(1)=2.
  • A168414 (program): a(n) = (18*n - 9*(-1)^n - 3)/4.
  • A168415 (program): a(n) = 2^n + 7.
  • A168416 (program): a(n) = 1 + 9*floor(n/2).
  • A168418 (program): a(n) = 9*n - a(n-1) - 8 with n>1, a(1)=5.
  • A168419 (program): a(n) = 9*floor(n/2).
  • A168420 (program): a(n) = 4 + 10*floor(n/2).
  • A168427 (program): 3^n mod 30.
  • A168428 (program): a(n) = 4^n mod 10.
  • A168429 (program): a(n) = 4^n mod 11.
  • A168430 (program): a(n) = 4^n mod 13.
  • A168432 (program): a(n) = n^5*(n^7 + 1)/2.
  • A168437 (program): a(n) = 3 + 10*floor(n/2).
  • A168441 (program): Expansion of 1/(1-x/(1-2x/(1-4x/(1-6x/(1-8x/(1-…. (continued fraction).
  • A168444 (program): Number of partitions of the set {1,2,…,n} such that no block is a sequence of consecutive integers (including 1-element blocks)
  • A168455 (program): 3^n+n mod 7.
  • A168456 (program): a(n) = (10*n - 5*(-1)^n + 1)/2.
  • A168457 (program): a(n) = (10*n + 5*(-1)^n - 1)/2.
  • A168458 (program): a(n) = 7 + 10*floor((n-1)/2).
  • A168459 (program): a(n) = (10*n + 5*(-1)^n - 3)/2.
  • A168460 (program): a(n) = 6 + 10*floor((n-1)/2).
  • A168461 (program): a(n) = 10*floor(n/2).
  • A168462 (program): a(n) = n^5*(n^8 + 1)/2.
  • A168463 (program): a(n) = 5 + 11*floor(n/2).
  • A168465 (program): Numbers that are congruent to 2 or 7 mod 11.
  • A168471 (program): a(n) = n^5*(n^9 + 1)/2.
  • A168472 (program): Partial sums of products of two distinct primes (A006881).
  • A168480 (program): G.f.: Sum_{n>=0} 2^(n^2)*(1 + 2^n*x)^n*x^n.
  • A168484 (program): Numbers that are congruent to {2, 3, 5, 7} mod 11.
  • A168485 (program): A165342(3n)/3.
  • A168486 (program): Numbers that are congruent to {2, 5} mod 11.
  • A168489 (program): Numbers that are congruent to {7,11} mod 12.
  • A168491 (program): a(n) = (-1)^n*Catalan(n).
  • A168493 (program): a(n) = 3^floor(n^2/2).
  • A168495 (program): a(n) = 3^floor(n^2/3).
  • A168496 (program): The positions of non-single or nonisolated numbers in A001477.
  • A168497 (program): The halfs of even single (or even isolated) numbers.
  • A168504 (program): Hankel transform of A168503.
  • A168505 (program): Expansion of 1/(1-x/(1+x/(1-x/(1-x/(1+x/(1-x/(1-x/(1+x/(1-… (continued fraction).
  • A168506 (program): Number of rooted plane trees of total weight n whose nodes are themselves planted plane trees whose roots are distinguished as either red or blue, the weight of each such node being equal to the size of the corresponding planted tree.
  • A168507 (program): a(n) = n^5*(n^10 + 1)/2.
  • A168509 (program): Triangle read by rows, A051731 * A101688
  • A168510 (program): Products across consecutive rows of the denominators of the Leibniz harmonic triangle (A003506).
  • A168512 (program): Sum of divisors of n weighted by divisor multiplicity in n.
  • A168517 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = -1, b = 1, and c = 1, read by rows.
  • A168518 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = -4, b = 2, and c = 2, read by rows.
  • A168520 (program): a(n) = 98*a(n-1) - a(n-2); a(1) = 0, a(2) = 10.
  • A168522 (program): a(n) = 98*a(n-1) - 2*a(n-2); a(1) = 0, a(2) = 1.
  • A168523 (program): Triangle of coefficients of g.f. a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2), with a = -1, b = 1, c = 1.
  • A168524 (program): Triangle of coefficients of g.f. a*(1+x)^n + b*(1-x)^(n+2)*polylog(-n-1, x)/x + 2^n*c*(1-x)^(n+1)*LerchPhi(x, -n, 1/2), with a = -2, b = 2, c = 1.
  • A168526 (program): a(n) = n^6*(n + 1)/2.
  • A168527 (program): a(n) = n^6*(n^2 + 1)/2.
  • A168538 (program): a(n) = (n+6)*(n+1)*(n^2 + 7*n + 16)/4.
  • A168539 (program): Terms of A123239 which are prime in Z(i), Z(rho) and Z(sqrt(2)).
  • A168543 (program): pi(n-th single or isolated number).
  • A168547 (program): a(n) = 1 - 2*n^2 + 4*n*(1 + 2*n^2)/3.
  • A168550 (program): Natural numbers k for which 1 + 2*k^3 is prime.
  • A168551 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = 1, b = -1, and c = 1, read by rows.
  • A168552 (program): Expansion of g.f. (1/2)*( a*(1+x)^n + b*(1-x)^(n+2)*LerchPhi(x, -n-1, 1) + c*2^(n+1)*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), where a = 3, b = -3, and c = 1, read by rows.
  • A168553 (program): a(n) = 1 if it is possible to place n sets of n queens on an n X n chessboard with no two queens of the same set attacking each other.
  • A168555 (program): a(n) = n^6*(n^3 + 1)/2.
  • A168559 (program): a(n) = n^2 + a(n-1), with a(1)=0.
  • A168561 (program): Riordan array (1/(1-x^2), x/(1-x^2)). Unsigned version of A049310.
  • A168562 (program): Sum of squares of Eulerian numbers in row n of triangle A008292 with a(0)=1.
  • A168563 (program): a(n) = (n-th prime > 3) minus (n-th composite number).
  • A168564 (program): a(n) = n^6*(n^4 + 1)/2.
  • A168565 (program): Let p = prime(n); then a(n) = p + (p-1)/2.
  • A168566 (program): a(n) = (n-1)*(n+2)*(n^2 + n + 2)/4.
  • A168569 (program): a(n) = 9*(3^n - 1)/2.
  • A168570 (program): Exponent of 3 in 2^n - 1.
  • A168571 (program): a(n) = 25*(5^n - 1)/4.
  • A168572 (program): a(n) = Sum_{k=2..n}(7^k).
  • A168574 (program): a(n) = (4*n + 3)*(1 + 2*n^2)/3.
  • A168575 (program): a(n) = (10^n + 1)^3.
  • A168577 (program): Pascal’s triangle, first two columns and diagonal removed.
  • A168579 (program): G.f.: 1/(1-x-16*x^2).
  • A168580 (program): a(n) = (n-th prime > 3) minus 3*n.
  • A168582 (program): a(n) = (4*n^3 - 6*n^2 + 8*n + 9 + 3*(-1)^n)/12.
  • A168583 (program): The number of ways of partitioning the multiset {1,1,2,3,…,n-1} into exactly three nonempty parts.
  • A168584 (program): Number of ways of partitioning the multiset {1,1,2,3,…,n-1} into exactly four nonempty parts.
  • A168585 (program): Number of ways of partitioning the multiset {1,1,2,3,…,n-1} into exactly five nonempty parts.
  • A168587 (program): Smallest digit sum of an n-digit prime with only digits 0 add 1 (or 0, if no such prime exists).
  • A168589 (program): a(n) = (2 - 3^n)*(-1)^n.
  • A168592 (program): G.f.: exp( Sum_{n>=1} A082758(n)*x^n/n ), where A082758(n) = sum of the squares of the trinomial coefficients in row n of triangle A027907.
  • A168595 (program): a(n) = Sum_{k=0..2n} C(2n,k)*A027907(n,k) where A027907 is the triangle of trinomial coefficients.
  • A168596 (program): a(n) = 2*a(n-1) - 1 with a(0)=14.
  • A168597 (program): Squares of the central trinomial coefficients (A002426).
  • A168598 (program): G.f.: exp( Sum_{n>=1} A002426(n)^2*x^n/n ), where A002426(n) is the central trinomial coefficients.
  • A168599 (program): G.f.: exp( Sum_{n>=1} A002426(n)^n * x^n/n ), where A002426(n) is the central trinomial coefficients.
  • A168604 (program): a(n) = 2^(n-2) - 1.
  • A168605 (program): Number of ways of partitioning the multiset {1,1,1,2,3,…,n-2} into exactly three nonempty parts.
  • A168606 (program): The number of ways of partitioning the multiset {1,1,1,2,3,…,n-2} into exactly four nonempty parts.
  • A168607 (program): a(n) = 3^n + 2.
  • A168608 (program): Decimal expansion of average of two-digit primes.
  • A168609 (program): a(n) = 3^n + 4.
  • A168610 (program): a(n) = 3^n + 5.
  • A168611 (program): a(n) = 3^n - 4.
  • A168613 (program): a(n) = 3^n - 5.
  • A168614 (program): a(n) = 2^n + 5.
  • A168615 (program): Inverse binomial transform of A169609, or of A144437 preceded by 1.
  • A168616 (program): a(n) = 2^n - 5.
  • A168617 (program): a(n) = 7*2^(n-1) - 2*n - 5.
  • A168618 (program): Numbers n such that 17*n-1, 17*n+1 are twin primes.
  • A168619 (program): Triangle T(n,k) read by rows with the coefficient [x^k] of the polynomial (x+1)^n + (2*n-3) *( (x+1)^n -x^n -1 ) in column k, row n.
  • A168620 (program): Table T(n,k) with the coefficient [x^k] of the polynomial 5*(x+1)^n - 4*(x^n+1) in column 0<=k<=n. T(0,0)=1.
  • A168622 (program): Triangle T(n,k) with the coefficient [x^k] of the polynomial 7*(x+1)^n - 6*(x^n+1) in row n, column k. T(0,0)=1.
  • A168623 (program): Table T(n,k) read by rows: Coefficients [x^k] of the polynomial 9*(x+1)^n -8*(x^n+1); T(0,0)=1.
  • A168624 (program): a(n) = 1 - 10^n + 100^n.
  • A168625 (program): Triangle T(n,k) = 8*binomial(n,k) - 7 with columns 0 <= k <= n.
  • A168627 (program): a(n) = n^6*(n^5 + 1)/2.
  • A168631 (program): a(n) = n^6*(n^7 + 1)/2.
  • A168632 (program): a(n) = n^6*(n^8 + 1)/2.
  • A168633 (program): a(n) = n^6*(n^9 + 1)/2.
  • A168634 (program): a(n) = n^6*(n^10 + 1)/2.
  • A168635 (program): a(n) = n^7*(n + 1)/2.
  • A168636 (program): a(n) = n^7*(n^2 + 1)/2.
  • A168637 (program): a(n) = a(n-1) + a(n-2) - a(n-4) starting a(0)=0, a(1)=1, a(2)=a(3)=3.
  • A168638 (program): Number of distinct prime divisors of n is 2 or 3.
  • A168639 (program): Expansion of x*(1 + x^2 - x^3) ) / ( (1-x)*(1-x-x^4) ).
  • A168642 (program): a(n) = (8*2^n + (-1)^n)/3 for n > 0; a(0) = 1.
  • A168645 (program): Numbers with 2 or 3 prime divisors (counted with multiplicity).
  • A168647 (program): Reverse (palindrome) of A164844.
  • A168648 (program): a(n) = (10*2^n + 2*(-1)^n)/3 for n > 0; a(0) = 1.
  • A168649 (program): a(n) = (1/n)*Sum_{d|n} moebius(d)*2^(n^2/d).
  • A168650 (program): Integers that can be generated with a C/C++ expression that is shorter than their decimal representation.
  • A168651 (program): Integers that can be generated with a C/C++ expression that is two or more characters shorter than their decimal representation.
  • A168652 (program): Integers that can be generated with a C/C++ expression that is three or more characters shorter than their decimal representation.
  • A168658 (program): a(n) = ceiling(n^n/2).
  • A168660 (program): a(n) = n^7*(n^3 + 1)/2.
  • A168661 (program): a(n) = n^7*(n^4 + 1)/2.
  • A168662 (program): a(n) = n^7*(n^5 + 1)/2.
  • A168663 (program): a(n) = n^7*(n^6 + 1)/2.
  • A168664 (program): a(n) = n^7*(n^7 + 1)/2.
  • A168665 (program): a(n) = n^7*(n^8 + 1)/2.
  • A168666 (program): a(n) = n^7*(n^9 + 1)/2.
  • A168667 (program): a(n) = n^7*(n^10 + 1)/2.
  • A168668 (program): a(n) = n*(2 + 5*n).
  • A168669 (program): Numbers n such that sqrt(36*n+49) is prime.
  • A168670 (program): Numbers that are congruent to {1, 8} mod 11.
  • A168671 (program): Numbers that are congruent to {1, 10} mod 13.
  • A168672 (program): Numbers that are congruent to {2,13} mod 17.
  • A168673 (program): Binomial transform of A169609.
  • A168674 (program): a(n) = 2*A001610(n).
  • A168675 (program): a(n) = n^8*(n + 1)/2.
  • A168676 (program): Coefficients of characteristic polynomials for a two diagonal Matrix type that has determinant equal to trace:M(n)=Table[If[ k == m && m < n, 1, If[k == m + 1, 1, If[k == 1 && m == n, (-1)^(n + 1)*(n - 1), 0]]], {k, n}, {m, n}]
  • A168677 (program): Lexicographically earliest positive integer sequence such that no sum of consecutive terms is a positive power of 4.
  • A168834 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168835 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168836 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168837 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168838 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168839 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168840 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168841 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168842 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168843 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168844 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168845 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168846 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168847 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168848 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168849 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168850 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168851 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168852 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168853 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168854 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168855 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168856 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168857 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168858 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168859 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168860 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168861 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168862 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168863 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168864 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168865 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168866 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168867 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168868 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168869 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168870 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168871 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.
  • A168876 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168877 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168878 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168879 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168880 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168882 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168883 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168884 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168885 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168886 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168887 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168888 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168889 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168890 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168891 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168892 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168893 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168894 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168895 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168896 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168897 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168898 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168899 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168900 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168901 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168902 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168903 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168904 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168905 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168906 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168907 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168908 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168909 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168910 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168911 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168912 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168913 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168914 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168915 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168916 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168917 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168918 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168919 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.
  • A168923 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168924 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168925 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168926 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168927 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168928 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168929 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168930 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168931 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168932 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168933 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168934 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168935 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168936 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168937 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168938 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168939 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168940 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168941 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168942 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168943 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168944 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168945 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168946 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168947 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168948 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168949 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168950 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168951 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168952 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168953 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168954 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168955 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168956 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168957 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168958 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168959 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168960 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168961 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168962 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168963 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168964 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168965 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168966 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168967 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.
  • A168971 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168972 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168973 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168974 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168975 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168976 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168977 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168978 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168979 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168980 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168981 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168982 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168983 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168984 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168985 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168986 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168987 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168988 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168989 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168990 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168991 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168992 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168993 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168994 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168995 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168996 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168997 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168998 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A168999 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169000 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169001 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169002 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169003 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169004 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169005 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169006 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169007 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169008 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169009 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169010 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169011 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169012 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169013 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169014 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169015 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.
  • A169018 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169019 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169021 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169022 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169023 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169024 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169025 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169026 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169027 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169028 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169029 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169030 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169031 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169032 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169033 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169034 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169035 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169036 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169037 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169038 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169039 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169040 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169041 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169042 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169043 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169044 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169045 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169046 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169047 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169048 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169049 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169050 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169051 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169052 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169053 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169054 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169055 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169056 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169057 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169058 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169059 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169060 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169061 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169062 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169063 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.
  • A169066 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169067 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169068 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169069 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169070 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169071 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169072 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169073 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169074 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169075 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169076 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169077 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169078 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169079 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169080 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169081 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169082 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169083 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169084 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169085 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169086 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169087 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169088 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169089 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169090 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169092 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169093 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169094 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169095 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169096 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169097 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169098 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169099 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169100 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169101 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169102 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169103 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169104 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169105 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169106 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169107 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169108 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169109 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169110 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169111 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.
  • A169113 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169115 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169116 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169117 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169118 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169119 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169120 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169121 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169122 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169123 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169124 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169125 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169126 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169127 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169128 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169129 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169130 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169131 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169132 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169134 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169135 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169136 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169137 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169138 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169139 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169140 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169141 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169142 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169143 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169144 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169145 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169146 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169148 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169149 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169150 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169151 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169152 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169153 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169154 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169155 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169156 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169157 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169158 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169159 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.
  • A169161 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169162 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169163 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169164 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169165 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169166 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169167 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169168 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169169 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169170 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169171 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169172 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169173 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169174 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169175 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169176 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169177 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169178 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169179 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169180 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169181 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169182 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169183 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169184 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169185 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169186 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169187 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169188 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169189 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169190 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169192 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169193 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169194 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169195 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169196 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169197 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169198 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169199 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169200 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169201 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169202 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169203 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169204 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169205 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169206 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169207 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.
  • A169209 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169210 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169211 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169212 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169214 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169215 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169216 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169217 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169218 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169219 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169220 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169221 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169222 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169223 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169224 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169225 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169226 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169227 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169228 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169229 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169230 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169231 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169232 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169233 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169234 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169235 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169236 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169237 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169238 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169240 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169241 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169242 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169243 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169244 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169245 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169246 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169247 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169248 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169249 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169250 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169251 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169252 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169253 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169254 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169255 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.
  • A169257 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169258 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169259 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169260 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169261 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169262 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169263 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169264 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169265 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169266 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169267 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169268 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169269 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169270 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169271 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169272 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169273 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169274 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169275 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169276 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169277 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169278 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169279 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169280 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169281 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169282 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169283 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169284 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169285 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169286 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169288 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169289 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169290 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169291 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169292 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169293 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169294 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169295 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169296 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169297 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169298 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169299 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169300 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169301 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169302 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169303 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.
  • A169305 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169306 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169307 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169308 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169309 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169310 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169311 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169312 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169313 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169314 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169315 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169316 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169317 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169318 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169319 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169320 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169321 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169322 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169323 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169324 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169325 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169326 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169327 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169328 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169329 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169330 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169331 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169332 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169333 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169334 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169335 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169336 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169337 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169338 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169339 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169340 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169341 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169342 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169343 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169344 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169346 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169347 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169348 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169349 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169350 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169351 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.
  • A169353 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169354 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169355 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169356 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169358 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169359 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169360 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169361 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169362 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169363 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169364 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169365 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169366 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169367 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169368 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169369 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169370 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169371 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169372 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169373 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169374 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169375 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169376 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169377 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169378 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169379 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169380 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169381 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169382 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169383 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169384 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169385 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169386 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169387 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169388 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169389 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169391 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169392 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169393 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169394 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169395 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169396 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169397 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169398 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169399 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.
  • A169406 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169407 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169408 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169409 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169410 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169411 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169412 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169413 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169414 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169415 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169416 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169417 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169418 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169419 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169420 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169421 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169422 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169423 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169424 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169425 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169426 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169427 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169428 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169429 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169430 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169431 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169432 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169433 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169434 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169435 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169436 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169437 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169438 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169439 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169440 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169441 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169442 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169443 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169444 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169445 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169446 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169447 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.
  • A169448 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169449 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169450 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169451 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169453 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169454 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169455 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169456 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169457 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169458 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169459 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169460 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169461 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169462 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169464 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169465 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169466 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169467 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169468 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169469 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169470 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169471 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169472 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169473 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169474 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169475 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169476 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169477 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169478 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169479 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169480 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169481 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169482 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169483 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169485 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169486 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169487 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169488 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169489 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169490 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169491 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169492 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169493 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169494 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169495 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.
  • A169496 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169497 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169498 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169499 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169500 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169501 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169502 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169503 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169504 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169505 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169506 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169507 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169508 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169509 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169510 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169511 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169512 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169513 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169514 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169515 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169516 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169517 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169518 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169519 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169520 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169521 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169522 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169523 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169524 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169525 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169526 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169527 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169528 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169529 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169530 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169531 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169532 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169533 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169534 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169535 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169536 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169537 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169538 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169539 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169540 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169541 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169542 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169543 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.
  • A169544 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169545 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169547 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169548 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169549 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169550 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169551 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169552 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169553 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169554 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169555 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169556 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169558 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169559 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169560 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169561 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169562 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169563 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169564 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169565 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169567 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169568 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169569 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169570 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169571 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169572 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169573 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169574 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169575 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169576 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169577 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169578 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169579 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A169580 (program): Squares of the form x^2+y^2+z^2 with x,y,z positive integers.
  • A169581 (program): Positions in A002260(n) and A002024(n) when canonically enumerating A038566(n)/A038567(n), the positive rational numbers <= 1.
  • A169582 (program): Complement of A169581.
  • A169585 (program): A000004 preceded by 1, 3.
  • A169587 (program): The total number of ways of partitioning the multiset {1,1,1,2,3,…,n-2}.
  • A169589 (program): A number triangle with repeated columns of triangle in A039599.
  • A169590 (program): Triangle T(n,k) with : column n = A000034 if n even and column n = A000007 if n odd.
  • A169591 (program): Triangle T(n,k) with column n = A059841 if n even and column n = A000007 if n odd.
  • A169594 (program): Number of divisors of n, counting divisor multiplicity in n.
  • A169597 (program): Numbers that are congruent to {2, 15} mod 19.
  • A169598 (program): Numbers that are congruent to {3,18} mod 23.
  • A169599 (program): Numbers that are congruent to {4, 23} mod 29.
  • A169600 (program): Numbers that are congruent to {4, 25} mod 31.
  • A169601 (program): a(n) = (10^n-1)^2 + 2.
  • A169603 (program): Triangle T(n,k) = k*(4*n+k+2), read by rows.
  • A169604 (program): a(n) = 3*6^n.
  • A169605 (program): Numbers x of the form x = 2*y - 3 = 3*z - 2 where y and z are primes.
  • A169606 (program): a(2n-1) = prime(n+2)-3, a(2n) = prime(n+2)-2.
  • A169607 (program): a(n) = 7*A000330(n).
  • A169609 (program): Period 3: repeat [1, 3, 3].
  • A169610 (program): Numbers that are congruent to {5, 30} mod 37.
  • A169611 (program): Number of prime divisors of n that are not greater than 3, counted with multiplicity.
  • A169622 (program): a(n) = a(n-1) + Fibonacci(n), a(1)=5.
  • A169623 (program): Generalized Pascal triangle read by rows: T(n,0) = T(0,n) = 1 for n >= 0, T(n,k) = 0 for k < 0 or k > n; otherwise T(n,k) = T(n-2,k-2) + T(n-2,k-1) + T(n-2,k) for 1 <= k <= n-1.
  • A169629 (program): Array T(n,k) read by antidiagonals: T(n,k) = Sum_{v=1..n, v odd} binomial(n,v)*k^v.
  • A169630 (program): a(n) = n times the square of Fibonacci(n).
  • A169634 (program): a(n) = 3*7^n.
  • A169642 (program): a(n) = A005408(n) * A022998(n).
  • A169643 (program): Numbers n such that neither composite(n)-+1 is composite.
  • A169644 (program): Numbers with two or more distinct factorizations m*k such that m <= k <= 2*m.
  • A169646 (program): Number of squarefree numbers of form k*n, 1 <= k <= n.
  • A169650 (program): a(1) = 3; thereafter a(n) = 3*a(n-1)+2^n-6.
  • A169651 (program): a(0)=a(1)=1, a(2)=2; thereafter a(n) = 3*a(n-1) + 3*2^(n-3) - 2.
  • A169656 (program): Triangle, read by rows, T(n, k) = (-1)^n*(n!/k!)^2*binomial(n-1, k-1).
  • A169666 (program): Numbers divisible by the sum of 5th powers of their digits.
  • A169669 (program): (first digit of n) * (last digit of n) in decimal representation.
  • A169675 (program): Lexicographically earliest de Bruijn sequence for n = 3 and k = 2.
  • A169676 (program): Lexicographically earliest de Bruijn sequence for n = 2 and k = 3.
  • A169683 (program): The canonical skew-binary numbers.
  • A169686 (program): a(n) = sqrt(T(k-1)*T(k)*T(k+1) as k runs through the terms of A072221 and T(i)=i*(i+1)/2.
  • A169687 (program): a(n) = 3^n - 3*2^(n-2).
  • A169690 (program): Let S be the sequence Fibonacci(2n), n>0 (cf. A001906); sequence lists the differences S(j)-S(i) for i<j.
  • A169691 (program): Let T be the sequence Fibonacci(2n+1), n>=0 (cf. A001519); sequence lists the differences T(j)-T(i) for i<j.
  • A169692 (program): Numbers that are in neither A169690 nor A169691.
  • A169693 (program): A169690 union A169691.
  • A169695 (program): a(n) = 1 if n is a square, otherwise a(n) = 2.
  • A169697 (program): The rows of A169689 converge to 4 times this sequence.
  • A169698 (program): A bisection of A169697.
  • A169703 (program): Total number of ON cells at stage n of two-dimensional cellular automaton defined by “Rule 174”.
  • A169704 (program): First differences of A169703.
  • A169707 (program): Total number of ON cells at stage n of two-dimensional cellular automaton defined by “Rule 750” using the von Neumann neighborhood.
  • A169708 (program): First differences of A169707.
  • A169711 (program): The function W_n(6) (see Borwein et al. reference for definition).
  • A169712 (program): The function W_n(8) (see Borwein et al. reference for definition).
  • A169713 (program): The function W_n(10) (see Borwein et al. reference for definition).
  • A169718 (program): Number of ways of making change for n cents using coins of 1, 5, 10, 25, 50 and 100 cents.
  • A169720 (program): a(n) = (3*2^(n-1)-1)*(3*2^n-1).
  • A169721 (program): a(n) = (2*(3*2^(n-1)-1))^2.
  • A169722 (program): a(n) = (3*2^(n-1)-1)*(18*2^(n-1)-7).
  • A169723 (program): 3^(n-1)*(2*3^(n-1)+3)+1.
  • A169724 (program): (2*3^(n-1)+1)^2.
  • A169725 (program): a(n) = 3^(n-1)*(6*3^(n-1) + 5) + 1.
  • A169726 (program): a(n) = 3*2^n*(2^n-1) + 1.
  • A169727 (program): a(n) = 3*(2^(n+1)-2)*(2^(n+1)-1) + 1.
  • A169734 (program): a(1) = 1000; for n>1, a(n) = a(n-1) + digitsum(a(n-1)).
  • A169735 (program): a(1) = 100; for n>1, a(n) = a(n-1) - digitsum(a(n-1)).
  • A169736 (program): First differences of A169735.
  • A169737 (program): a(1) = 100; for n>1, a(n) = a(n-1) + digitsum(a(n-1)).
  • A169739 (program): a(n) = A030068(4n+1).
  • A169740 (program): a(n) = A030068(4n+3).
  • A169760 (program): A169759(n)/6.
  • A169783 (program): Number of solutions to a^2 + b^2 + 4*c^2 = n.
  • A169792 (program): Expansion of ((1-x)/(1-2x))^5.
  • A169793 (program): Expansion of ((1-x)/(1-2*x))^6.
  • A169794 (program): Expansion of ((1-x)/(1-2*x))^7.
  • A169795 (program): Expansion of ((1-x)/(1-2x))^8.
  • A169796 (program): Expansion of ((1-x)/(1-2x))^9.
  • A169797 (program): Expansion of ((1-x)/(1-2x))^10.
  • A169801 (program): a(n) = ((n-1)^2*n^2*(n+1)^2)/6 - 2*Sum_{l=2..n}Sum_{k=2..n}(n-k+1)*(n-l+1)*(k-1)*(l-1).
  • A169803 (program): Triangle read by rows: T(n,k) = binomial(n+1-k,k) (n >= 0, 0 <= k <= n).
  • A169805 (program): Twice the sum of the digits of n.
  • A169810 (program): a(n) = n XOR n^2.
  • A169811 (program): a(n) = n XOR n*(n+1)/2.
  • A169812 (program): a(n) = n XOR d(n) (cf. A000005).
  • A169813 (program): a(n) = n XOR sigma(n), where sigma(n) is the number of divisors of n, A000203.
  • A169814 (program): a(n) = n XOR phi(n).
  • A169823 (program): Multiples of 60.
  • A169825 (program): Multiples of 420.
  • A169827 (program): Multiples of 840.
  • A169830 (program): Numbers n such that 2*reverse(n) - n = 1.
  • A169831 (program): a(n) = 5*2^(n+1) - 3*(n+3).
  • A169832 (program): a(n) = 15*2^(n+1) - (5*n^2+22*n+30).
  • A169833 (program): a(n) = 25*2^(n+3) - (198+392*n/3+36*n^2+10*n^3/3).
  • A169860 (program): Floor of n inches converted to millimeters.
  • A169861 (program): Ceiling of n inches converted to millimeters.
  • A169864 (program): The sequence S of a pair S, T generalizing Golomb’s sequence A001462 and the pair A093848, A169863. See Comments for definition.
  • A169865 (program): The sequence T of a pair S, T generalizing Golomb’s sequence A001462 and the pair A093848, A169863. See Comments for definition.
  • A169868 (program): Positions of zeros in binary expansion of the reciprocal of the golden ratio (0.618…).
  • A169869 (program): Maximum number of rational points on a smooth absolutely irreducible projective curve of genus n over the field F_2.
  • A169900 (program): Earliest sequence such that xy | a(x+y) for all x>=1, y>=1.
  • A169902 (program): Earliest sequence such that xy | a(x+y) and (x+y) | a(xy) for all x >= 1, y >= 1.
  • A169909 (program): a(n) = n+n in carryless arithmetic mod 9 in base 10.
  • A169910 (program): a(n) = n+n in carryless digital root arithmetic in base 10.
  • A169915 (program): Numbers n such that 2n+A067076(n) is prime.
  • A169919 (program): a(n) = n*n in the arithmetic where digits are added in base 10 (as usual) but when digits are to be multiplied they are also added in base 10.
  • A169922 (program): Values of n >= 0 such that 3*n-36+360/(n+10) is an integer.
  • A169924 (program): Values of n >= 0 such that 4*n-40+360/(n+9) is an integer.
  • A169926 (program): Values of n >= 0 such that 3*n-45+360/(n/2+8) is an integer.
  • A169928 (program): Values of n >= 7 such that 10*n-122+360/n is an integer.
  • A169931 (program): a(n) = 2*n in the arithmetic defined in A169918.
  • A169932 (program): a(n) = 0+n in the arithmetic defined in A169918.
  • A169933 (program): a(n) = 2+n in the arithmetic defined in A169918.
  • A169937 (program): a(n) = binomial(m+n-1,n)^2 - binomial(m+n,n+1)*binomial(m+n-2,n-1) with m = 14.
  • A169938 (program): a(n) = n*(n+1)*(n*(n+1)+1).
  • A169958 (program): a(n) = binomial(9*n, n).
  • A169959 (program): a(n) = binomial(10*n, n).
  • A169960 (program): a(n) = binomial(11*n,n).
  • A169961 (program): a(n) = binomial(12*n, n).
  • A169963 (program): Number of (2n+1)-digit squares in carryless arithmetic mod 10.
  • A169964 (program): Numbers whose decimal expansion contains only 0’s and 5’s.
  • A169965 (program): Numbers whose decimal expansion contains only 0’s and 2’s.
  • A169966 (program): Numbers whose decimal expansion contains only 0’s and 3’s.
  • A169967 (program): Numbers whose decimal expansion contains only 0’s and 4’s.
  • A169968 (program): Positive integers not in A169884.
  • A169969 (program): Locations of row maxima in “crushed” version of Stern’s diatomic array.
  • A169972 (program): Product of Eulerian numbers T(n,k), k=0..n-1.
  • A169974 (program): Sum_{i=0..n} { 2^C(n,i) } - n.
  • A169975 (program): Expansion of Product_{i>=0} (1 + x^(4*i+1)).
  • A169976 (program): Expansion of (psi(x)^24 + psi(-x)^24) / 2 in powers of x^2 where psi() is a Ramanujan theta function.
  • A169985 (program): Round phi^n to the nearest integer.
  • A169986 (program): Ceiling(phi^n) where phi = (1+sqrt(5))/2.
  • A169987 (program): Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=4.
  • A169988 (program): Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=5.
  • A169989 (program): Expansion of Product_{i=0..m-1} 1 + x^(2*i+1) for m=6.
  • A169990 (program): Expansion of Product_{i=0..m-1} (1 + x^(2*i+1)) for m=7.
  • A169998 (program): a(0)=1, a(1)=1; thereafter a(n) = -a(n-1) - 2*a(n-2).
  • A170000 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170001 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170002 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170003 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170004 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170005 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170006 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170007 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170008 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170009 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170010 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170011 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.
  • A170012 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170013 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170014 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170015 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170016 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170017 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170018 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170019 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170020 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170021 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170022 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170023 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170024 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170025 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170026 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170027 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170028 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170029 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170030 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170031 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170032 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170033 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170034 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170035 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170036 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170037 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170038 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170039 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170040 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170041 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170042 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170043 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170044 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170045 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170046 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170047 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170048 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170049 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170050 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170051 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170052 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170053 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170054 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170055 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170056 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170057 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170058 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170059 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.
  • A170060 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170061 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170062 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170063 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170064 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170065 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170066 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170067 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170068 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170069 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170070 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170071 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170072 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170073 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170075 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170076 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170077 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170078 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170079 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170080 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170081 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170082 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170083 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170084 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170085 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170086 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170087 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170088 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170089 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170090 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170091 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170092 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170093 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170094 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170095 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170096 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170097 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170098 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170099 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170100 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170101 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170102 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170103 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170104 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170105 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170106 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170107 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.
  • A170108 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170110 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170111 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170112 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170113 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170114 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170115 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170116 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170117 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170118 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170119 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170120 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170121 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170122 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170123 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170124 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170125 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170126 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170127 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170128 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170129 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170130 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170131 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170132 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170133 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170134 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170135 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170137 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170138 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170139 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170140 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170141 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170143 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170144 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170145 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170146 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170147 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170148 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170149 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170150 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170151 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170152 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170153 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170154 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170155 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.
  • A170156 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170157 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170158 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170159 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170160 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170161 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170162 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170163 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170164 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170165 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170166 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170167 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170168 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170169 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170170 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170171 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170172 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170173 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170174 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170175 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170176 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170177 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170178 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170179 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170180 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170181 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170182 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170184 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170185 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170186 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170187 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170188 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170189 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170190 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170191 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170192 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170193 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170194 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170195 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170196 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170197 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170198 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170199 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170200 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170201 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170202 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170203 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.
  • A170204 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170205 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170206 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170207 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170208 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170209 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170210 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170211 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170212 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170213 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170214 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170215 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170216 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170217 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170218 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170219 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170220 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170221 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170222 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170223 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170224 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170225 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170226 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170227 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170228 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170229 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170230 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170231 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170232 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170233 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170234 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170235 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170236 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170237 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170238 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170239 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170240 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170241 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170242 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170243 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170244 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170245 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170246 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170247 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170248 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170249 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170250 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170251 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.
  • A170252 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170253 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170254 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170255 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170256 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170257 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170258 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170259 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170260 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170261 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170262 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170263 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170264 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170265 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170266 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170267 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170268 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170269 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170270 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170271 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170272 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170273 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170274 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170275 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170276 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170277 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170278 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170279 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170280 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170281 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170282 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170283 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170284 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170285 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170286 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170287 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170288 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170289 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170290 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170291 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170292 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170293 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170294 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170295 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170296 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170297 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170298 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170299 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.
  • A170300 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170301 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170302 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170303 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170304 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170305 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170306 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170307 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170308 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170309 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170310 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170311 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170312 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170313 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170314 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170315 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170316 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170317 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170318 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170319 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170320 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170321 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170322 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170323 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170324 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170325 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170326 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170327 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170328 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170329 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170330 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170331 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170332 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170333 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170334 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170335 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170336 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170337 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170338 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170339 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170340 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170341 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170342 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170343 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170344 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170345 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170346 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170347 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.
  • A170348 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170349 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170350 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170351 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170352 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170353 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170354 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170355 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170356 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170357 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170358 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170359 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170360 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170361 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170362 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170363 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170364 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170366 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170367 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170369 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170370 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170371 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170372 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170373 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170374 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170375 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170376 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170377 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170378 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170379 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170380 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170381 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170382 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170383 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170384 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170385 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170386 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170387 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170388 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170389 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170390 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170391 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170392 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170393 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170394 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170395 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.
  • A170396 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170397 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170398 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170399 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170400 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170401 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170402 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170403 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170404 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170405 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170406 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170407 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170408 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170409 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170410 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170411 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170412 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170413 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170415 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170416 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170417 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170418 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170419 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170420 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170421 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170422 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170423 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170424 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170425 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170426 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170427 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170428 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170429 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170430 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170431 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170432 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170433 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170434 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170435 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170436 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170437 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170438 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170439 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170440 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170441 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170442 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170443 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.
  • A170444 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170445 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170446 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170447 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170448 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170449 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170450 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170451 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170452 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170453 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170454 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170456 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170457 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170458 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170459 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170460 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170461 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170462 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170463 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170464 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170465 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170466 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170467 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170468 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170469 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170470 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170471 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170472 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170473 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170474 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170475 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170476 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170477 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170478 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170479 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170480 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170481 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170482 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170483 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170484 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170485 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170486 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170487 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170488 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170489 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170490 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170491 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.
  • A170492 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170493 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170494 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170495 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170496 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170497 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170498 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170499 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170500 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170501 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170502 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170503 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170504 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170505 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170506 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170507 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170508 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170509 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170510 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170511 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170512 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170513 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170514 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170515 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170516 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170517 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170518 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170519 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170520 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170521 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170522 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170523 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170524 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170525 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170526 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170527 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170528 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170529 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170530 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170531 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170532 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170533 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170534 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170535 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170536 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170537 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170538 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170539 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.
  • A170540 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170541 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170542 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170543 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170544 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170545 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170546 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170547 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170548 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170549 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170550 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170551 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170552 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170553 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170554 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170555 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170556 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170557 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170558 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170559 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170560 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170561 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170562 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170563 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170564 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170565 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170566 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170567 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170568 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170569 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170570 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170571 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170572 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170573 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170574 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170575 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170576 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170577 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170578 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170579 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170580 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170581 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170582 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170583 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170584 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170585 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170586 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170587 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.
  • A170588 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170589 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170590 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170591 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170592 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170593 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170594 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170595 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170596 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170597 (program): Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170598 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170599 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170600 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170601 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170602 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170603 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170604 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170605 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170606 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170607 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170608 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170609 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170610 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170611 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170612 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170613 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170614 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170615 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170616 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170617 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170618 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170619 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170620 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170621 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170622 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170623 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170624 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170625 (program): Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170626 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170627 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170628 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170629 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170630 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170631 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170632 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170633 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170634 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170635 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.
  • A170636 (program): Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170637 (program): Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170638 (program): Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170639 (program): Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170640 (program): Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170641 (program): Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170642 (program): Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170643 (program): Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170644 (program): Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170646 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170647 (program): Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170648 (program): Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170649 (program): Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170650 (program): Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170651 (program): Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170652 (program): Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170653 (program): Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170654 (program): Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170655 (program): Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170656 (program): Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170657 (program): Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170658 (program): Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170659 (program): Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170660 (program): Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170661 (program): Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170662 (program): Number of reduced words of length n in Coxeter group on 29 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170663 (program): Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170664 (program): Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170665 (program): Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170666 (program): Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170667 (program): Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170668 (program): Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170669 (program): Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170670 (program): Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170671 (program): Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170672 (program): Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170674 (program): Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170675 (program): Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170676 (program): Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170677 (program): Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170678 (program): Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170679 (program): Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170680 (program): Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170681 (program): Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170682 (program): Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170683 (program): Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.
  • A170694 (program): Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.
  • A170732 (program): Expansion of g.f.: (1+x)/(1 - 12*x).
  • A170733 (program): Expansion of g.f.: (1+x)/(1-13*x).
  • A170734 (program): Expansion of g.f.: (1+x)/(1-14*x).
  • A170735 (program): Expansion of g.f.: (1+x)/(1-15*x).
  • A170736 (program): Expansion of g.f.: (1+x)/(1-16*x).
  • A170737 (program): Expansion of g.f.: (1+x)/(1-17*x).
  • A170738 (program): Expansion of g.f.: (1+x)/(1-18*x).
  • A170739 (program): Expansion of g.f.: (1+x)/(1-19*x).
  • A170740 (program): Expansion of g.f.: (1+x)/(1-20*x).
  • A170741 (program): Expansion of g.f.: (1+x)/(1-21*x).
  • A170742 (program): Expansion of g.f.: (1+x)/(1-22*x).
  • A170743 (program): Expansion of g.f.: (1+x)/(1-23*x).
  • A170744 (program): Expansion of g.f.: (1+x)/(1-24*x).
  • A170745 (program): Expansion of g.f.: (1+x)/(1-25*x).
  • A170746 (program): Expansion of g.f.: (1+x)/(1-26*x).
  • A170747 (program): Expansion of g.f.: (1+x)/(1-27*x).
  • A170748 (program): Expansion of g.f.: (1+x)/(1-28*x).
  • A170749 (program): Expansion of g.f.: (1+x)/(1-29*x).
  • A170750 (program): Expansion of g.f.: (1+x)/(1-30*x).
  • A170751 (program): Expansion of g.f.: (1+x)/(1-31*x).
  • A170752 (program): Expansion of g.f.: (1+x)/(1-32*x).
  • A170753 (program): Expansion of g.f.: (1+x)/(1-33*x).
  • A170754 (program): Expansion of g.f.: (1+x)/(1-34*x).
  • A170755 (program): Expansion of g.f.: (1+x)/(1-35*x).
  • A170756 (program): Expansion of g.f.: (1+x)/(1-36*x).
  • A170757 (program): Expansion of g.f.: (1+x)/(1-37*x).
  • A170758 (program): Expansion of g.f.: (1+x)/(1-38*x).
  • A170759 (program): Expansion of g.f.: (1+x)/(1-39*x).
  • A170760 (program): Expansion of g.f.: (1+x)/(1-40*x).
  • A170761 (program): Expansion of g.f.: (1+x)/(1-41*x).
  • A170762 (program): Expansion of g.f.: (1+x)/(1-42*x).
  • A170763 (program): Expansion of g.f.: (1+x)/(1-43*x).
  • A170764 (program): Expansion of g.f.: (1+x)/(1-44*x).
  • A170765 (program): Expansion of g.f.: (1+x)/(1-45*x).
  • A170766 (program): Expansion of g.f.: (1+x)/(1-46*x).
  • A170767 (program): Expansion of g.f.: (1+x)/(1-47*x).
  • A170768 (program): Expansion of g.f.: (1+x)/(1-48*x).
  • A170769 (program): Expansion of g.f.: (1+x)/(1-49*x).
  • A170770 (program): Expansion of ( phi(q) * phi(q^63) + phi(-q) * phi(-q^63) + 4 * q^16 * psi(q^2) * psi(q^126) ) / 2 in powers of q^2 where phi(), psi() are Ramanujan theta functions.
  • A170774 (program): a(n) = n^8*(n^2+1)/2.
  • A170775 (program): a(n) = n^8*(n^3 + 1)/2.
  • A170776 (program): a(n) = n^8*(n^4 + 1)/2.
  • A170777 (program): a(n) = n^8*(n^5 + 1)/2.
  • A170778 (program): a(n) = n^8*(n^6 + 1)/2.
  • A170779 (program): a(n) = n^8*(n^7 + 1)/2.
  • A170780 (program): a(n) = n^8*(n^8 + 1)/2.
  • A170781 (program): a(n) = n^8*(n^9 + 1)/2.
  • A170782 (program): a(n) = n^8*(n^10 + 1)/2.
  • A170783 (program): a(n) = n^9*(n + 1)/2.
  • A170784 (program): a(n) = n^9*(n^2 + 1)/2.
  • A170785 (program): a(n) = n^9*(n^3 + 1)/2.
  • A170786 (program): a(n) = n^9*(n^4 + 1)/2.
  • A170787 (program): a(n) = n^9*(n^5 + 1)/2.
  • A170788 (program): a(n) = n^9*(n^6 + 1)/2.
  • A170789 (program): a(n) = n^9*(n^7 + 1)/2.
  • A170790 (program): a(n) = n^9*(n^8 + 1)/2.
  • A170791 (program): a(n) = n^9*(n^9 + 1)/2.
  • A170792 (program): a(n) = n^9*(n^10 + 1)/2.
  • A170793 (program): a(n) = n^10*(n + 1)/2.
  • A170794 (program): a(n) = n^10*(n^2 + 1)/2.
  • A170795 (program): a(n) = n^10*(n^3 + 1)/2.
  • A170796 (program): a(n) = n^10*(n^4 + 1)/2.
  • A170797 (program): a(n) = n^10*(n^5+1)/2.
  • A170798 (program): a(n) = n^10*(n^6 + 1)/2.
  • A170799 (program): a(n) = n^10*(n^7 + 1)/2.
  • A170800 (program): a(n) = n^10*(n^8 + 1)/2.
  • A170801 (program): a(n) = n^10*(n^9 + 1)/2.
  • A170802 (program): a(n) = n^10*(n^10 + 1)/2.
  • A170803 (program): Partial sums of A006899.
  • A170804 (program): Partial sums of (A006899, prefixed by a 1).
  • A170805 (program): a(n) = A170803(n-1) + 2, with a(0) = 1, a(1) = 2.
  • A170816 (program): a(n)=A140475(n)-A141468(n).
  • A170817 (program): a(n) = product of distinct primes of form 4k+1 that divide n.
  • A170818 (program): a(n) is the product of primes (with multiplicity) of form 4*k+1 that divide n.
  • A170819 (program): a(n) = product of distinct primes of the form 4k-1 that divide n.
  • A170821 (program): Let p = n-th prime; a(n) = smallest k >= 0 such that 4k == 3 mod p.
  • A170823 (program): An infinite word on the alphabet 1, 2, 3 by Bollobas.
  • A170824 (program): a(n) = product of distinct primes of form 6k+1 that divide n.
  • A170825 (program): a(n) is the product of the distinct primes of form 6*k-1 that divide n.
  • A170826 (program): a(n) = gcd(n^2, n!).
  • A170827 (program): Sum of digits after the decimal point in the decimal expansion of (3/2)^n.
  • A170828 (program): Partial sums of A170827.
  • A170829 (program): a(n) = gcd(Catalan(n), n!).
  • A170831 (program): a(n) = 2^(floor(n/2))+2^(floor(n/2)-1)-2^(floor((n-1)/3)).
  • A170832 (program): a(n) = 3^(floor(n/2))+3^(floor(n/2)-1)-3^(floor((n-1)/3)).
  • A170833 (program): a(n) = 4^(floor(n/2))+4^(floor(n/2)-1)-4^(floor((n-1)/3)).
  • A170834 (program): a(n) = 5^(floor(n/2))+5^(floor(n/2)-1)-5^(floor((n-1)/3)).
  • A170836 (program): First differences of A170837.
  • A170837 (program): a(0)=0, a(1)=1 and a(n) = 16n-27 for n >= 2.
  • A170844 (program): G.f.: Product_{k>=0} (1 + 3x^(2^k-1) + x^(2^k)).
  • A170878 (program): First differences of A072272.
  • A170881 (program): a(0)=0; thereafter a(n) = (3*n+1)*2^(n-2)+1.
  • A170888 (program): Similar to A160406, but always staying outside the wedge, starting at stage 0 with a vertical half-toothpick which protrudes from the vertex of the wedge.
  • A170894 (program): Similar to A160406, always staying outside the wedge, but starting with a horizontal toothpick whose endpoint touches the vertex of the wedge.
  • A170895 (program): First differences of A170894.
  • A170903 (program): a(n) = 2*A160552(n)-1.
  • A170925 (program): G.f.: eta(q)*eta(q^2)*eta(q^4)*eta(q^8)*eta(q^16)*eta(q^32)*…, where eta(q) = Product((1-q^m), m=1..oo).
  • A170930 (program): G(n,1) with n index G(n,i)=n*(G(n,i-1)+G(n,i-2))=(a^i-b^i)*d where d=sqrt(n*(n+4)); a=(n+d)/2; b=(n-d)/2
  • A170931 (program): Extended Lucas L(n,i) = n*(L(n,i-1) + L(n,i-2)) = a^i + b^i where d = sqrt(n*(n+4)); a=(n+d)/2; b=(n-d)/2.
  • A170932 (program): a(n) = binomial(n + 8, 8)*7^n .
  • A170933 (program): a(n) = A000930(n) + A000930(n+3) + 4.
  • A170934 (program): a(n) = b(n) + b(n+1) + 2, where b() = A000930().
  • A170935 (program): b(n)*b(n+1), where b() = A000930().
  • A170938 (program): 4^n+2^n+2.
  • A170939 (program): 4^n-2^n+2.
  • A170940 (program): 4^n-2^n-2.
  • A170941 (program): a(n+1) = a(n) + n*a(n-1) - a(n-2) + a(n-3).
  • A170949 (program): “Conway’s Converger”: a reordering of the integers (see Comments for definition).
  • A170950 (program): Inverse permutation to A170949.
  • A170955 (program): a(n) = 10^n - 9.
  • A170956 (program): Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 3.
  • A170966 (program): Expansion of Product_{i=0..m-1} (1 + x^(4*i+1)) for m = 3.
  • A170985 (program): Carryless product n X n in base 4.
  • A171001 (program): Binomial(n-k,k)^2 where k = ceiling(n/4).
  • A171002 (program): Binomial(n-k,k) * binomial(n-k-1,k+1) where k = ceiling(n/4).
  • A171005 (program): (n+1)*(n-1)!/2.
  • A171006 (program): Binomial(n-k-1,k) * binomial(n-k,k+1) where k = ceiling(n/4).
  • A171008 (program): Write the n-th prime in binary and change all 0’s to 1’s and all 1’s to 0’s.
  • A171013 (program): In the sequence of prime numbers, replace all digits ‘1’ with ‘0’ and vice versa.
  • A171014 (program): In the sequence of prime numbers, replace all the ‘2’ digits with ‘0’ and vice versa.
  • A171015 (program): In the sequence of prime numbers, replace all the ‘2’ digits with ‘1’ and vice versa.
  • A171016 (program): In the sequence of prime numbers, replace all the ‘3’ digits with ‘0’ and vice versa.
  • A171018 (program): In the sequence of prime numbers, replace all the ‘3’ digits with ‘2’ and vice versa.
  • A171019 (program): In the sequence of prime numbers, replace all the ‘4’ digits with ‘0’ and vice versa.
  • A171020 (program): In the sequence of prime numbers, replace all the ‘4’ digits with ‘1’ and vice versa.
  • A171021 (program): In the sequence of prime numbers, replace all the ‘4’ digits with ‘2’ and vice versa.
  • A171022 (program): In the sequence of prime numbers, replace all the ‘4’ digits with ‘3’ and vice versa.
  • A171024 (program): In the sequence of prime numbers, replace all the ‘5’ digits with ‘1’ and vice versa.
  • A171025 (program): In the sequence of prime numbers, replace all the ‘5’ digits with ‘2’ and vice versa.
  • A171026 (program): In the sequence of prime numbers, replace all the ‘5’ digits with ‘3’ and vice versa.
  • A171027 (program): In the sequence of prime numbers, replace all the ‘5’ digits with ‘4’ and vice versa.
  • A171028 (program): In the sequence of prime numbers, replace all the ‘6’ digits with ‘0’ and vice versa.
  • A171030 (program): In the sequence of prime numbers, replace all the ‘6’ digits with ‘2’ and vice versa.
  • A171031 (program): In the sequence of prime numbers, replace all the ‘6’ digits with ‘3’ and vice versa.
  • A171032 (program): In the sequence of prime numbers, replace all the ‘6’ digits with ‘4’ and vice versa.
  • A171033 (program): In the sequence of prime numbers, replace all the ‘6’ digits with ‘5’ and vice versa.
  • A171034 (program): In the sequence of prime numbers, replace all the ‘7’ digits with ‘0’ and vice versa.
  • A171035 (program): In the sequence of prime numbers, replace all the ‘7’ digits with ‘1’ and vice versa.
  • A171037 (program): In the sequence of prime numbers, replace all the ‘7’ digits with ‘3’ and vice versa.
  • A171038 (program): In the sequence of prime numbers, replace all the ‘7’ digits with ‘4’ and vice versa.
  • A171039 (program): In the sequence of prime numbers, replace all the ‘7’ digits with ‘5’ and vice versa.
  • A171040 (program): In the sequence of prime numbers, replace all the ‘7’ digits with ‘6’ and vice versa.
  • A171041 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘0’ and vice versa.
  • A171042 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘1’ and vice versa.
  • A171043 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘2’ and vice versa.
  • A171045 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘4’ and vice versa.
  • A171046 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘5’ and vice versa.
  • A171047 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘6’ and vice versa.
  • A171048 (program): In the sequence of prime numbers, replace all the ‘8’ digits with ‘7’ and vice versa.
  • A171049 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘0’ and vice versa.
  • A171050 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘1’ and vice versa.
  • A171051 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘2’ and vice versa.
  • A171052 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘3’ and vice versa.
  • A171054 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘5’ and vice versa.
  • A171055 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘6’ and vice versa.
  • A171056 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘7’ and vice versa.
  • A171057 (program): In the sequence of prime numbers, replace all the ‘9’ digits with ‘8’ and vice versa.
  • A171064 (program): G.f.: -x*(x-1)*(1+x)/(1-x-7*x^2-x^3+x^4).
  • A171065 (program): G.f. -x*(x-1)*(1+x)/(1-x-8*x^2-x^3+x^4).
  • A171066 (program): G.f. -x*(x-1)*(1+x)/(1-x-9*x^2-x^3+x^4).
  • A171067 (program): G.f. -x*(x-1)*(1+x)/((x^2+3*x+1)*(x^2-4*x+1)).
  • A171068 (program): G.f. -x*(x-1)*(1+x)/(1-x-11*x^2-x^3+x^4).
  • A171069 (program): G.f. -x*(x-1)*(1+x)/(1-x-12*x^2-x^3+x^4).
  • A171070 (program): A bisection of A178482.
  • A171071 (program): A bisection of A178482.
  • A171074 (program): A115112 with initial term changed from 0 to 1.
  • A171080 (program): a(n) = Product_{3 <= q <= 2n+1, q prime} q^floor((2n/(q-1)).
  • A171088 (program): To find 3 consecutive integers in the sequence, you have to take 4 consecutive terms, no more and no less.
  • A171089 (program): a(n) = 2*(Lucas(n)^2 - (-1)^n)).
  • A171091 (program): Digits in the order in which they appear in the fractional part of the decimal expansion of Pi.
  • A171102 (program): Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once.
  • A171108 (program): a(n) is the Severi degree for curves of degree n and cogenus 2.
  • A171126 (program): Numbers k such that A169611(k) = 1.
  • A171127 (program): Numbers k such that A169611(k) = 2.
  • A171128 (program): A117852*A130595 as lower triangular matrices.
  • A171129 (program): a(n)=(n^4-n^3-n^2-n)/2.
  • A171140 (program): Numbers k such that 6*k + 7 = p^2 (p=prime).
  • A171141 (program): Numbers that are congruent to {6,33} mod 41.
  • A171142 (program): Triangle T(n,k) of the coefficients [x^k] of the polynomial p_n(x), where p_n(x)=(1+x)*p_{n-1}(x) if n even, p_n(x) = (x^2+4x+1)^((n-1)/2) if n odd.
  • A171147 (program): The sequence of coefficients of a polynomial recursion: p(x,n)=If[Mod[n, 2] == 0, (x + 1)*p(x, n - 1), (x^2 + (2*n)*x + 1)^Floor[n/2]]
  • A171148 (program): 3+10^n+3*100^n.
  • A171151 (program): Expansion of (A(x)-1)/(x*A(x)), A(x) the g.f. of A004211.
  • A171152 (program): Partial sums of A118011.
  • A171153 (program): Numbers that are not in A169606.
  • A171155 (program): For two strings of length n, this is the number of pairwise alignments that do not have an insertion adjacent to a deletion.
  • A171156 (program): Numbers of the form 2p or 3p where p is a prime greater than 3.
  • A171157 (program): Number of distinct primes > 3 that divide n.
  • A171160 (program): a(n) = a(n-1) + 2*a(n-2) with a(0)=3, a(1)=4.
  • A171163 (program): Number of children at height n in a doubly logarithmic tree. Leaves are at height 0.
  • A171164 (program): A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.
  • A171165 (program): A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.
  • A171166 (program): A polyspiral path: a(n) represents the n-th vertex of a lattice path with an infinite number of finite square spirals.
  • A171172 (program): Triangle read by rows in which row n lists 3n-2 together with the first 2n-1 positive integers.
  • A171173 (program): Triangle read by rows in which row n lists A033627(n) together with the first 2n-1 positive integers.
  • A171174 (program): Triangle read by rows in which row n lists A033627(n) together with the first 2n-1 numbers <> 0 of A038608.
  • A171175 (program): Permutation of the natural numbers: 0 together with the partial sums of A171174.
  • A171176 (program): Triangle read by rows in which row n lists 3n-1 together with the first 2n-1 positive integers, in reverse order.
  • A171177 (program): Triangle read by rows in which row n lists 3n-1 together with the first 2n-1 numbers <> 0 of A038608, in reverse order.
  • A171178 (program): Permutation of the natural numbers: 0 together with the partial sums of A171177.
  • A171179 (program): Numbers that are divisible by exactly 3 primes (counted with multiplicity) and sandwiched between primes.
  • A171180 (program): a(n) = (4*n + 1)^(1/2)/(4*n + 1)*((1 - p)*q^n - (1 - q)*p^n), where p = (1 - (4*n + 1)^(1/2))/2 and q = (1 + (4*n + 1)^(1/2))/2.
  • A171182 (program): Period 6: repeat [0, 1, 1, 1, 0, 2].
  • A171185 (program): G.f.: exp( Sum_{n>=1} (x^n/n)*[Sum_{k=0..[n/2]} A034807(n,k)^3] ), where A034807 is a triangle of Lucas polynomials.
  • A171186 (program): G.f.: exp( Sum_{n>=1} (x^n/n)*[Sum_{k=0..[n/2]} A034807(n,k)^n] ), where A034807 is a triangle of Lucas polynomials.
  • A171187 (program): a(n) = Sum_{k=0..[n/2]} A034807(n,k)^n, where A034807 is a triangle of Lucas polynomials.
  • A171199 (program): G.f. satisfies: A(x) = exp( Sum_{n>=1} [A(x)^n + A(x)^-n]*x^n/n ).
  • A171215 (program): Row cubed sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..[n/2]} A034807(n,k)^3.
  • A171216 (program): (4^(5*n+1) + 7)/11.
  • A171218 (program): a(n) = sum(A109613(k)*A005843(n-k): 0<=k<=n).
  • A171219 (program): A138101(n)+A168142(n).
  • A171220 (program): a(n) = (2n + 1)*5^n.
  • A171226 (program): 9+10^n+9*100^n.
  • A171228 (program): n^(p-n) where p is smallest prime > n.
  • A171230 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 2 written in base 2.
  • A171231 (program): a(n) = (10*2^n + 3 - (-1)^n)/6.
  • A171232 (program): Array read by antidiagonals, T(n,k) = 2*(n/k) - 1, if n mod k = 0; otherwise, T(n,k) = 1.
  • A171233 (program): Array, T(n,k) = 2*(n/k), if n mod k = 0; otherwise, T(n,k) = 1. Read by antidiagonals.
  • A171237 (program): a(0)=2, a(1)=3, a(n) = 3 + a(n-1) + a(n-2) for n >= 2.
  • A171238 (program): Given M = triangle A122196 as an infinite lower triangular matrix, this sequence is lim_{k->infinity} M^k.
  • A171241 (program): Numbers k such that A169611(k) = 3.
  • A171248 (program): a(n) = 10^n*(2+3*10^n)+3.
  • A171270 (program): a(n) is the only number m such that m = pi(1^(1/n)) + pi(2^(1/n)) + … + pi(m^(1/n)).
  • A171272 (program): a(n) = 1 + 4*n*(1 + 2*n^2)/3.
  • A171369 (program): Triangle read by rows, replace 2’s with 3’s in A169695.
  • A171370 (program): Sequence generated from Lim:_{n..inf.} M^n, M = an infinite lower triangular matrix with (1,3,3,3,…) in every column, shifted down twice.
  • A171371 (program): a(n) = 6*a(n-1) + 8*a(n-2) with a(1) = 8, a(2) = 18.
  • A171372 (program): a(n) = Numerator of 1/(2*n)^2 - 1/(3*n)^2 for n > 0, a(0) = 1.
  • A171373 (program): Binomial transform of A171372.
  • A171375 (program): 1+3*10^n+100^n.
  • A171378 (program): a(n) = (n+1)^2 - A006046(n+1).
  • A171379 (program): Triangle, read by rows, T(n, k) = A059481(n,k)*(A059481(n,k) - 1)/2.
  • A171382 (program): a(n) = (2*2^n+7*(-1)^n)/3.
  • A171384 (program): a(n) = A140475(n) - A167707(n).
  • A171386 (program): The characteristic function of 2 and 3: 1 if n is prime such that either n-1 or n+1 is prime, else 0.
  • A171387 (program): The characteristic function of primes > 3: 1 if n is prime such that neither prime+-1 is prime else 0.
  • A171389 (program): a(n) = 21*2^n - 1.
  • A171390 (program): a(n) = 37*2^(n-1)-1.
  • A171405 (program): Sum of divisors of n, excluding divisors 2 and 3.
  • A171408 (program): a(n) = A171373(n+1) - 2*A171373(n).
  • A171410 (program): 1+5*10^n+100^n.
  • A171415 (program): a(n) = 99*a(n-1) - a(n-2); a(0) = 0, a(1) = 1.
  • A171416 (program): A sequence with Somos-4 Hankel transform.
  • A171417 (program): Decimal expansion of (5+sqrt(65))/4.
  • A171418 (program): Expansion of (1+x)^4/(1-x).
  • A171419 (program): Decimal expansion of (5+sqrt(65))/10.
  • A171420 (program): Numbers n such that composite(n)={2 or 3}*{prime > 3}.
  • A171421 (program): Euler totient function of the n-th single or isolated number.
  • A171422 (program): A (4,-5) Somos-4 sequence.
  • A171423 (program): Decimal expansion of C_1 constant of Melas for the centered Hardy-Littlewood maximal inequality.
  • A171424 (program): (n-1)^(p-n+1)+n where p is the smallest prime > n-1.
  • A171435 (program): Product of odd prime factors < n, with multiplicity.
  • A171438 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 3 written in base 10.
  • A171440 (program): Expansion of (1+x)^5/(1-x).
  • A171441 (program): Expansion of (1+x)^6/(1-x).
  • A171442 (program): Expansion of (1+x)^7/(1-x).
  • A171443 (program): Expansion of (1+x)^8/(1-x).
  • A171444 (program): Sum of three consecutive reversed primes.
  • A171445 (program): Sequence whose G.f is given by f(z)=(1+z)^(24)/(1-z).
  • A171446 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 3 written in base 3.
  • A171447 (program): Numbers n such that n+1 is prime, and (n+1)^3-n^3 is prime.
  • A171449 (program): Powers of 2 (A000079) with 1 changed to -1.
  • A171451 (program): a(n) = 2^C(n, 2) * 2^floor(n/3).
  • A171452 (program): a(n) = C(n,2) + floor(n/3).
  • A171453 (program): a(n) = sum_i p_i^(e_i-1) where n = product_i p_i^e_i is the prime number decomposition of n.
  • A171461 (program): a(n) = 1 + 6*10^n + 100^n.
  • A171462 (program): Number of hands a bartender needs to have in order to win at the blind bartender’s problem with n glasses in a cycle.
  • A171463 (program): The natural numbers excluding 2 and 3.
  • A171464 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 4 written in base 10.
  • A171470 (program): a(n) = 6*a(n-1) - 8*a(n-2) for n > 2; a(0) = 11, a(1) = 90, a(2) = 372.
  • A171471 (program): a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 2; a(0) = 35, a(1) = 225, a(2) = 837.
  • A171472 (program): a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 7, a(1) = 30.
  • A171473 (program): a(n) = 6*a(n-1) - 8*a(n-2)-3 for n > 1; a(0) = 35, a(1) = 135.
  • A171475 (program): a(n) = 6*a(n-1) - 8*a(n-2), for n > 2, with a(0) = 1, a(1) = 6, a(2) = 27.
  • A171476 (program): a(n) = 6*a(n-1) - 8*a(n-2) for n > 1, a(0)=1, a(1)=6.
  • A171477 (program): a(n) = 6*a(n-1) - 8*a(n-2) + 1 for n > 1; a(0) = 1, a(1) = 7.
  • A171478 (program): a(n) = 6*a(n-1) - 8*a(n-2) + 2 for n > 1; a(0) = 1, a(1) = 8.
  • A171479 (program): a(n) = 6*a(n-1)-8*a(n-2)+3 for n > 1; a(0) = 1, a(1) = 8.
  • A171480 (program): a(n) = 6*a(n-1) - 8*a(n-2) + 4 for n > 1; a(0) = 1, a(1) = 9.
  • A171483 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 4 written in base 4.
  • A171486 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A033321.
  • A171487 (program): Product of odd prime anti-factors < n, with multiplicity.
  • A171488 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A005773(n+1)= 1,2,5,13,35,96,267,…
  • A171491 (program): Natural numbers not divisible by their number of decimal digits.
  • A171494 (program): a(n) = 2*a(n-1) for n > 1; a(0) = 6, a(1) = 16.
  • A171495 (program): a(n) = 3*a(n-1)+4 for n > 0; a(0) = 6.
  • A171496 (program): a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 6, a(1) = 28.
  • A171497 (program): a(n) = 2*a(n-1) for n > 1; a(0) = 3, a(1) = 8.
  • A171498 (program): 4*3^n-1.
  • A171499 (program): a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 3, a(1) = 14.
  • A171501 (program): Inverse binomial transform of A084640.
  • A171503 (program): Number of 2 X 2 integer matrices with entries from {0,1,…,n} having determinant 1.
  • A171504 (program): a(n) = n-th nonprime + n.
  • A171507 (program): a(n) = (5*2^(n+1)-9-(-1)^n)/6-2*n.
  • A171508 (program): Numbers that are not the sum of the k-th noncomposite number and k for any k >= 1.
  • A171510 (program): Generalized Lucas numbers: a(n) = 10*a(n-1) + a(n-2), with a(1)=2 and a(2)=1.
  • A171511 (program): Numbers that are not the sum of the k-th composite number and k for any k >= 1.
  • A171512 (program): a(n) = numbers m such that are not the sum of k-th nonprime number and k for any k >= 1.
  • A171513 (program): 1+8*10^n+100^n.
  • A171515 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A033543.
  • A171516 (program): a(n) = a(n-1) + a(n-2) + k, n>1; with a(0) = 1, a(1) = 2, k = 3.
  • A171517 (program): Primes p such that 2*p+11 is prime.
  • A171519 (program): a(n) = numbers m such that are not the product of k-th noncomposite number and k for any k >= 1.
  • A171520 (program): Integers m that are not the product of k-th prime and k for any k >= 1.
  • A171521 (program): Numbers that are not the product of k-th composite number and k for any k >= 1.
  • A171522 (program): Denominator of 1/n^2-1/(n+2)^2.
  • A171523 (program): a(n) = n*(n-th nonprime number).
  • A171524 (program): a(n) = numbers m such that are not the product of k-th nonprime number and k for any k >= 1.
  • A171525 (program): Numerator of (n-th noncomposite/n).
  • A171526 (program): Denominator of (n-th noncomposite/n).
  • A171527 (program): Numerator of (n-th composite/n).
  • A171528 (program): Denominator of (n-th composite/n).
  • A171529 (program): Numerator of (n-th nonprime/n).
  • A171535 (program): Decimal expansion of 2*sqrt(2/15).
  • A171536 (program): Decimal expansion of 2/sqrt(7).
  • A171537 (program): Decimal expansion of sqrt(3/7).
  • A171538 (program): Decimal expansion of 4/sqrt(35).
  • A171539 (program): Decimal expansion of sqrt(6/35).
  • A171540 (program): Decimal expansion of sqrt(5/14).
  • A171541 (program): Decimal expansion of 2*sqrt(3/35).
  • A171542 (program): Decimal expansion of sqrt(27/70).
  • A171543 (program): Decimal expansion of 2/sqrt(35).
  • A171544 (program): Decimal expansion of 3*sqrt(2/35).
  • A171545 (program): Decimal expansion of sqrt(2/7).
  • A171546 (program): Decimal expansion of sqrt(3/35).
  • A171547 (program): Decimal expansion of sqrt(3/14).
  • A171548 (program): Decimal expansion of 2*sqrt(2/35).
  • A171552 (program): a(n)=2^n*floor((5-2n)/3).
  • A171553 (program): 1+9*10^n+100^n.
  • A171555 (program): Numbers of the form prime(n)*(prime(n)-1)/4.
  • A171556 (program): a(n)=3*C(n)-2, where C(n)=A000108(n).
  • A171557 (program): a(n) = 3^n*A168053(n).
  • A171559 (program): Powers of 2 (cf. A000079) with 1 replaced by 3.
  • A171560 (program): The product of the n-th run of identical consecutive values of A123387.
  • A171561 (program): (n-th prime number)^(n-th non-single or nonisolated number) with duplicates removed.
  • A171562 (program): Numbers k such that the k-th non-single or nonisolated number is prime.
  • A171567 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A168491.
  • A171568 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A064613.
  • A171569 (program): Triangular numbers T such that T-2 is a prime.
  • A171570 (program): Triangular numbers T such that T+2 is a prime.
  • A171571 (program): A050278/9, where A050278 are the pandigital numbers.
  • A171572 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 5 written in base 10.
  • A171573 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 5 written in base 5.
  • A171574 (program): Primes of the form p=floor(T/4), T are Triangular numbers.
  • A171575 (program): n-th noncomposite number plus n-th even nonprime number.
  • A171576 (program): a(n) = abs(n-th noncomposite number minus n-th even nonprime number).
  • A171577 (program): 0, 1 and primes > 3.
  • A171581 (program): The natural numbers without primes > 3.
  • A171583 (program): 10^n*(4+3*10^n)+3.
  • A171587 (program): Sequence of the diagonal variant of the Fibonacci word fractal. Sequence of the Fibonacci tile.
  • A171588 (program): The Pell word: Fixed point of the morphism 0->001, 1->0.
  • A171589 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A104455.
  • A171590 (program): 1+4^(n+1)-4*(-2)^n.
  • A171592 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 6 written in base 10.
  • A171593 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 6 written in base 6.
  • A171595 (program): Primes of the form p=floor(T/6), T are triangular numbers.
  • A171597 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 7 written in base 10.
  • A171598 (program): Record values of A175047.
  • A171599 (program): Where record values occur in A175047.
  • A171600 (program): Primes of the form floor(T/8) where T is a triangular number.
  • A171605 (program): Coefficients of Hankel moment polynomials for c=1/2:f(a,b) = Gamma[a + b]/Gamma[a] p(x,n)=Sum[Binomial(n, k)*(f(c, n)/(f(c, n - k)*f(c, k)))*x^k, {k, 0, n}]
  • A171608 (program): Triangle by columns, T(n,k); (…, n, (n+1)) preceded by (n-1) zeros, as an infinite lower triangular matrix.
  • A171609 (program): Lim_{n->inf.} (A171608)^n, = left-shifted vector considered as a sequence.
  • A171610 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 7 written in base 7.
  • A171611 (program): From Goldbach problem: number of decompositions of 2n into unordered sums of two primes > 3.
  • A171613 (program): a(n) = n^2 + sum of the digits of n^2.
  • A171614 (program): Numbers n with property that (n^2 + sum of the digits of n^2) is even.
  • A171615 (program): Numbers n with property that (n^2 + sum of the digits of n^2) is odd.
  • A171616 (program): Triangle T : T(n,k)= binomial(n,k)*A000957(n+1-k).
  • A171621 (program): Numerator of 1/4 - 1/n^2, each fourth term multiplied by 4.
  • A171622 (program): Floor(n-th noncomposite / n).
  • A171623 (program): Floor(n-th composite / n).
  • A171624 (program): Floor(n-th nonprime / n).
  • A171626 (program): Ceiling(n-th noncomposite/n).
  • A171627 (program): Ceiling(n-th composite/n).
  • A171630 (program): 10^n*(5+3*10^n)+3
  • A171631 (program): Triangle read by rows: T(n,k) = n*(binomial(n-2, k-1) + n*binomial(n-2, k)), n > 0 and 0 <= k <= n - 1.
  • A171638 (program): Denominator of 1/(n-2)^2 - 1/(n+2)^2.
  • A171639 (program): Sum of n-th nonprime number and n-th noncomposite number.
  • A171640 (program): a(n) = 10*a(n-1)-a(n-2)-4 with a(1)=1 and a(2)=3.
  • A171645 (program): Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*…; p = primes, A000040, a(1) = 2.
  • A171646 (program): a(1) = 1, then partial products of Product_{n>=1} (p(n)/p(n-1)*p(n)/p(n-1)) = 1*1*1*(2)*(2)*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*…*; p = partition numbers, A000041 starting (1, 2, 3, 5, …).
  • A171647 (program): a(1) = 1; for n > 1, a(n) = 2*a(n-1) if n is even, a(n) = ((n+1)/(n-1))*a(n-1) if n is odd.
  • A171648 (program): a(1) = 1, a(n) = 2*a(n-1) if n is even; a(n) = a(n-1)*Fibonacci((n+1)/2)/Fibonacci((n-1)/2) if n is odd.
  • A171649 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 8 written in base 10.
  • A171650 (program): Triangle T, read by rows : T(n,k) = A007318(n,k)*A026641(n-k).
  • A171651 (program): Triangle T, read by rows : T(n,k) = A007318(n,k)*A005773(n+1-k).
  • A171654 (program): Period 10: repeat 0, 1, 6, 7, 2, 3, 8, 9, 4, 5.
  • A171656 (program): 10^n*(7+3*10^n)+3.
  • A171661 (program): Triangle T(n,k) (n >= 0, 0 <= k <= n) read by rows: T(n,0) = T(n,1) = A000984(n); for n >= 2 and k >= 2, T(n,k) = T(n,k-1) - T(n-1,k-2).
  • A171662 (program): a(n) = floor((2*n^2 + n)/6).
  • A171663 (program): Expansion of (1 + 4*x - 6*x^2 - 16*x^3 + 20*x^4)/((1-x)*(1-2*x)*(1+2*x)*(1-2*x^2)).
  • A171670 (program): Triangle T read by rows : T(n,k)= A007318(n,k)*A005773(n-k).
  • A171677 (program): Period 9:repeat 7,5,7,4,2,4,1,8,1.
  • A171678 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 8 written in base 8.
  • A171682 (program): Number of compositions of n with the smallest part in the first position.
  • A171688 (program): Twin primes > 3.
  • A171689 (program): Nonprimes n such that either n+-1 is prime.
  • A171691 (program): Number of unordered partitions {k1, k2} of n such that k1 and k2 are nonnegative nonprimes A141468.
  • A171696 (program): Nonnegative numbers k such that neither 6*k+-1 is prime.
  • A171697 (program): 1 together with pairs of composites of the form (6n-1, 6n+1).
  • A171700 (program): Triangle T : T(n,k)= A007318(n,k)*a(n-k) with a(0)=0 and a(n)= A077957(n-1) for n>0.
  • A171709 (program): Numerator of 1/9 - 1/n^2.
  • A171711 (program): Euler characteristic of relative homology of some varieties related to cluster algebras of type A.
  • A171712 (program): Triangle T(n,k) read by rows. Coloring of sectors in a circle.
  • A171714 (program): a(n) = ceiling((n+1)^4/2).
  • A171718 (program): 10^n*(8+3*10^n)+3.
  • A171722 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 9 written in base 10.
  • A171723 (program): a(n) = 0+1+2+…+n in lunar arithmetic in base 9 written in base 9.
  • A171729 (program): Triangle of differences of Fibonacci numbers.
  • A171730 (program): Triangle of differences of Fibonacci numbers.
  • A171731 (program): Triangle T : T(n,k)= binomial(n,k)*Fibonacci(n-k)= A007318(n,k)*A000045(n-k).
  • A171732 (program): a(n) = sum_{d|n} d*2^(d^2).
  • A171733 (program): a(2n)=A165568(n). a(2n+1)=A165563(n).
  • A171734 (program): First differences of A171733.
  • A171736 (program): 10^n*(2+7*10^n)+7.
  • A171739 (program): a(n) = 2^(n*(n-1)/2)*3^(n*(n+1)/2).
  • A171743 (program): a(n) = A000010(A001043(n)).
  • A171746 (program): Let f(n) = n + floor(sqrt(n)). Then a(n) is the smallest number of iterations of f on n such that a perfect square is obtained.
  • A171747 (program): Smallest prime > n-th prime of the form 3*k-1.
  • A171748 (program): Primes of the form (2+n)*(1+2*n)+(1+n)*(2+2*n).
  • A171749 (program): Odd primes of the form (1+n)*(2+2*n)+n*(3+2*n) = 4*n^2+7*n+2.
  • A171751 (program): Maximum k with 1 <= k <= n such that nk + 1 is prime (or 0 if no such prime exists).
  • A171753 (program): Expansion of 1/(1-3x-x^2/(1-3x-x^2/(1-3x))).
  • A171754 (program): Hyperbolic sine of the prime numbers, rounded to the nearest integer.
  • A171757 (program): Even numbers whose binary expansion begins 10.
  • A171758 (program): Binary expansion of numbers in A171757.
  • A171760 (program): The maximum number of sets of n queens which can be placed on an n X n chessboard such that no queen attacks another queen in the same set.
  • A171762 (program): a(n) = Sum_{k=n^2+1..(n+1)^2-1} tau(k).
  • A171763 (program): Odd numbers whose binary expansion begins 10.
  • A171764 (program): Binary expansion of numbers in A171763.
  • A171766 (program): a(n) = 10^n*(3 + 7*10^n) + 7.
  • A171769 (program): Partial sums of A042964 (numbers congruent to 2 or 3 mod 4).
  • A171774 (program): Radix expansion of -1/6 in radix -exp(Pi/sqrt(3)).
  • A171776 (program): E.g.f.: A(x) = exp( Sum_{n>=1} 2^(n(n-1)) * x^n/n ).
  • A171777 (program): E.g.f.: A(x) = exp( Sum_{n>=1} 2^(n(n-1)/2) * x^n/n ).
  • A171781 (program): Numbers for which the second bit of the binary expansion is equal to the last bit.
  • A171782 (program): Binary expansion of numbers in A171781.
  • A171783 (program): Third smallest divisor of smallest number having exactly n divisors.
  • A171784 (program): Fourth smallest divisor of smallest number having exactly n divisors.
  • A171790 (program): G.f. A(x) satisfies: A(x*(1+x)^3) = 1 + x.
  • A171799 (program): O.g.f.: Sum_{n>=0} 2^(n^2)*x^n/(1 - 2^n*x)^n.
  • A171800 (program): a(n) = ((n+1)*2^n + 1)*(2^n + 1)^(n-1).
  • A171801 (program): O.g.f.: Sum_{n>=0} (n+1)*2^(n^2)*x^n/(1 - 2^n*x)^n.
  • A171803 (program): G.f. satisfies: A(x) = P(x*A(x))^2 where A(x/P(x)^2) = P(x)^2 and P(x) is the g.f. for Partition numbers (A000041).
  • A171814 (program): Triangle T : T(n,k)= A007318(n,k)*A001700(n-k).
  • A171815 (program): Values of A171743 that are 1 less than a prime, listed in the order in which they appear.
  • A171816 (program): Smallest number of rank n in the poset of lunar numbers.
  • A171818 (program): Lunar product 2 X n in base 10.
  • A171820 (program): Numbers n such that the n-th prime is of the form 3k + 1/2 +- 1/2.
  • A171821 (program): 2 together with twin primes.
  • A171822 (program): Triangle T(n,k) = binomial(2*n-k, k)*binomial(n+k, 2*k), read by rows.
  • A171824 (program): Triangle T(n,k)= binomial(n + k,n) + binomial(2*n-k,n) read by rows.
  • A171833 (program): Pythagorean primes with Pythagorean prime index.
  • A171834 (program): Partial sums of numbers congruent to {0, 1, 2, 7} mod 8 (A047527).
  • A171835 (program): Partial sums of numbers congruent to {3, 4, 5, 6} mod 8 (A047425).
  • A171836 (program): Primes of the form 6n+1 with prime index of the form 6n+1.
  • A171838 (program): Primes of the form 3*k^2 + 9*k + 5.
  • A171842 (program): Binomial transform of 1,0,1,0,2,0,4,0,8,0,16,…
  • A171845 (program): Numbers n >= 0 such that n-1 and n+1 are both primes or both nonprimes, but excluding primes.
  • A171853 (program): Sum of the trapezoid weights of all peakless Motzkin paths of length n (n>=0).
  • A171854 (program): Number of ladders in all peakless Motzkin paths of length n (n>=0).
  • A171856 (program): Number of n-step up-side self-avoiding walks on the lattice strip {-1,0,1} x Z (up-side means that the walks move up and sideways but not down).
  • A171857 (program): Number of n-step up-side self-avoiding walks on the lattice strip {0,1,2} x Z (up-side means that the walks move up and sideways but not down).
  • A171858 (program): Number of n-step up-side self-avoiding walks on the lattice strip {0,1,2,3} x Z (up-side means that the walks move up and sideways but not down).
  • A171859 (program): a(n) = Bell(n) - Sum_{j=0..n-1} Bell(j), where the Bell numbers are given in A000110.
  • A171861 (program): Expansion of x*(1+x+x^2) / ( (x-1)*(x^3+x^2-1) ).
  • A171869 (program): a(n) is the period of A175555(n) in the sequence {A175555}.
  • A171870 (program): For odd numbers x, a(x) is the number of complex numbers z in the zx + 1 problem giving the same number of iterations as the 3x + 1 problem requires to reach 1.
  • A171881 (program): Square array, read by antidiagonals, where T(n,k)=n^^k for n>=0, k>=1.
  • A171885 (program): Representation of n in D. E. Knuth’s second prefix-unambiguous, order-preserving binary string system.
  • A171886 (program): Numbers n such that A008949(n) is a power of 2.
  • A171891 (program): 1 and all numbers >= 10.
  • A171892 (program): 0, 1 and all numbers >= 9.
  • A171893 (program): 1, 2 and all numbers >= 10.
  • A171900 (program): Backwards van Eck transform of A010060.
  • A171905 (program): a(1) = 1 and a(2) = 2, a(n) = |(sum of previous terms) - n|.
  • A171941 (program): Backwards van Eck transform of A000120.
  • A171942 (program): Forward van Eck transform of A000120.
  • A171944 (program): N-positions for game of misere version of Mark.
  • A171945 (program): P-positions for game of misere version of Mark.
  • A171946 (program): N-positions for game of UpMark.
  • A171947 (program): P-positions for game of UpMark.
  • A171948 (program): N-positions for game of Mark-4.
  • A171949 (program): P-positions for game of Mark-4.
  • A171950 (program): a(1)=1. a(n) = the absolute difference between (the sum of previous terms) and A000217(n-2), n>1.
  • A171960 (program): Values of the 2-complement of n in ternary representation.
  • A171963 (program): Number of partitions of the n-th semiprime into two semiprimes.
  • A171965 (program): Partial sums of floor(n^2/6) (A056827).
  • A171968 (program): Odd numbers of A181733 in the order of appearance.
  • A171970 (program): Integer part of the height of an equilateral triangle with side length n.
  • A171971 (program): Integer part of the area of an equilateral triangle with side length n.
  • A171972 (program): Greatest integer k such that k/n^2 < sqrt(3).
  • A171973 (program): Integer part of the volume of a regular tetrahedron with edge length n.
  • A171974 (program): Integer part of the height of a regular tetrahedron with edge length n.
  • A171975 (program): Integer part of the circumsphere radius of a regular tetrahedron with edge length n.
  • A171977 (program): a(n) = 2^(k+1) where 2^k is the highest power of 2 dividing n.
  • A171982 (program): Beatty sequence for sqrt(11).
  • A171983 (program): Beatty sequence for sqrt(13).
  • A171984 (program): Beatty sequence for sqrt(17).
  • A171987 (program): Best explained by example: in the binary representation, start with 10000, then add 1 and push the 1 to the left: 10001, 10010, 10100, 11000, then add another one, 11001, 11010, 11100, etc: 11101, 11110, 11111. Then proceed with the next length of numbers: 100000, etc.
  • A171993 (program): Numbers that are neither prime nor multiples of 3.
  • A171997 (program): a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2) - floor(a(n-5)/2); initial terms are 1, 1, 2, 3, 4.
  • A172011 (program): 12*A002605(n).
  • A172012 (program): Expansion of (2-3*x)/(1-3*x-3*x^2) .
  • A172015 (program): Numbers of the form 6*k-+1 such that 6*k-1=prime and 6*k+1=nonprime.
  • A172016 (program): Numbers of the form 6*k-+1 such that 6*k-1=nonprime and 6*k+1=prime.
  • A172019 (program): Numbers k such that 4 divides phi(k) (i.e., A000010(k)).
  • A172020 (program): Number of subsets S of {1,2,3,…,n} with the property that if x is a member of S then at least one of x-2 and x+2 is also a member of S.
  • A172021 (program): Start with the triangle A171661, reverse its rows, add missing powers of 2 at beginning of each row.
  • A172022 (program): a(n) = prime(n) + (-1)^n.
  • A172025 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=3.
  • A172026 (program): Riordan array (f(x^2), x*f(x^2)) where f(x) is the g.f. of A001764.
  • A172033 (program): Number of partitions of n into distinct parts that are 1 or even, i.e., into distinct terms of A004277.
  • A172038 (program): Smallest nonnegative integer such that n + (a(n))^2 is a perfect square, or -1 if no such integer exists.
  • A172042 (program): a(n) = A000010(A083553(n)).
  • A172043 (program): a(n) = 5*n^2 - n + 1.
  • A172044 (program): 5*n^2+11*n+1.
  • A172045 (program): a(n) = (9*n^4+10*n^3-3*n^2-4*n)/12.
  • A172046 (program): Partial sums of floor(n^2/7) (A056834).
  • A172047 (program): n*(n+1)*(15*n^2-n-8)/12.
  • A172048 (program): a(n) = A104275(n) + A014076(n).
  • A172049 (program): Irregular triangle T(n,k) = 2k-1 with A008794(n+2) values in row n.
  • A172050 (program): A008585+A029907.
  • A172051 (program): Decimal expansion of 1/999999.
  • A172052 (program): a(n)=abs(A171696(n)-A002822(n)).
  • A172053 (program): n-th nonnegative number k such that neither 6*k+-1 is prime plus n-th number m such that 6*m+-1 are both twin primes.
  • A172057 (program): Primes p such that either p-5/2-+1/2 is prime.
  • A172060 (program): The number of returns to the origin in all possible one-dimensional walks of length 2n.
  • A172061 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=4.
  • A172062 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=5.
  • A172063 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=6.
  • A172064 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=7.
  • A172065 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=8.
  • A172066 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=9.
  • A172067 (program): Expansion of (2/(3*sqrt(1-4*z)-1+4*z))*((1-sqrt(1-4*z))/(2*z))^k with k=10.
  • A172070 (program): Primes p such that either p-1/2-+5/2, but not both, is prime.
  • A172071 (program): Primes p such that either p - 5/2 -+ 7/2 is prime.
  • A172072 (program): Numbers n such that either prime(n)-5/2-+7/2 is prime.
  • A172073 (program): a(n) = (4*n^3 + n^2 - 3*n)/2.
  • A172075 (program): a(n) = n*(n+1)*(9*n^2 - n - 5)/6.
  • A172076 (program): a(n) = n*(n+1)*(14*n-11)/6.
  • A172077 (program): a(n) = n*(n+1)*(7*n^2 - n - 4)/4.
  • A172078 (program): a(n) = n*(16*n^2 + 3*n - 13)/6.
  • A172080 (program): a(n) = n*(12*n^3 + 10*n^2 - 9*n - 7)/6.
  • A172082 (program): a(n) = n*(n+1)*(6*n-5)/2.
  • A172083 (program): 1, followed by numerators of first differences of Bernoulli numbers (B(i) - B(i-1)).
  • A172085 (program): a(n) = n*(27*n^3 + 22*n^2 - 21*n - 16)/12.
  • A172086 (program): Numerators of sum (C(n) = A051716/A051717) + (1 followed by first differences A172083/A051717 of Bernoulli numbers).
  • A172087 (program): A001897 with terms repeated.
  • A172090 (program): Triangle T(n, k) = f(n-k) + f(k) - f(n), where f(n) = -3*n with f(0) = 1, f(1) = -2, read by rows.
  • A172094 (program): The Riordan square of the little Schröder numbers A001003.
  • A172097 (program): Table T(n,k) read by rows which contains in row n the 2^n terms of A171968 starting at the (n+1)st 3.
  • A172100 (program): Diagonal of the 26 X 26 Caesar Shift table.
  • A172103 (program): Partial sums of A167020 where A167020(n)=1 iff 6*n-1 is prime.
  • A172104 (program): Partial sums of A167021 where A167021(n)=1 iff 6*n+1 is prime.
  • A172109 (program): a(n) is the number of ordered partitions of {1,1,2,3,…,n-1}.
  • A172110 (program): a(n) is the number of ordered partitions of {1, 1, 1, 2, 3, …, n-2}.
  • A172111 (program): a(n) is the number of ordered partitions of {1, 1, 1, 1, 2, 3, …, n-3}.
  • A172112 (program): Partial sums of A023200.
  • A172113 (program): Partial sums of the generalized Cuban primes A007645.
  • A172117 (program): a(n) = n*(n+1)*(20*n-17)/6.
  • A172118 (program): a(n) = n*(n+1)*(5*n^2 - n - 3)/2.
  • A172123 (program): Number of ways to place 2 nonattacking bishops on an n X n board.
  • A172126 (program): Members of A181666 of form 3k+1.
  • A172128 (program): a(n) = floor(phi^n/n), where phi = golden ratio = (1+sqrt(5))/2.
  • A172131 (program): Partial sums of floor(n^2/9) (A056838).
  • A172132 (program): Number of ways to place 2 nonattacking knights on an n X n board.
  • A172137 (program): Number of ways to place 2 nonattacking zebras on an n X n board.
  • A172141 (program): Number of ways to place 2 nonattacking nightriders on an n X n board.
  • A172143 (program): (A172126(n) - 1)/3.
  • A172151 (program): Number of partitions of n into two nonsquares.
  • A172155 (program): a(n) = Omega(6*n-1)*Omega(6*n+1).
  • A172157 (program): Triangle T(n,m) = numerator of 1/n^2 - 1/m^2, read by rows, with T(n,0) = -1.
  • A172160 (program): a(0)=1. a(n) = 2^(n-2)*(5-n), for n>0.
  • A172161 (program): Greedy Coppersmith-Winograd sequence.
  • A172165 (program): A simple sequence a(n) = n + n^(n-1).
  • A172170 (program): 1 followed by the duplicated entries of A090368.
  • A172171 (program): (1, 9) Pascal Triangle read by horizontal rows. Same as A093644, but mirrored and without the additional row/column (1, 9, 9, 9, 9, …).
  • A172172 (program): Sums of NW-SE diagonals of triangle A172171.
  • A172173 (program): Sums of NE-SW diagonals of triangle A172171.
  • A172174 (program): a(n) = 90*a(n-1) + 1.
  • A172175 (program): a(n) = 110*a(n-1) + 1.
  • A172178 (program): a(n) = 99*n + 1.
  • A172179 (program): (1,[99n+1]) Pascal Triangle.
  • A172181 (program): Odd composites not of the form 6k + 1.
  • A172182 (program): Nonprimes of the form 6k + 1 or 6k + 2.
  • A172185 (program): (9,11) Pascal triangle.
  • A172186 (program): Numbers k such that k, k+1 and 2*k+1 are squarefree.
  • A172188 (program): Partial sums of primes of the form 3*k-1.
  • A172190 (program): a(n) = 2*prime(n)^3.
  • A172191 (program): a(n) = 2*prime(n)^4.
  • A172193 (program): a(n) = 5*n^2 + 31*n + 1.
  • A172200 (program): Number of ways to place 2 nonattacking amazons (superqueens) on an n X n board
  • A172202 (program): Number of ways to place 3 nonattacking kings on a 3 X n board.
  • A172225 (program): Number of ways to place 2 nonattacking wazirs on an n X n board.
  • A172229 (program): Number of ways to place 3 nonattacking wazirs on a 3 X n board.
  • A172236 (program): Array T(n,k) = n*T(n,k-1) + T(n,k-2) read by upward antidiagonals, starting T(n,0) = 0, T(n,1) = 1.
  • A172237 (program): T(n,k) = T(n-1,k) + k*T(n-2,k) for k >= 1 and n >= 3 with T(0,k) = 0 and T(1,k) = T(2,k) = 1 for all k >= 1; array T(n,k), read by descending antidiagonals, with n >= 0 and k >= 1.
  • A172238 (program): Primes p such that either p+5/2+-3/2 is prime.
  • A172241 (program): a(n) = (1/18)*(8^n - (-1)^n - 9).
  • A172242 (program): Number of 10-D hypercubes in an n-dimensional hypercube.
  • A172243 (program): Partial sums of Proth primes A080076.
  • A172244 (program): Integers (up to a sign) that are not representable in the form 2x^2 + xy + 3y^2 + z^3 - z for integer x,y,z.
  • A172249 (program): Triangle, read by rows, given by [0,1/3,-1/3,0,0,0,0,0,0,0,…] DELTA [3,-1/3,1/3,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A172250 (program): Triangle, read by rows, given by [0,1,-1,0,0,0,0,0,0,0,…] DELTA [1,-1,1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A172252 (program): a(n) = 4*2^n - 9.
  • A172253 (program): a(n) = Successive numbers x such that value of function N(9^x-1,9^x) defined as product of different prime factors of product 9^x(9^x-1) is equal 3(9^x-1)/4
  • A172254 (program): 1 followed by period 4: repeat [-1, 3, -2, -1].
  • A172264 (program): a(n) = floor(n*(sqrt(3)-sqrt(2))).
  • A172265 (program): Partial sums of A024810(n) = floor(2^(n+1)/Pi).
  • A172266 (program): a(n) = floor(n*(sqrt(5)-sqrt(2))).
  • A172267 (program): a(n) = floor(n*(sqrt(7)-sqrt(5))).
  • A172272 (program): a(n) = floor(n*(sqrt(11)-sqrt(3))).
  • A172274 (program): a(n) = floor(n*(sqrt(13)-sqrt(11))).
  • A172276 (program): a(n) = floor(n*(sqrt(13)-sqrt(5))).
  • A172277 (program): floor(n*(sqrt(13)-sqrt(3))).
  • A172278 (program): a(n) = floor(n*(sqrt(13)-sqrt(2))).
  • A172282 (program): Squares of Bernoulli number denominators A027642.
  • A172283 (program): (-9,11) Pascal triangle.
  • A172284 (program): First positive zeros of Bessel function of order n rounded to nearest integer
  • A172285 (program): a(n) = (5*2^n - 5*(-1)^n - 3*n*(-1)^n) / 9.
  • A172286 (program): Numbers of circuits of length 2n in K_{n,n} (the complete bipartite graph on 2n vertices).
  • A172292 (program): Triangle read by rows: T(n, k) = (2*n+1)*(2*k+1), n>=1, 1<=k<=n.
  • A172295 (program): Partial sums of A023201.
  • A172298 (program): a(n) = A027641(n) * A164555(n).
  • A172299 (program): First differences of A172298.
  • A172316 (program): 7th column of the array A172119.
  • A172317 (program): 8th column of A172119.
  • A172318 (program): 9th column of the array A172119.
  • A172319 (program): 10th column of A172119.
  • A172320 (program): 11th column of A172119.
  • A172323 (program): Floor(n*(sqrt(5)+sqrt(2))).
  • A172324 (program): Floor(n*(sqrt(7)+sqrt(5))).
  • A172325 (program): Floor(n*(sqrt(7)+sqrt(3))).
  • A172327 (program): Floor(n*(sqrt(11)+sqrt(5))).
  • A172328 (program): a(n) = floor(n*(sqrt(11)+sqrt(3))).
  • A172329 (program): a(n) = floor(n*(sqrt(11) + sqrt(2))).
  • A172331 (program): Floor(n*(sqrt(13)+sqrt(7))).
  • A172332 (program): Floor(n*(sqrt(13)+sqrt(5))).
  • A172334 (program): Floor(n*(sqrt(13)+sqrt(3))).
  • A172337 (program): Floor(n*(sqrt(11)+sqrt(7))).
  • A172340 (program): a(n)=((2^n+1)^n-(2^n-1)^n)/2
  • A172341 (program): a(n)=((2^n+1)^n+(2^n-1)^n)/2
  • A172361 (program): Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0), and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)}.
  • A172362 (program): a(n) = binomial(n+10, 10)*3^n.
  • A172366 (program): Number of partitions of prime(n) into the sum of two semiprimes.
  • A172367 (program): Numbers k > 0 such that k+4 is a prime.
  • A172370 (program): Mirrored triangle A120072 read by rows.
  • A172372 (program): Least number k such that the n-th prime not dividing 10 (A004139(n)) divides the repunit (10^k-1)/9.
  • A172388 (program): a(n) = Sum_{k=0..n} (-1)^k*C(n,k)*2^(k*(n-k)).
  • A172389 (program): a(n) = Sum_{k=0..n} C(n,k)*3^(k*(n-k))/2^n.
  • A172392 (program): a(n) = C(2n,n)*C(2n+2,n+1)/(n+2).
  • A172397 (program): a(n) = a(n-1) + a(n-2) - a(n-3) - a(n-8), starting 1,1,2,2,3,3,4,4.
  • A172398 (program): Number of partitions of n into the sum of two refactorable numbers (A033950).
  • A172399 (program): Expansion of x^7/(1-2*x-2*x^2+x^3+x^8).
  • A172404 (program): Numbers k such that 3 is the first digit of 2^k.
  • A172407 (program): Positive numbers n such that n+10 is a prime.
  • A172409 (program): Numbers n such that neither n-2 nor n-3 is prime.
  • A172410 (program): Numbers k such that 2k + 9 and 2k + 27 are prime.
  • A172412 (program): Multiples of 4 with the property that addition of a square gives a square that is not larger than the square for any later term.
  • A172414 (program): Triangle read by rows: Catalan number C(n) repeated 2*n+1 times.
  • A172416 (program): a(n) = 5*2^n/9 + 1/4 + (-1)^n*(n/6 + 7/36).
  • A172417 (program): Triangle read by rows: Catalan number C(n) repeated n times.
  • A172423 (program): Period length 10: repeat 0,9,2,7,4,5,6,3,8,1.
  • A172430 (program): Period length 10: repeat 2,1,6,7,0,3,4,9,8,5 .
  • A172431 (program): Even row Pascal-square read by antidiagonals.
  • A172434 (program): G.f.: Sum_{n>=0} a(n)*x^n/n!^4 = [ Sum_{n>=0} x^n/n!^4 ]^3.
  • A172447 (program): a(n) = (-1 + 5*2^(2*n + 1) - 3*n)/9.
  • A172458 (program): Nonprimes n such that exactly one of 2n-1 and 2n+1 is prime.
  • A172462 (program): Numbers k such that 2k-3, 2k-1, 2k+1 and 2k+3 are composite.
  • A172469 (program): Primes congruent to +/-1 or +/-7 modulo 25.
  • A172471 (program): a(n) = floor(sqrt(2*n)).
  • A172472 (program): a(n) = floor(sqrt(2*n^3)).
  • A172473 (program): a(n) = floor(sqrt(2*n^5)).
  • A172474 (program): a(n) = floor(n*sqrt(2)/4).
  • A172475 (program): a(n) = floor(n*sqrt(3)/2).
  • A172476 (program): a(n) = floor(n/sqrt(6)).
  • A172481 (program): a(n) = (3*n*2^n+2^(n+4)+2*(-1)^n)/18.
  • A172482 (program): a(n) = (1+n)*(9 + 11*n + 4*n^2)/3.
  • A172485 (program): The case S(-1,-2,3) of the family of self-convolutive recurrences studied by Martin and Kearney.
  • A172486 (program): Number of prime knots up to nine crossings with determinant 2n+1 and signature 6.
  • A172487 (program): Lesser of twin primes in A172240.
  • A172492 (program): a(n)=(n!)^2*(n+1)!, n=0,1… .
  • A172498 (program): a(n) = denominator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form 0.(1)(2)(3)…(n-1)(n)… with period (1)(2)(3)…(n-1)(n).
  • A172500 (program): Numerator of fraction whose decimal representation has form 0.(n)(n)(n)…with repeating part n.
  • A172501 (program): a(n) = binomial(n+8,8)*6^n.
  • A172502 (program): Denominator of fraction whose decimal representation has form 0.(n)(n)(n)…with repeating part n.
  • A172503 (program): a(n) = numerator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form (n).(n)(n)(n)… with period (n).
  • A172504 (program): a(n) = denominator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form (n).(n)(n)(n)… with period (n).
  • A172507 (program): a(n) = numerator of fraction a/b, where gcd(a, b) = 1, whose decimal representation has the form (n).(n).
  • A172510 (program): a(n) = binomial(n + 4, 4) * 8^n.
  • A172511 (program): a(n) = a(n-1) * (11*a(n-1) - a(n-2)) / (a(n-1) + 4*a(n-2)), with a(0) = a(1) = 1.
  • A172513 (program): Complement of A167389.
  • A172517 (program): Number of ways to place 2 nonattacking queens on an n X n toroidal board.
  • A172520 (program): Triangle in which row n gives the number of divisors of numbers in the range n to n+k for k=0..n-1.
  • A172524 (program): Partial sums of Iccanobif numbers A001129.
  • A172525 (program): 9*n*12345679.
  • A172526 (program): a(n)=floor(3*n^2*(2+sqrt(3))).
  • A172634 (program): Number of n X 3 0..2 arrays with row sums 3 and column sums n.
  • A172968 (program): a(n) = 7*a(n-1) - a(n-2) for n>1, a(0)=1, a(1)=2.
  • A172978 (program): a(n) = binomial(n+10, 10)*4^n.
  • A172979 (program): Primes with locations of right angle turns in Ulam square spiral (primes in A033638).
  • A172984 (program): For n <= 18, a(n) = Fibonacci(n) mod 5, using representatives {5,1,2,3,4} (i.e., 5 instead of the usual 0), and a(19)=2.
  • A172988 (program): Primes p such that either p-3 or p-6 is prime.
  • A173000 (program): a(n) = binomial(n + 4, 4)*9^n.
  • A173003 (program): Antidiagonal triangle sequence based on recursion: f(n,a)=a*n*f(n-1,a)+f(n-2,a)
  • A173004 (program): Antidiagonal triangle sequence based on recursion: f(n,a)=a*f(n-1,a)+n*f(n-2,a)
  • A173009 (program): Expansion of o.g.f. x*(1 - x + x^2)/(1 -3*x +x^2 +3*x^3 -2*x^4).
  • A173010 (program): a(n) = round((2^n - n - 1)/4).
  • A173012 (program): a(1) = 1, for n >= 2; a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + 2, a(n) = 0 if no such number exists.
  • A173013 (program): a(1) = 1, for n >= 2; a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + 3, a(n) = 0 if no such number exists.
  • A173014 (program): a(1) = 1, for n >= 2; a(n) = the smallest number h such that sigma(h) = A000203(h) = a(n-1) + 4, a(n) = 0 if no such number exists.
  • A173018 (program): Euler’s triangle: triangle of Eulerian numbers T(n,k) (n>=0, 0 <= k <= n) read by rows.
  • A173019 (program): a(n) is the value of row n in triangle A083093 seen as ternary number.
  • A173020 (program): Triangle of Generalized Runyon numbers R_{n,k}^(3) read by rows.
  • A173021 (program): Number of numbers <= n having in binary representation neither isolated ones nor isolated double ones.
  • A173022 (program): Number of numbers <= n having no isolated ones in their binary representations.
  • A173023 (program): Number of numbers <= n having no isolated digits “11” in their binary representations.
  • A173025 (program): Numbers having no isolated digits “11” in their binary representations.
  • A173027 (program): Numbers of rows R of the Wythoff array such that R is the n-th multiple of a tail of the Fibonacci sequence.
  • A173031 (program): Sequence whose G.f is given by: 1/(1-z)/(1-2*z)^2/(1-z-z^2).
  • A173033 (program): Second diagonal under the main diagonal in A172119 written in a square (see comment).
  • A173034 (program): Sequence whose G.f is f such that: f(z)=8/(1-2*z)-12/(1-z)+z+5.
  • A173035 (program): Cat years in human years: a(0) = 0, a(1) = 15, a(2) = 24, a(n) = a(n-1) + 4 for n >= 3.
  • A173036 (program): a(n) = binomial(n+1, 2) + 13.
  • A173038 (program): a(n) = (1/4)*(n^2 - 5*n + 2)*(n-2)! + 1.
  • A173039 (program): Odd numerators of the fractions (1/4-1/n^2), n>= -2.
  • A173041 (program): a(n) = 2*10^n + 3.
  • A173044 (program): Product plus sum of five consecutive nonnegative numbers.
  • A173059 (program): Nonnegative numbers n such that 2*n + 17 is prime.
  • A173064 (program): a(n) = prime(n) - 5.
  • A173067 (program): a(n) = A130665(n-1) - A160715(n).
  • A173072 (program): n-th prime minus n-th even number.
  • A173073 (program): (n-th nonnegative nonprime) minus (n-1).
  • A173075 (program): T(n,k) = binomial(n, k) - 1 + q^(floor(n/2))*binomial(n-2, k-1) for 0 < k < n with T(n,0) = T(n,n) = 1 and q = 1. Triangle read by rows.
  • A173078 (program): a(n) = (5*2^n - 2*(-1)^n - 9)/3.
  • A173089 (program): a(n) = 25*n^2 + n.
  • A173090 (program): a(1)=1, a(2)=2, a(n)=a(n-1)+floor(a(n-2)*a(n-1)/(a(n-2)+a(n-1))).
  • A173091 (program): a(1)=2, a(2)=2, a(n)=a(n-2)+floor(a(n-2)*a(n-1)/(a(n-2)+a(n-1))).
  • A173093 (program): a(1)=1, a(2)=3, a(n)=a(n-2)*a(n-1)-a(n-2).
  • A173094 (program): a(1)=2, a(2)=3, a(n)=a(n-2)*a(n-1)-a(n-1).
  • A173096 (program): a(1) = 3, a(2) = 4, a(n) = a(n-2)*a(n-1)-a(n-2)-a(n-1).
  • A173097 (program): a(1)=1, a(2)=2, a(n)=2*a(n-2)*a(n-1)-a(n-2).
  • A173098 (program): a(1)=1, a(2)=2, a(n)=2*a(n-2)*a(n-1)-a(n-1).
  • A173099 (program): a(1)=1, a(2)=3, a(n)=2*a(n-2)*a(n-1)-a(n-2)-a(n-1).
  • A173100 (program): a(1)=2, a(2)=2, a(n)=2*a(n-2)*a(n-1)-a(n-2)-a(n-1).
  • A173102 (program): Number of partitions x + y = z with {x,y,z} in {1,2,3,..,3n} and z > y >= x.
  • A173105 (program): The 15 supersingular primes written in octal.
  • A173106 (program): Partial sums of A005100.
  • A173107 (program): Partial sums of abundant numbers (A005101).
  • A173108 (program): Triangle, A000110 in every column > 0, shifted down twice.
  • A173109 (program): Row sums of triangle A173108.
  • A173110 (program): Given triangle A173108 = M, then A173110 = Lim_{n->inf.} M^n; the left-shifted vector considered as a sequence.
  • A173113 (program): a(n) = binomial(n + 10, 10) * 5^n.
  • A173114 (program): a(0)=a(1)=1, a(n) = 2*a(n-1)- A010686(n), n>1.
  • A173115 (program): a(n) = -(sin(2*n*arccos(sqrt(3))))^2.
  • A173116 (program): a(n) = sinh(2*arcsinh(n))^2 = 4*n^2*(n^2 + 1).
  • A173121 (program): a(n) = sinh(2*arccosh(n))^2 = 4*n^2*(n^2 - 1).
  • A173123 (program): a(n) = binomial(n+9,9)*6^n.
  • A173124 (program): a(n) = binomial(n+10,10)*6^n.
  • A173125 (program): Sum_{k=floor[n/2] mod 5} C(n,k).
  • A173126 (program): sum_{k=floor[(n+5)/2] mod 5} C(n,k)
  • A173127 (program): a(n) = sinh((2n-1)*arcsinh(3)).
  • A173128 (program): a(n) = cosh(2*n*arcsinh(n)).
  • A173129 (program): a(n) = cosh(2 * n * arccosh(n)).
  • A173130 (program): a(n) = Cosh[(2 n - 1) ArcCosh[n]].
  • A173133 (program): a(n) = Sinh[(2n-1) ArcSinh[n]].
  • A173135 (program): Primes other than 3 and 5.
  • A173137 (program): n-th nonnegative noncomposite number plus n.
  • A173141 (program): a(n) = 49*n^2 + n.
  • A173142 (program): a(n) = n^n - (n-1)^(n-1) - (n-2)^(n-2) - … - 1.
  • A173143 (program): Partial sums of the squarefree numbers, A005117.
  • A173147 (program): Numbers n such that exactly one of prime(n-1) and prime(n+1) is a generalized cuban prime (A007645).
  • A173148 (program): a(n) = cos(2*n*arccos(sqrt(n))).
  • A173151 (program): a(n) = a(n-1) - [a(n-1)/2] + a(n-2) - [a(n-5)/2] where [k] = floor(k).
  • A173154 (program): a(n) = n^3/6 + 3*n^2/4 + 7*n/3 + 7/8 + (-1)^n/8.
  • A173155 (program): a(n) = binomial(n + 5, 5) * 8^n.
  • A173165 (program): Numbers k such that 2*k^2 -+ 1 is a twin prime pair.
  • A173173 (program): a(n) = ceiling(Fibonacci(n)/2).
  • A173174 (program): a(n) = cosh(2*n*arcsinh(sqrt(n))).
  • A173175 (program): a(n) = sinh^2( 2n*arcsinh(sqrt n)).
  • A173176 (program): Greater twin primes in A172240.
  • A173177 (program): Numbers k such that 2k+3 is a prime of the form 3*A034936(m) + 4.
  • A173178 (program): Numbers k such that 2k+3 is a prime of the form 3*A024893(m) + 2.
  • A173184 (program): Partial sums of A000166.
  • A173185 (program): Partial sums of A003418.
  • A173186 (program): Numbers k such that k^2-1 is not squarefree.
  • A173187 (program): a(n) = binomial(n + 3, 3)*9^n.
  • A173188 (program): a(n) = binomial(n + 5, 5)*9^n.
  • A173191 (program): a(n) = binomial(n + 6, 6)*9^n.
  • A173192 (program): a(n) = binomial(n + 7, 7)*9^n.
  • A173193 (program): (2*10^n+43)/9.
  • A173194 (program): a(n) = -sin^2 (2*n*arccos n) = - sin^2 (2*n*arcsin n).
  • A173195 (program): Values of n such that 4^x + 4^y + 4^z = n^2 with arbitrary integers x <= y <= z.
  • A173196 (program): Partial sums of A002620.
  • A173197 (program): a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.
  • A173200 (program): Solutions y of the Mordell equation y^2 = x^3 - 3a^2 - 1 for a = 0,1,2, … (solutions x are given by A053755).
  • A173202 (program): Solutions y of the Mordell equation y^2 = x^3 - 3a^2 + 1 for a = 0,1,2, … (solutions x are given by the sequence A000466)
  • A173205 (program): a(n) = 98*a(n-1)-a(n-2) for n>2, a(1)=1, a(2)=98.
  • A173209 (program): Partial sums of A000069.
  • A173217 (program): G.f.: A(x) = Sum_{n>=0} (1 + x)^(n^2) / 2^(n+1).
  • A173218 (program): G.f.: A(x) = Sum_{n>=0} (1 + x)^(n^2+n) / 2^(n+1).
  • A173219 (program): G.f.: A(x) = Sum_{n>=0} (1 + x)^(n(n+1)/2) / 2^(n+1).
  • A173226 (program): Partial sums of A000364.
  • A173227 (program): Partial sums of A000262.
  • A173228 (program): The number of trailing zeros in (10^n)!
  • A173230 (program): Primes p of the form 6k+1 such that 6p+1 is also prime.
  • A173234 (program): Expansion of x*(1+3*x^2-2*x^3+2*x^4-x^5)/((1+x)*(x-1)^2*(x^2+1)^2).
  • A173235 (program): a(n) = n^(n-1) + n - 1.
  • A173237 (program): Alternate n and 10n for each n.
  • A173238 (program): Triangle by columns, A000041 in every column shifted down twice for columns > 0.
  • A173239 (program): Triangle by columns, A000041 shifted down thrice, k>=0.
  • A173242 (program): Partial sums of A027642.
  • A173247 (program): a(0) = -1 and a(n) = (-1)^n*(n - 4 - 3*n^2)/2 for n >= 1.
  • A173249 (program): Partial sums of A000272.
  • A173250 (program): Positive odd nonprimes of the form prime-10.
  • A173251 (program): Positive odd nonprimes of the form prime-6.
  • A173253 (program): Partial sums of A000111.
  • A173254 (program): a(n) = a(n-1) + a(n-2) - [a(n-2)/2] - [a(n-4)/2].
  • A173256 (program): Partial sums of A001481.
  • A173257 (program): Pell sequence entry points for primes == 1 (mod 4).
  • A173259 (program): Period 3: repeat [4, 1, 4].
  • A173261 (program): Array T(n,k) read by antidiagonals: T(n,2k)=1, T(n,2k+1)=n, n>=2, k>=0.
  • A173262 (program): a(n) = (2*10^n+61)/9
  • A173263 (program): Successive numbers n such that ChebyshevT[n/2, n] is not an integer.
  • A173267 (program): a(n) = 121*n^2 + n.
  • A173270 (program): Partial sums of A001037, the number of degree-n irreducible polynomials over GF(2).
  • A173275 (program): a(n) = 169*n^2 + n.
  • A173276 (program): a(n) = a(n-2) + a(n-3) - floor(a(n-3)/2) - floor(a(n-4)/2).
  • A173277 (program): A(x) satisfies A000290(x)/x^2 = A(x)/A(x^2); A000290 = integer squares
  • A173278 (program): Partial sums of A000048.
  • A173279 (program): Irregular triangle read by rows: M(n,k) = (n-2*k)!, k=0..floor(n/2).
  • A173280 (program): First column of the matrix power A173279(.,.)^j in the limit j->infinity.
  • A173283 (program): A(x) satisfies A005408(x) = A(x)/A(x^2), A005408 = odd numbers.
  • A173285 (program): A(x) satisfies: Fibonacci(x)/x = A(x)/A(x^2).
  • A173290 (program): Partial sums of A001615.
  • A173294 (program): Values of 16*n^2+24*n+7, n>=0, each duplicated.
  • A173296 (program): Numerators of the inverse binomial transform of the Leibniz series for Pi/4.
  • A173297 (program): Numbers k such that exactly one of k^2 + k - 1 and k^2 + k + 1 is prime.
  • A173299 (program): Numerators of fractions x^n + y^n, where x + y = 1 and x^2 + y^2 = 2.
  • A173300 (program): Denominators of fractions that answer the question “If x + y = 1 and x^2 + y^2 = 2, then x^n + y^n =”
  • A173303 (program): Row sums of triangle A173302.
  • A173305 (program): Triangle by columns, A000009 in every column shifted down twice for k > 0.
  • A173307 (program): a(n) = 13*n*(n+1).
  • A173308 (program): 17*n*(n+1).
  • A173309 (program): 19*n*(n+1).
  • A173314 (program): a(n) = 6*n!+1.
  • A173315 (program): Inverse binomial transform of A131800.
  • A173316 (program): 6*n! - 1.
  • A173317 (program): 5*n! - 1.
  • A173318 (program): Partial sums of A005811.
  • A173319 (program): 5*n! + 1.
  • A173321 (program): a(n) = 4*n! - 1.
  • A173322 (program): 4*n! + 1.
  • A173323 (program): a(n) = 3*n! - 1.
  • A173324 (program): 3*n! + 1.
  • A173333 (program): Triangle read by rows: T(n,k) = n! / k!, 1<=k<=n.
  • A173339 (program): Positive integers n for which the number of divisors of n^n is a square.
  • A173340 (program): Numbers n for which the factorial of the number of divisors of n is divisible by n.
  • A173343 (program): a(n+4) = a(n+3) - 2*a(n+2) - a(n+1) - a(n)
  • A173344 (program): a(n+4) = a(n+3) - 2*a(n+2) - a(n+1) - a(n), starting with (0, 1, 0, -2).
  • A173345 (program): Number of trailing zeros of the superfactorial of n (A000178).
  • A173382 (program): Partial sums of A074206.
  • A173384 (program): a(n) = A001803(n) - A046161(n).
  • A173386 (program): The absolute values of n-th natural noncomposite number minus n-th number k such that 6*k-+1 is a twin prime pair.
  • A173387 (program): The absolute value of n-th prime number minus n-th number k such that 6*k-+1 is a twin prime pair.
  • A173388 (program): a(n) = a(n - 3) + a(n - 4) if n is even, else a(n - 2) + a(n - 3).
  • A173391 (program): a(n) = 6n + 3^n.
  • A173392 (program): Product of nonzero remainders of n mod k, for k = 1,2,3,…,n.
  • A173393 (program): 10n+12^n.
  • A173395 (program): a(n) = (A002260(n) + 1) * (A004736(n) + 1).
  • A173396 (program): a(n) = A046161(n) + A001803(n).
  • A173398 (program): (A007318 + A112468)/2
  • A173402 (program): (A007318 - A112468)/2.
  • A173403 (program): Inverse binomial transform of A002416.
  • A173416 (program): Exactly one of 2n^2-1 and 2n^2+1 is prime.
  • A173424 (program): Triangle T(n,m) read by rows: (2*n - 2*m)!*(2*m)!/( 2^n*(n - m)!*m! )
  • A173426 (program): a(n) is obtained by starting with 1, sequentially concatenating all decimal numbers up to n, and then, starting from n-1, sequentially concatenating all decimal numbers down to 1.
  • A173427 (program): Decimal value a(n) of the binary number b(n) obtained by starting from 1, sequentially concatenating all binary numbers up to n and then sequentially concatenating all binary numbers from n-1 down to 1.
  • A173432 (program): NW-SE diagonal sums of Riordan array A112468.
  • A173433 (program): a(n) = (A000045(n)+A173432(n))/2.
  • A173434 (program): a(n) = (A000045(n)-A173432(n))/2.
  • A173435 (program): Inverse binomial transform of A143025, assuming offset zero there.
  • A173438 (program): Number of divisors d of number n such that d does not divide sigma(n).
  • A173444 (program): Either (n-th prime-1)^2-+1, but not both, is prime.
  • A173449 (program): Partial sums of A006894.
  • A173450 (program): Decimal expansion of (69^2)*10^6 + 69^3.
  • A173455 (program): Row sums of triangle A027751.
  • A173464 (program): When regarded as a triangle, the rows of A162797 converge to this sequence.
  • A173468 (program): Sum n^k, k=0..n+1.
  • A173472 (program): Numbers k such that exactly one of prime(k)^2 - 2 and prime(k)^2 + 2 is prime.
  • A173474 (program): Numbers n such that n*2^n + 1 is not prime.
  • A173478 (program): a(n) = the smallest number ending in n-1 zeros divisible by n.
  • A173479 (program): a(n) = the smallest n-digit number ending in n-1 zeros that is divisible by n, else 0.
  • A173481 (program): a(n) = the smallest number ending in n zeros divisible by n.
  • A173482 (program): a(n) = the smallest (n+1)-digit number ending in n zeros that is divisible by n, else 0.
  • A173483 (program): a(n) = the largest (n+1)-digit number ending in n zeros that is divisible by n, else 0.
  • A173484 (program): a(n) = the smallest number ending in n+1 zeros divisible by n.
  • A173485 (program): a(n) = the smallest (n+2)-digit number ending in n+1 zeros that is divisible by n, else 0.
  • A173486 (program): a(n) = the largest (n+2)-digit number ending in n+1 zeros that is divisible by n, else 0.
  • A173490 (program): Even abundant numbers (even numbers n whose sum of divisors exceeds 2n).
  • A173495 (program): a(n) = Lucas(n) - floor(Lucas(n)/2).
  • A173497 (program): a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2), starting 2,1.
  • A173499 (program): Number of sequences of length n with terms from {0,1,…,n-1} such that the sum of terms is 0 modulo n and the i-th term is not i.
  • A173508 (program): a(n) = ceiling(A173497(n)/2).
  • A173510 (program): a(n) = a(n-1) + a(n-2) - floor( a(n-1)/2 ).
  • A173511 (program): a(n) = 4*n^2 + floor(n/2).
  • A173512 (program): a(n) = 8*n + 4 + n mod 2.
  • A173513 (program): a(n) = ceiling(A173510(n)/2).
  • A173516 (program): a(1)=1, a(n)= 3*n*a(n-1)+1, n>1
  • A173517 (program): a(n) = k if n is the k-th nonsquare, zero otherwise.
  • A173521 (program): a(n) is the concatenation of n 1’s, 0, n 1’s and 0.
  • A173522 (program): Zero together with the partial sums of A105321.
  • A173523 (program): 1+A053735(n-1), where A053735 is the sum-of-digits function in base 3.
  • A173524 (program): a(n) = A053737(4^k+n-1) in the limit k->infinity, where k plays the role of a row index in A053737.
  • A173525 (program): a(n) = 1 + A053824(n-1), where A053824 = sum of digits in base 5.
  • A173526 (program): a(n) = 1 + A053827(n-1), where A053827 is the sum-of-digits function in base 6.
  • A173527 (program): a(n) = 1 + A053828(n-1), where A053828 is the sum of digits in base 7.
  • A173528 (program): a(n) = 1 + sum of digits of n-1 written in base 8.
  • A173529 (program): a(n) = 1 + A053830(n-1), where A053830 is the sum of the digits of its argument in base 9.
  • A173530 (program): Number of ON cells after n generations of three-dimensional cellular automaton related to Sierpinski’s triangle and the toothpick sequences (See Comments for definition)
  • A173531 (program): a(0)=0: For n>0, a(n) = A060632(n)*A060632(n-1).
  • A173535 (program): a(n) = (1/11) * (5*12^n + 6).
  • A173536 (program): A173039(n) + A173259(n).
  • A173537 (program): a(n) = A173522(n)/2.
  • A173539 (program): Square array read by antidiagonals: T(n,k)=0 if k is a divisor of n, otherwise T(n,k)=k.
  • A173541 (program): Triangle read by rows: T(n,k)=k if k is a proper non-divisor of n, otherwise T(n,k)=0 (1<=k<=n).
  • A173552 (program): Numbers n such that 5+38*n^2 is a prime.
  • A173553 (program): Numbers n such that 5+38*n^2 is not a prime.
  • A173554 (program): Primes of form 5+38*n^2.
  • A173557 (program): a(n) = Product_{primes p dividing n} (p-1).
  • A173558 (program): a(n) is the smallest number whose factorial has 10^n trailing zeros.
  • A173559 (program): a(n)= +2*a(n-2) +4*a(n-3), n>3.
  • A173562 (program): a(n) = n^2 + floor(n/4).
  • A173565 (program): Arises in analysis of Algorithm O for generating oriented trees.
  • A173588 (program): T(n,k) = (k^n)*U(n, (1/k + k)/2), where U(n,x) is the n-th Chebyshev polynomial of the second kind, square array read by antidiagonals upward (n >= 0, k >= 1).
  • A173589 (program): Integers whose binary representation contains exactly three 1’s, no two 1’s being adjacent.
  • A173593 (program): Numbers having in binary representation exactly two ones in three consecutive digits.
  • A173598 (program): Period 6: repeat [1, 8, 7, 2, 4, 5].
  • A173601 (program): Greatest inverse of A071542, i.e., a(n) = maximal i such that A071542(i) = n.
  • A173614 (program): a(n) = lcm_{p is prime and divisor of n} p-1.
  • A173621 (program): Triangle of Generalized Runyon numbers R_{n,k}^(4) read by rows.
  • A173622 (program): Triangle T(n,m) read by rows: The number of m-Schroeder paths of order n with 2 diagonal steps.
  • A173625 (program): Decimal expansion of 3(Pi - 1).
  • A173630 (program): Denominator of A002445(n)/A145979(n).
  • A173631 (program): a(n) = ceiling(sqrt(4*P_n)), where P_n is product of first n primes
  • A173633 (program): a(n) = a(n-2) + a(n-3) - [a(n-3)/4] - [a(n-4)/2] - [a(n-5)/4].
  • A173635 (program): Period 5 sequence: 1, 1, 4, 4, 2, …
  • A173636 (program): Number of positive solutions of equation x(x+n)=y*y.
  • A173639 (program): Numbers n such that the sum of the digits of 11*n is odd.
  • A173643 (program): Positive numbers of form 2^m - 2^l - 3*2^k (A172233) divisible by 9, divided by 9.
  • A173644 (program): a(n) = smallest positive integer m such that n^2+7m is a square.
  • A173645 (program): Partial sums of floor(n^2/11).
  • A173650 (program): Expansion of x^2*(1 + 2*x - x^2) / ((1 + x)*(1 - x - 4*x^2 + 2*x^3)).
  • A173651 (program): Triangle T(n,m) read by rows: numerator of 1/(n-m)^2-1/m^2, or -1 if m=0.
  • A173653 (program): Partial sums of floor(n^2/10) (A056865)
  • A173655 (program): Triangle read by rows: R(n,k) = prime(n) mod prime(k), 0 < k <= n.
  • A173657 (program): 2+2^n+3^n.
  • A173661 (program): Logarithmic derivative of the squares of the Fibonacci numbers (A007598, with offset).
  • A173664 (program): Sums of 2 primes that are not product of 2 primes.
  • A173667 (program): Number of real zeros of the polynomial whose coefficients are the decimal expansion of n.
  • A173673 (program): a(2k) = floor(F(k)/2), a(2k+1) = ceiling(F(k)/2), where F = A000045 is the Fibonacci sequence.
  • A173674 (program): a(n) = ceiling(A003269(n)/2).
  • A173676 (program): Number of ways of writing n as a sum of seven nonnegative cubes.
  • A173677 (program): Number of ways of writing n as a sum of two nonnegative cubes.
  • A173678 (program): Number of ways of writing n as a sum of 4 nonnegative cubes.
  • A173679 (program): Number of ways of writing n as a sum of 5 nonnegative cubes.
  • A173680 (program): Number of ways of writing n as a sum of 6 nonnegative cubes.
  • A173681 (program): Number of ways of writing n as a sum of 8 nonnegative cubes.
  • A173682 (program): Number of ways of writing n as a sum of 9 nonnegative cubes.
  • A173686 (program): Periodic with period 12: repeat [2,8,2,2,8,5,5,8,5,5,8,2].
  • A173687 (program): Numbers m such that the sum of factorial of the decimal digits of m is square.
  • A173690 (program): Partial sums of round(n^2/5).
  • A173691 (program): Partial sums of round(n^2/6).
  • A173692 (program): a(n) = ceiling(A000931(n)/2).
  • A173693 (program): a(n) = ceiling(A107293(n)/2).
  • A173696 (program): a(n) = ceiling(A117791(n)/2).
  • A173697 (program): a(n) = ceiling(A013984(n)/2).
  • A173704 (program): Partial sums of floor(n^3/2).
  • A173706 (program): Triangle read by rows, of p*(q-1) for primes p, q with p>q.
  • A173707 (program): Partial sums of floor(n^3/3).
  • A173711 (program): Nonnegative integers, six even followed by two odd.
  • A173712 (program): Numbers n such that (n+n+1) divides the decimal concatenation [n, n+1].
  • A173714 (program): Floor(Lucas(n+1)/2), Lucas(n) = A000032(n).
  • A173721 (program): Partial sums of A056833.
  • A173722 (program): Partial sums of round(n^2/8).
  • A173731 (program): a(n) = a(n-1) * (11*a(n-1) - a(n-2)) / (a(n-1) + 4*a(n-2)), a(0) = a(1) = 0, a(2) = 1.
  • A173732 (program): a(n) = (A016957(n)/2^A007814(A016957(n)) - 1)/2, with A016957(n) = 6*n+4 and A007814(n) the 2-adic valuation of n.
  • A173734 (program): (10^n+62)/9 for n>0.
  • A173735 (program): a(n) = (10^n + 26)/9.
  • A173736 (program): (10^n+35)/9 for n>0.
  • A173737 (program): (10^n+44)/9 for n>0.
  • A173740 (program): Triangle T(n,k) = binomial(n,k) + 2 for 1 <= k <= n - 1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
  • A173741 (program): T(n,k) = binomial(n,k) + 4 for 1 <= k <= n - 1, n >= 2, and T(n,0) = T(n,n) = 1 for n >= 0, triangle read by rows.
  • A173742 (program): Triangle T(n,k) = binomial(n,k) + 6 with T(n,0) = T(n,n) = 1 for n >= 0, read by rows.
  • A173756 (program): Partial sums of A058313.
  • A173764 (program): (3*10^n+51)/9 for n>0.
  • A173766 (program): (10^n+11)/3.
  • A173768 (program): a(n) = (4*10^n-31)/9.
  • A173770 (program): a(n)=(4*10^n-13)/9.
  • A173772 (program): (4*10^n + 23)/9.
  • A173773 (program): a(3*n) = 8*n+2, a(3*n+1) = 2*n+1, a(3*n+2) = 8*n+6.
  • A173774 (program): The arithmetic mean of (21*k + 8)*binomial(2*k,k)^3 (k=0..n-1).
  • A173776 (program): a(n) = (4*10^n + 41)/9.
  • A173777 (program): Infinite sequence gradually builds a triangle plus another more widely spaced triangle on top of it, or overlapping, if you will.
  • A173781 (program): a(n) is the smallest entry of the n-th column of the matrix of Super Catalan numbers S(m,n).
  • A173785 (program): Expansion of 2*(1 -4*x +14*x^2 +4*x^3 +9*x^4)/(1-x)^5.
  • A173786 (program): Triangle read by rows: T(n,k) = 2^n + 2^k, 0 <= k <= n.
  • A173787 (program): Triangle read by rows: T(n,k) = 2^n - 2^k, 0 <= k <= n.
  • A173796 (program): Partial sums of A051489.
  • A173797 (program): Partial sums of A046065.
  • A173802 (program): a(n)=(5*10^n-23)/9.
  • A173804 (program): a(n) = (5*10^n - 41)/9 for n > 0.
  • A173805 (program): a(n) = (6*10^n-51)/9 for n>0.
  • A173806 (program): a(n) = (7*10^n-61)/9 for n>0.
  • A173807 (program): (7*10^n-43)/9 for n>0.
  • A173808 (program): (7*10^n+11)/9 for n>0.
  • A173809 (program): a(2n+1) = 1+A131941(2n+1). a(2n) = A131941(2n).
  • A173810 (program): (8*10^n-71)/9 for n>0.
  • A173811 (program): (8*10^n-53)/9 for n>0.
  • A173812 (program): (8*10^n-17)/9 for n>0.
  • A173813 (program): 2*(10^n-5), n>0.
  • A173830 (program): Primes of the form p - floor(sqrt(p)), p prime.
  • A173831 (program): Largest prime < n^4.
  • A173832 (program): Largest prime < n^5.
  • A173833 (program): 10^n - 3.
  • A173834 (program): a(n)=10^n-2*n
  • A173835 (program): 10^n+2*n.
  • A173841 (program): Number of permutations of 1..n with no adjacent pair summing to n+1.
  • A173842 (program): Number of permutations of 1..n with no adjacent pair summing to n+2.
  • A173843 (program): Number of permutations of 1..n with no adjacent pair summing to n+3.
  • A173844 (program): Number of permutations of 1..n with no adjacent pair summing to n+4.
  • A173845 (program): Number of permutations of 1..n with no adjacent pair summing to n+5.
  • A173846 (program): Number of permutations of 1..n with no adjacent pair summing to n+6.
  • A173847 (program): Number of permutations of 1..n with no adjacent pair summing to n+7.
  • A173848 (program): Number of permutations of 1..n with no adjacent pair summing to n + 8.
  • A173849 (program): Number of permutations of 1..n with no adjacent pair summing to n + 9.
  • A173850 (program): Number of permutations of 1..n with no adjacent pair summing to n+10.
  • A173855 (program): a(n) = A173039(n+4) - A173039(n+1).
  • A173856 (program): Expansion of 10/9 in base phi.
  • A173857 (program): Expansion of 3/2 in base phi.
  • A173858 (program): Expansion of 4/3 in base phi.
  • A173861 (program): Expansion of 8/7 in base phi.
  • A173862 (program): a(n) = A158772(n-1)/21.
  • A173864 (program): Expansion of 9/8 in base phi.
  • A173873 (program): a(n) = 2*a(n-1) + 13, a(1)=1.
  • A173881 (program): Triangle T(n,k) = k*binomial(n,k)*binomial(n-1,k) with T(n,0) = T(n,n) = 1, read by rows.
  • A173894 (program): a(n) = ceiling(A029826(n)/2).
  • A173904 (program): Numbers n such that 7*n+-1 are prime.
  • A173905 (program): {2,3} and the nonprimes A141468.
  • A173919 (program): Numbers that are prime or one less than a prime.
  • A173922 (program): In the sequence of nonnegative integers substitute all n by 2^floor(n/4) occurrences of (n mod 2).
  • A173923 (program): In the sequence of nonnegative integers substitute all n by 2^floor(n/8) occurrences of (n mod 2).
  • A173926 (program): First differences of A054270.
  • A173936 (program): The determinant of an n X n matrix derived from the matrix X(s,k) = s^2 - 2*s + k.
  • A173945 (program): a(n) = numerator of (Pi^2)/2 - Zeta(2,(2*n-1)/2), where Zeta is the Hurwitz Zeta function.
  • A173947 (program): a(n) = numerator of (Zeta(2, 1/4) - Zeta(2, n+1/4)), where Zeta is the Hurwitz Zeta function.
  • A173948 (program): a(n) = denominator of (Zeta(2, 1/4) - Zeta(2, n+1/4)), where Zeta is the Hurwitz Zeta function.
  • A173949 (program): a(n) = numerator of (Zeta(2, 1/4) - Zeta(2, n+1/4))/16, where Zeta is the Hurwitz Zeta function.
  • A173950 (program): a(n) = 1 if 6 divides (prime(n) + 1), a(n) = -1 if 6 divides (prime(n) - 1), a(n) = 0 otherwise.
  • A173952 (program): a(1)=32 and, for n > 1, a(n) = 9*a(n-1) + 32.
  • A173953 (program): a(n) = numerator of (Zeta(2, 3/4) - Zeta(2, n-1/4)), where Zeta is the Hurwitz Zeta function.
  • A173954 (program): a(n) = denominator of (Zeta(2, 3/4) - Zeta(2, n-1/4)), where Zeta is the Hurwitz Zeta function.
  • A173955 (program): a(n) = numerator of (Zeta(2, 3/4) - Zeta(2, n-1/4))/16 where Zeta(n, a) is the Hurwitz Zeta function.
  • A173956 (program): n-th primorial modulo n.
  • A173960 (program): Averages of four consecutive odd squares.
  • A173961 (program): Averages of two consecutive even cubes: (n^3+(n+2)^3)/2.
  • A173962 (program): Averages of two consecutive odd cubes; a(n) = (n^3+(n+2)^3)/2.
  • A173963 (program): Number of nonoverlapping placements of one 1 X 1 square and one 2 X 2 square on an n X n board.
  • A173964 (program): Sequence derived from a memorization technique.
  • A173965 (program): Averages of four consecutive cubes.
  • A173967 (program): 14=2*7;15=3*5;14+15=29, 21=3*7;22=2*11;21+22=43,..
  • A173977 (program): Integers k > 1 for which A020639(2*k-1) < A020639(2*k-3).
  • A173982 (program): a(n) = numerator of (Zeta(0,2,1/3) - Zeta(0,2,n+1/3)), where Zeta is the Hurwitz Zeta function.
  • A173983 (program): a(n) = numerator((Zeta(2, 1/3) - Zeta(2, n + 1/3))/9), where Zeta(n, z) is the Hurwitz Zeta function.
  • A173984 (program): a(n) is the denominator of (Zeta(0,2,1/3) - Zeta(0,2,n+1/3)) where Zeta is the Hurwitz Zeta function.
  • A173985 (program): a(n) = numerator of (Zeta(0,2,2/3) - Zeta(0,2,n+2/3)), where Zeta is the Hurwitz Zeta function.
  • A173986 (program): a(n) = numerator((Psi(1, 2/3) - Psi(1, n+2/3))/9), where Psi(1, z) is the Trigamma function.
  • A173987 (program): a(n) = denominator of ((Zeta(0,2,2/3) - Zeta(0,2,n+2/3))/9), where Zeta is the Hurwitz Zeta function.
  • A173989 (program): a(n) is the 2-adic valuation of A173300(n).
  • A173997 (program): Irregular triangle by columns derived from (1, 2, 3, …) * (1, 2, 3, …).
  • A173998 (program): For n>=1, a(n) = n + 2 + sum(i=1..n-1, a(i)*a(n-i) ).
  • A173999 (program): Successive positions of odd digits in decimal expansion of Pi (position 0 means 3 before comma or decimal point)
  • A174000 (program): Successive positions of even digits after comma in decimal expansion of Pi
  • A174002 (program): a(n) = n*binomial(n+4, 4).
  • A174007 (program): a(2n+1)=2. a(2n)= 1-n.
  • A174008 (program): n-th prime plus n-th even nonnegative nonprime.
  • A174010 (program): Primes p of the form p = A000040(k) - A163300(k) for some k (includes duplicates).
  • A174012 (program): a(n) = 3 * A064680(n).
  • A174015 (program): A generalized Catalan number sequence.
  • A174017 (program): A (1,1) Somos-4 sequence.
  • A174026 (program): Convolved with its aerated variant = (1, 2, 3, …).
  • A174028 (program): Triangle T(n,k) = 2+4k read by rows.
  • A174029 (program): a(n) = 3*(3*n+1)*(5 - (-1)^n)/4.
  • A174030 (program): Partial sums of A007694.
  • A174032 (program): Triangle T(n, k) = Sum_{j>=0} floor(binomial(n, k)/2^j), read by rows.
  • A174035 (program): A triangle sequence of the form:t(n,m]=Binomial[n, m] + Floor[Eulerian[n + 1, m]/2]
  • A174037 (program): Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2, read by rows.
  • A174038 (program): Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 3, read by rows.
  • A174041 (program): Composites of the form 6n+2 or 6n+3.
  • A174047 (program): Numbers k such that exactly one of 2*k-1 and 2*k+1 is prime.
  • A174048 (program): Prime(A173919(n))
  • A174060 (program): Sum_{k=1..n} {floor(sqrt(k))^2}.
  • A174088 (program): Number of pairs (i,j) such that i*j == 0 (mod k), 0 <= i <= j < k.
  • A174090 (program): Powers of 2 and odd primes; alternatively, numbers that cannot be written as a sum of at least three consecutive positive integers.
  • A174091 (program): a(n) = n OR 2.
  • A174098 (program): Symmetrical triangle T(n, m) = floor(Eulerian(n+1, m)/2), read by rows.
  • A174100 (program): Numbers k such that both 2*k + 1 and 6*k + 1 are prime.
  • A174101 (program): n*{2,6}+1 are both prime of form 6n+1.
  • A174102 (program): Triangle read by rows: T(n, m) = floor(binomial(n+1, m)* binomial(n+2, m)/(2*m+2)), 1 <= m <= n.
  • A174107 (program): Expansion of (1/(1-x+x^2))c(x/(1-x+x^2)), c(x) the g.f. of A000108.
  • A174108 (program): Hankel transform of A174107 and A061639(n+1).
  • A174111 (program): Denominators of the image of a modified Bernoulli-number sequence under the Akiyama-Tanigawa transform.
  • A174114 (program): Even central polygonal numbers (A193868) divided by 2.
  • A174116 (program): Triangle T(n, k) = (n/2)*binomial(n-1, k-1)*binomial(n-1, k) with T(n, 0) = T(n, n) = 1, read by rows.
  • A174120 (program): Partial sums of A024012.
  • A174121 (program): Partial sums of A001580.
  • A174122 (program): Partial sums of A001831.
  • A174123 (program): Partial sums of A002893.
  • A174124 (program): Triangle T(n, k, q) = (q+1)*binomial(n, k)*(Pochhammer(q+1, n)/(Pochhammer(q+1, k)*Pochhammer(q+1, n-k))), with T(n, 0) = T(n, n) = 1, and q = 1, read by rows.
  • A174126 (program): Triangle T(n, k) = (n-k)^2 * binomial(n-1, k-1)^2 with T(n, 0) = T(n, n) = 1, read by rows.
  • A174127 (program): Triangle T(n, k) = (n-k)^3 * binomial(n-1, k-1)^3 with T(n, 0) = T(n, n) = 1, read by rows.
  • A174132 (program): 2*3^(n-1)-(-1)^n.
  • A174138 (program): Numbers congruent to {5,6,7,8,9,15,16,17,18,19} mod 25.
  • A174139 (program): Numbers congruent to {0,1,2,3,4,10,11,12,13,14,20,21,22,23,24} mod 25.
  • A174140 (program): Numbers congruent to k mod 25, where 10 <= k <= 24.
  • A174141 (program): Numbers congruent to k mod 25, where 0 <= k <= 9.
  • A174147 (program): a(n) = n-th sum{p-1|p is prime and divisor of n} plus n-th product{p-1|p is prime and divisor of n}
  • A174148 (program): A symmetrical binomial product triangle sequence:q=2; t(n,m,q)=If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, -Floor[q/2], Floor[q/2]}] + Product[Binomial[n + i, n - m + i], {i, -Floor[q/2], Floor[q/2]}]]
  • A174158 (program): Triangle read by rows: T(n,m) = (binomial(n - 1, m - 1)*binomial(n, m - 1)/m)^2.
  • A174159 (program): Triangle read by rows. T(n, k) = 2 * Eulerian(n, k - 1) - binomial(n - 1, k - 1)* binomial(n, k - 1) / k.
  • A174160 (program): A symmetrical triangular sequence:t(n,m)=2*Eulerian[n, m - 1] - (Binomial[n - 1, m - 1]*Binomial[n, m - 1]/m)^2
  • A174163 (program): a(n) = (A173919(k)*A173919(k+1))/2.
  • A174165 (program): Numbers n for which (prime(n) - 1)^2 +1 is prime.
  • A174166 (program): Composites n such that 2*n-1 is prime.
  • A174168 (program): A (1,3) Somos-4 sequence.
  • A174170 (program): A (1,3) Somos-4 sequence.
  • A174172 (program): Partials sums of A001694.
  • A174183 (program): a(n) is the period k such that binomial(m, n) (mod 10) = binomial(m + k, n) (mod 10).
  • A174184 (program): Prime(n)+even nonprime(n) is prime.
  • A174185 (program): Numbers k such that the k-th prime minus the k-th even nonprime is prime.
  • A174190 (program): Triangle T(n,m) = numerator of 1/n^2-1/(n-m)^2, read by rows.
  • A174191 (program): Expansion of (1+x)*(2*x-1)/((1-x)*(x^2+2*x-1)).
  • A174192 (program): Expansion of (1-x+2x^2)/ ((1-x)*(1-2x-x^2)).
  • A174194 (program): 10n-7 and 10n-3 are both primes.
  • A174199 (program): Bisection of A137921.
  • A174213 (program): Natural numbers n such that the concatenation n//1331 is a prime number.
  • A174219 (program): Integers equal to sqrt of A147846(n)+A147846(n+1)
  • A174227 (program): Expansion of -(10*x + sqrt((1-10*x)*(1-14*x)))/(2*x).
  • A174233 (program): Triangle T(n,k) read by rows: the numerator of 1/n^2 - 1/(k-n)^2, 0 <= k < 2n.
  • A174236 (program): n-th number k such that k*4-+1 is twin prime pair plus n-th number m such that m*4+2-+1 is twin prime pair.
  • A174237 (program): Numbers n such that 4n-1 and 4n+3 are prime.
  • A174238 (program): Inverse Moebius transform of even part of n (A006519).
  • A174239 (program): a(n) = (3*n + 1 + (-1)^n*(n+3))/4.
  • A174240 (program): The multiplicative order of 2 mod n, where n an odd squarefree semiprime (A046388).
  • A174256 (program): Number of 3 X 3 reduced magic squares with distinct values and maximum value 2n; also, with magic sum 3n.
  • A174257 (program): Number of symmetry classes of 3 X 3 reduced magic squares with distinct values and maximum value 2n; also, with magic sum 3n.
  • A174261 (program): Either n*3-+1 is prime.
  • A174273 (program): Inverse Moebius transform of A035263.
  • A174275 (program): a(n) = 2^n mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.
  • A174278 (program): Partial sums of A004123.
  • A174282 (program): a(n) = 3^n mod M(n) where M(n) = A014963(n) is the exponential of the Mangoldt function.
  • A174296 (program): Row sums of A174294.
  • A174297 (program): First column of A174295.
  • A174298 (program): Triangle T(n, k) = binomial(n, k)*( n!/k! if floor(n/2) >= k otherwise n!/(n-k)! ), read by rows.
  • A174301 (program): A symmetrical triangle: T(n,k) = binomial(n, k)*if(floor(n/2) greater than or equal to k then 4^k, otherwise 4^(n-k)).
  • A174302 (program): Riordan array ((1-x^2c(x)^2)/(1-xc(x)-x^2c(x)^2),xc(x)), c(x) the g.f. of A000108.
  • A174303 (program): A symmetrical triangle: T(n,k) = A008292(n+1, k) * f(n,k), where f(n,k) = 2^k when floor(n/2) >= k, otherwise 2^(n-k).
  • A174312 (program): 32*n.
  • A174315 (program): a(n) = 3F0( -n,-n+1,-n+2;;-1)= n!*(n-1)!* 1F2(-n+2;2,3;-1)/2, where nFm(;;z) are generalized hypergeometric series.
  • A174316 (program): Sequence defined by a(0)=a(1)=a(2)=1, a(3)=2, a(4)=6 and the formula a(n)=2^(n-2)+2 for n>=5.
  • A174317 (program): a(0)=1, a(1)=2, a(2)=1; for n>2, a(n) = 7*2^(n-3)-2.
  • A174318 (program): a(n) = ceiling(n!/e) with e = A001113 = exp(1).
  • A174321 (program): Index of the smallest prime greater than (6n+1)^2.
  • A174324 (program): a(n) = 3F0(-n,-n+1,-n+2;;-1/2) = n!*(n-1)!*2^(1-n)* 1F2(-n+2;2,3;-2), where nFm(;;) are generalized hypergeometric series.
  • A174325 (program): Trisection A061037(3*n-2) of the Balmer spectrum numerators extended to negative indices.
  • A174333 (program): 61*n^2.
  • A174334 (program): 73*n^2.
  • A174335 (program): Upper bound in enumerating what majority decisions are possible with possible abstaining.
  • A174337 (program): 94*n^2.
  • A174338 (program): a(n) = 97*n^2.
  • A174339 (program): a(n) = 109*n^2.
  • A174344 (program): List of x-coordinates of point moving in clockwise square spiral.
  • A174345 (program): Triangle T(n, k) = (1/k)*binomial(n-1, k-1)*binomial(n, k-1)*2^(k-1) if floor(n/2) >= k, otherwise (1/k)*binomial(n-1, k-1)*binomial(n, k-1)*2^(n-k), read by rows.
  • A174346 (program): Triangle T(n, k) = (binomial(n-1, k-1)*binomial(n, k-1)/k) * ( 3^(k-1) if floor(n/2) >= k, otherwise 3^(n-k) ), read by rows.
  • A174347 (program): Expansion of (1 - 2*x - sqrt(1 - 8*x + 8*x^2))/(2*x*(1-x)).
  • A174359 (program): Numbers n such that 6n-1, 6n+1, and 6n+5 are prime.
  • A174371 (program): a(n) = (6*n-1)^2.
  • A174373 (program): Triangle T(n,m) = nextprime(binomial(n,m)) read by rows.
  • A174374 (program): Derivative Pascal’s triangle (version 2) read by rows: smallest prime(n)>C(m,k)=binomial(m,k)=m!/(k!*(m-k)!), 0<=k<=m.
  • A174375 (program): a(n) = n^2 - XOR(n^2, n).
  • A174376 (program): Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 2, read by rows.
  • A174377 (program): Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 3, read by rows.
  • A174378 (program): Triangle T(n, k) = n!*q^k/(n-k)! if floor(n/2) > k-1 otherwise n!*q^(n-k)/k!, with q = 4, read by rows.
  • A174383 (program): Product of two consecutive odd numbers n such that n+-2 are primes.
  • A174390 (program): a(2n) = -n, a(2n+1) = 2n+4.
  • A174392 (program): Neither n-1 nor n+1 is prime.
  • A174394 (program): Fourth root of largest n-digit number with exactly five divisors
  • A174395 (program): The number of different 4-colorings for the vertices of all triangulated planar polygons on a base with n vertices if the colors of two adjacent boundary vertices are fixed.
  • A174396 (program): Numbers congruent to {1,4,5,8} mod 9.
  • A174398 (program): Numbers that are congruent to {1, 4, 5, 8} mod 12.
  • A174400 (program): Hankel transform of A174399.
  • A174403 (program): Expansion of (1-2*x-2*x^2-sqrt(1-4*x-4*x^2+8*x^3+4*x^4))/(2*x^2).
  • A174404 (program): A (4,5)-Somos 4 sequence.
  • A174405 (program): Partial sums of Sum_{k=1..n} n/gcd(n,k), or partial sums of Sum_{d|n} d*phi(d) (see A057660).
  • A174415 (program): Numbers such that when expressed in base 2 and then interpreted in base 10, is not a multiple of the original number.
  • A174416 (program): Numbers whose binary expansion is a decimal nonprime.
  • A174417 (program): Nonprimes that contain digits 0 and 1 only.
  • A174418 (program): Alternately sum and multiply with a(1) = 2 and a(2) = 3.
  • A174424 (program): Number of “non-iterative” n x n adjacency matrices of sphere packings in R^3.
  • A174426 (program): Denominator of fractions in A171676.
  • A174429 (program): Collatz-Fibonacci numbers: a(1) = a(2) = 1; if n > 2, a(n) = a(C(n)) + a(C(C(n))), where C(n) = A006370(n).
  • A174430 (program): Triangle read by rows: T(n,m) = gcd(Fibonacci(n), Fibonacci(m)).
  • A174438 (program): Numbers that are congruent to {0, 2, 5, 8} mod 9.
  • A174440 (program): Partial sums of A022544.
  • A174442 (program): a(n) = a(n-1)+a(n-2) if n is odd, otherwise a(n) = a(n-1)*a(n-2) with a(1)=3 and a(2)=5.
  • A174443 (program): Generating function x/(1+4*x-8*x^2).
  • A174446 (program): Triangle T(n, k, q) = ceiling(binomial(n, k)/f(n, q)) with T(0, 0) = 1, f(n, q) = 1 + tanh((n-1)/q), and q = 1, read by rows.
  • A174452 (program): a(n) = n^2 mod 1000.
  • A174458 (program): Partial sums of A053519.
  • A174461 (program): G.f.: exp( Sum_{n>=1} A174462(n)*x^n/n ) where A174462(n) = Sum_{d|n} C(n,d)^2.
  • A174462 (program): a(n) = Sum_{d|n} binomial(n,d)^2.
  • A174465 (program): G.f.: exp( Sum_{n>=1} A174466(n)*x^n/n ) where A174466(n) = Sum_{d|n} d*sigma(n/d)*tau(d).
  • A174466 (program): a(n) = Sum_{d|n} d*sigma(n/d)*tau(d).
  • A174467 (program): G.f.: exp( Sum_{n>=1} A174468(n)*x^n/n ) where A174468(n) = Sum_{d|n} d*sigma(n/d)*sigma(d).
  • A174468 (program): a(n) = Sum_{d|n} d*sigma(n/d)*sigma(d).
  • A174469 (program): Number of permutations p of {1,…,n} satisfying p(1)=1 and, if n>1, |p(i)-p((i mod n)+1)| is in {2,3} for i from 1 to n.
  • A174471 (program): G.f.: exp( Sum_{n>=1} A174472(n)*x^n/n ) where A174472(n) = Sum_{d|n} d^sigma(d).
  • A174472 (program): a(n) = Sum_{d|n} d^sigma(d).
  • A174473 (program): G.f.: exp( Sum_{n>=1} A174937(n)*x^n/n ) where A174937(n) = Sum_{d|n} d^tau(d).
  • A174474 (program): a(n) = (2*n^2 - 2*n - 3)/8 + 3*(-1)^n*(1-2*n)/8.
  • A174476 (program): a(n) = Sum_{d|n} d^phi(d).
  • A174477 (program): G.f.: exp( Sum_{n>=1} A174478(n)*x^n/n ) where A174478(n) = Sum_{d|n} d*2^(n/d)*tau(d).
  • A174478 (program): a(n) = Sum_{d|n} d*2^(n/d)*tau(d).
  • A174491 (program): Denominator in the coefficient of x^n in exp( Sum_{m>=1} x^m/(m*2^(m^2)) ).
  • A174497 (program): Triangle read by rows: T(n,k) = prime(n) mod (prime(n+1)-prime(k)) for 0<k<n+1.
  • A174500 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A003500(n)) ), where A003500(n) = (2+sqrt(3))^n + (2-sqrt(3))^n.
  • A174501 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A003499(n)) ), where A003499(n) = (3+sqrt(8))^n + (3-sqrt(8))^n.
  • A174502 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A086903(n)) ), where A086903(n) = (4+sqrt(15))^n + (4-sqrt(15))^n.
  • A174503 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A087799(n)) ), where A087799(n) = (5+sqrt(24))^n + (5-sqrt(24))^n.
  • A174504 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A002203(n)) ), where A002203(n) = (1+sqrt(2))^n + (1-sqrt(2))^n.
  • A174506 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A014448(n)) ), where A014448(n) = (2+sqrt(5))^n + (2-sqrt(5))^n.
  • A174510 (program): Continued fraction expansion for exp( Sum_{n>=1} 1/(n*A080040(n)) ), where A080040(n) = (1+sqrt(3))^n + (1-sqrt(3))^n.
  • A174515 (program): Expansion of g.f. exp( Sum_{n>=1} (2^n+3^n)^2*x^n/n ).
  • A174516 (program): Partial sums of A002896.
  • A174518 (program): Sums of two consecutive primes and composite numbers in-between.
  • A174519 (program): Sum of 3 consecutive primes and of all composite numbers in-between.
  • A174520 (program): Sum of all composite numbers in-between prime numbers p(n) and p(n+2).
  • A174522 (program): Expansion of 1/(1 - x - x^4 + x^6).
  • A174530 (program): Numerators of the second row of the Akiyama-Tanigawa table for the sequence 1/n!.
  • A174532 (program): Expansion of x^5/((1-x)*(1+x-x^5)).
  • A174542 (program): Partial sums of odd Fibonacci numbers (A014437).
  • A174548 (program): Decimal expansion of e - 1/e.
  • A174549 (program): a(n) = (2*n-1)! + (2*n)!.
  • A174551 (program): Triangular array T(n,k): functions f:{1,2,…,n}-> {1,2,…,n} such that each of k fixed (but arbitrary) elements are in the image of f.
  • A174552 (program): Triangular array T(n,k): The differences in the columns of A174551.
  • A174554 (program): Smallest k > 2 such that 2|k, 3|k+1, 4|k+2,…, n|k+n-2.
  • A174557 (program): Triangle T(n, k) = -floor(n/k) with T(n, n) = 1, read by rows.
  • A174562 (program): a(1)=2, a(2)=3, then a(n)=a(n-1)+a(n-2) if n odd, a(n)=a(n-1)-a(n-2) if n even.
  • A174565 (program): Expansion of (1+3*x)/((1-x)*(1+3*x+4*x^2)).
  • A174571 (program): a(4n)=n, a(4n+1)=4, a(4n+2)=1, a(4n+3)=4.
  • A174574 (program): Partial sums of A065363.
  • A174577 (program): Expansion of -1/(-1 + x^2 + x^3 - x^7 + x^8 - x^10).
  • A174592 (program): Numbers n such that n^2 + 2*(n+2)^2 is a square.
  • A174595 (program): a(n) = 5*n^2/8 - n + 1/2 + (-1)^n*(-3*n^2/8 + n - 1/2).
  • A174605 (program): Partial sums of A011371.
  • A174618 (program): For n odd a(n) = a(n-2) + a(n-3), for n even a(n) = a(n-2) + a(n-5); with a(1) = 0, a(2) = 1.
  • A174619 (program): a(n) = A174618(n)+A174618(n+1).
  • A174622 (program): Partial sums of A005256.
  • A174623 (program): (2^p+1)^2 where p is prime.
  • A174626 (program): Antidiagonal of sequence: q=5; t(n,m) = Sum((2*cos(i*Pi/q))^m*cos[(m - 2*n)*i*Pi/q), {i, 0, q - 1}]/q.
  • A174628 (program): “Binary dates”: take the dates with the format dd/mm/yy that have only 0’s and 1’s and transform their value to base 10.
  • A174629 (program): “Binary dates” take the dates with the format mm/dd/yy that have only 0’s and 1’s and transform their value to decimal base
  • A174630 (program): A weight function for the case N = 24 and k = 6 in Butler-Graham shuffling.
  • A174634 (program): a(n) = 3^n*F(n+2).
  • A174642 (program): Number of ways to place 4 nonattacking amazons (superqueens) on a 4 X n board.
  • A174648 (program): Partial sums of A000452.
  • A174655 (program): Partial sums of A049486.
  • A174657 (program): Balanced ternary numbers with more negative trits than positive trits.
  • A174658 (program): Balanced ternary numbers with equal count of negative trits and positive trits.
  • A174659 (program): Balanced ternary numbers with more positive trits than negative trits.
  • A174662 (program): Partial sums of A003149.
  • A174665 (program): Sequence whose indices are based on the Fibonacci sequence as explained in comments.
  • A174666 (program): a(n) = 2 * a(n-2) * a(n-1) with a(1)=1 and a(2)=3.
  • A174669 (program): Sequence A154690 adjusted to leading one:t(n,m)=A154690(n,m)-A154690(n,0)+1
  • A174672 (program): Sequence A154693 adjusted to leading one:t(n,m)=A154693(n,m)-A154693(n,0)+1
  • A174674 (program): Sequence A154695 adjusted to leading one:t(n,m)=A154695(n,m)-A154695(n,0)+1
  • A174677 (program): a(n) = 2*a(n-1)*a(n-2) with a(0)=1 and a(1)=1.
  • A174679 (program): a(4n) = n^2. a(4n+1) = (4n-1)^2. a(4n+2) = (2n)^2. a(4n+3) = (4n+1)^2.
  • A174680 (program): Numerator of 1/16 - 1/n^2, using -1 at the pole where n=0.
  • A174685 (program): Indices of Sophie Germain pentagonal numbers: indices i of pentagonal numbers P(i) = A000326(i) such that 2*P(i)+1 is also a pentagonal number.
  • A174686 (program): Number of equivalence classes of 3 X 3 matrices filled with n colors so that no two rotations are identical.
  • A174687 (program): Central coefficients T(2n,n) of the Catalan triangle A033184.
  • A174689 (program): Triangle T(n, k) = n! * binomial(n, k)^2 - n! + 1, read by rows.
  • A174690 (program): Triangle T(n, k) = n!*binomial(n, k) - n! + 1, read by rows.
  • A174695 (program): Partial sums of A173950.
  • A174699 (program): Triangle read by rows: R(n,k)= 2^(2n) mod (2k+1).
  • A174709 (program): Partial sums of floor(n/6).
  • A174711 (program): Composites of the form 2*n^n + 1 = A216147(n).
  • A174712 (program): Triangle, right border = A000041, else zero; by rows, A000041(n) preceded by n zeros. By columns, n-th column = A000041(n) followed by zeros.
  • A174718 (program): Triangle T(n, k, q) = (1-q^n)*( binomial(n, k) - 1 ) + 1, with q = 2, read by rows.
  • A174719 (program): Triangle T(n, k, q) = (1-q^n)*( binomial(n, k) - 1 ) + 1, with q = 3, read by rows.
  • A174720 (program): Triangle T(n, k, q) = (1-q^n)*( binomial(n, k) - 1 ) + 1, with q = 4, read by rows.
  • A174723 (program): a(n) = n*(4*n^2 - 3*n + 5)/6.
  • A174724 (program): Sum_{k=1..n} Floor((k + 3*sqrt(k))/k).
  • A174725 (program): a(n) = (A002033(n-1) + A008683(n))/2.
  • A174726 (program): a(n) = (A002033(n-1) - A008683(n))/2
  • A174727 (program): a(n) = A091137(n+1))/(n+1).
  • A174728 (program): Triangle read by rows: T(n, m, q) = (1-q^n)*Eulerian(n+1, m) - (1-q^n) + 1, with q = 2.
  • A174729 (program): A symmetrical triangle sequence:q=3:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1
  • A174730 (program): A symmetrical triangle sequence:q=4:t(n,m,q)=(1 - q^n)*Eulerian[n + 1, m] - (1 - q^n) + 1
  • A174731 (program): Triangle T(n, k, q) = (1-q^n)*(1/k)*binomial(n-1, k-1)*binomial(n, k-1) - (1-q^n) + 1, for q = 2, read by rows.
  • A174732 (program): Triangle T(n, k, q) = (1-q^n)*(1/k)*binomial(n-1, k-1)*binomial(n, k-1) - (1-q^n) + 1, for q = 3, read by rows.
  • A174733 (program): Triangle T(n, k, q) = (1-q^n)*(1/k)*binomial(n-1, k-1)*binomial(n, k-1) - (1-q^n) + 1, for q = 4, read by rows.
  • A174737 (program): a(n) = a(n-1) - a(n-2), with a(0)=2, a(1)=-1.
  • A174738 (program): Partial sums of floor(n/7).
  • A174742 (program): Smallest of three consecutive primes whose sum is not a prime.
  • A174744 (program): (2^p-1)^2 where p is prime.
  • A174745 (program): y-values in the solution to x^2 - 21*y^2 = 1.
  • A174746 (program): x-values in the solution to x^2-31*y^2=1.
  • A174747 (program): x-values in the solution to x^2-37*y^2=1.
  • A174748 (program): x-values in the solution to x^2-33*y^2=1.
  • A174749 (program): x-values in the solution to x^2-34*y^2=1.
  • A174750 (program): x-values in the solution to x^2-38*y^2=1.
  • A174751 (program): x-values in the solution to x^2-39*y^2=1.
  • A174752 (program): x-values in the solution to x^2-41*y^2=1.
  • A174755 (program): x-values in the solution to x^2-47*y^2=1.
  • A174756 (program): x-values in the solution to x^2-51*y^2=1.
  • A174758 (program): x-values in the solution to x^2-55*y^2=1.
  • A174759 (program): x-values in the solution to x^2-57*y^2=1.
  • A174761 (program): x-values in the solution to x^2-59*y^2=1.
  • A174763 (program): x-values in the solution to x^2-62*y^2=1.
  • A174764 (program): Sum of the numerators for computing the second moment of the probability mass function (PMF) of the number of 2-cycles in the involutions on n elements (A000085) assuming the involutions are all equally likely.
  • A174765 (program): y-values in the solution to x^2 - 19*y^2 = 1.
  • A174766 (program): y-values in the solution to x^2 - 22*y^2 = 1.
  • A174767 (program): y-values in the solution to x^2 - 23*y^2 = 1.
  • A174768 (program): y-values in the solution to x^2 - 26*y^2 = 1.
  • A174771 (program): y-values in the solution to x^2 - 31*y^2 = 1.
  • A174772 (program): y-values in the solution to x^2 - 33*y^2 = 1.
  • A174773 (program): y-values in the solution to x^2 - 34*y^2 = 1.
  • A174775 (program): y-values in the solution to x^2 - 37*y^2 = 1.
  • A174776 (program): y-values in the solution to x^2 - 39*y^2 = 1.
  • A174777 (program): y-values in the solution to x^2 - 38*y^2 = 1.
  • A174778 (program): y-values in the solution to x^2 - 41*y^2 = 1.
  • A174779 (program): y-values in the solution to x^2 - 42*y^2 = 1.
  • A174780 (program): y-values in the solution to x^2-43*y^2=1.
  • A174783 (program): Expansion of (1+2x-sqrt(1-4x^2))/(2(1-x^2)*sqrt(1-4x^2)).
  • A174784 (program): Expansion of x*(1-x+x^3+x^4)/(1+x^6) (Period 12).
  • A174785 (program): Expansion of (1+2x-x^2+x^3-x^4-x^5)/(1+x^3)^2.
  • A174786 (program): Numbers n congruent to 3 (mod 6) such that n+2 and n+8 are primes.
  • A174787 (program): Cumulative sums of A174725.
  • A174788 (program): Cumulative sums of A174726.
  • A174790 (program): Triangle read by rows: T(n,m) = 1 + ((-1 + binomial(n, m))*(n!)^2)/(m!*(n - m)!).
  • A174791 (program): A symmetrical triangular sequence:t(n,m)=(n!^2/(m!(n - m)!))*Eulerian[n + 1, m] - (n!^2/(m!(n - m)!)) + 1
  • A174792 (program): Expansion of x*(1 - x^2)/(1 - x + 7*x^2 + x^3).
  • A174793 (program): Triangle read by rows: R(n,k)=n mod 2^Omega(k), where Omega( ) is number of prime divisors counted with multiplicity and 1 <= k <= n.
  • A174794 (program): a(0) = 0 and a(n) = (4*n^3 - 12*n^2 + 20*n - 9)/3 for n >= 1.
  • A174799 (program): Partial sums of A051034.
  • A174800 (program): Number whose product of digits is a square.
  • A174801 (program): Prime(n)+1 is prime or semiprime.
  • A174803 (program): a(n) = n + ceiling(sqrt(n))*floor(sqrt(n)).
  • A174804 (program): a(n) = n*ceiling(sqrt(n))*floor(sqrt(n)).
  • A174805 (program): n+ceiling[sqrt(n)]+floor[sqrt(n)].
  • A174806 (program): a(n)=n-floor(sqrt(n))^2-floor(sqrt(n-floor(sqrt(n))^2))^2; Difference between n and sum of two largest distinct squares <= n.
  • A174807 (program): Floor(10^n/4) - A173228(n).
  • A174808 (program): A transform of the large Schroeder numbers A006318.
  • A174810 (program): A transform of the little Schroeder numbers A001003.
  • A174812 (program): Primes of the form n^2+42.
  • A174813 (program): a(n) = number whose product of digits equals a power of 3.
  • A174814 (program): a(n) = n*(n+1)*(5*n+1)/3.
  • A174821 (program): Numbers n such that n^4 - n^2 - 1 is prime.
  • A174822 (program): Primes of form n^4 - n^2 - 1.
  • A174824 (program): a(n) = period of the sequence {m^m, m >= 1} modulo n.
  • A174828 (program): An averaging sum sequence based on:a(n,m)=Floor[(a(n - 1, m - 1) + a(n - 1, m))/2] with limit q
  • A174832 (program): a(n) is (the number of ones) - (the number of zeros) in the first n bits of the binary expansion of Pi-3.
  • A174836 (program): a(n) = 1 + ((6*n-1)*2^n + (-1)^n)/3.
  • A174838 (program): Numbers n such that semiprime(n)+1 is prime, where semiprime(n) is A001358.
  • A174841 (program): Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^abs(j-k).
  • A174850 (program): Quintisection A061037(5*n-2).
  • A174853 (program): y-values in the solution to x^2-47*y^2=1.
  • A174855 (program): y-values in the solution to x^2-51*y^2=1.
  • A174863 (program): Little omega analog to Liouville’s function L(n).
  • A174868 (program): Partial sums of Stern’s diatomic series A002487.
  • A174870 (program): Odd indices m for which A174869(m) is <>1.
  • A174871 (program): Numbers k such that the k-th triangular number ends in 6 or 8.
  • A174876 (program): Numbers n such that the sum of squares of their digits > n.
  • A174881 (program): Number of admissible graphs of order n.
  • A174882 (program): A (3/2,-1) Somos-4 sequence.
  • A174883 (program): Largest odd divisors of Fibonacci numbers.
  • A174887 (program): Numbers m such that sum of cubes of their digits > m.
  • A174889 (program): First column of A174888.
  • A174891 (program): Row indices for nonzero elements in first column of A174888.
  • A174892 (program): a(n) = A074206(n) - A174889(n).
  • A174896 (program): a(n) = numbers k in increasing order such that A007955(m) = k has no solution for any m, where A007955(m) = product of divisors of m.
  • A174897 (program): a(n) = characteristic function of numbers k such that A007955(m) = k has solution for some m, where A007955(m) = product of divisors of m.
  • A174898 (program): a(n) = characteristic function of numbers k such that A007955(m) = k has no solution for any m, where A007955(m) = product of divisors of m.
  • A174900 (program): a(n) = the smallest numbers k such that A007955(k) = n, or 0 if there is no such k, where A007955(m) = product of divisors of m.
  • A174901 (program): a(n) = the smallest numbers k such that A007955(k) >= n, where A007955(m) = product of divisors of m.
  • A174902 (program): Denominator of 1 - 1/n^2, using 0 at the pole where n=0.
  • A174905 (program): Numbers with no pair (d,e) of divisors such that d < e < 2*d.
  • A174908 (program): Numbers n such that the sum of the 4th powers of their digits > n.
  • A174910 (program): Partial sums of A028835.
  • A174912 (program): Triangle read by rows: T(n, m) = 1 + (binomial(n, m) - Eulerian(n+1, m))^2.
  • A174917 (program): Lesser of twin primes p1 such that p2+(p2^2-p1^2) is a prime number.
  • A174925 (program): Decimal expansion of (2+sqrt(6))/4.
  • A174927 (program): Periodic sequence: Repeat 1, 64.
  • A174928 (program): Partial sums of A174927.
  • A174929 (program): Partial sums of A174928.
  • A174930 (program): Decimal expansion of (4+sqrt(17))/8.
  • A174931 (program): Half of the digital sum of base 3 representations of 2^n.
  • A174932 (program): a(n) = Sum_{d|n} A007955(d) * A000027(n/d) = Sum_{d|n} A007955(d) * (n/d), where A007955(m) = product of divisors of m.
  • A174933 (program): a(n) = Sum_{d|n} A007955(d) * A000027(d) = Sum_{d|n} A007955(d) * (d), where A007955(m) = product of divisors of m.
  • A174934 (program): a(n) = Sum_{k<=n} A007955(k) * A000027(n-k+1) = Sum_{k<=n} A007955(k) * (n-k+1), where A007955(m) = product of divisors of m.
  • A174935 (program): a(n) = Sum_{k<=n} A007955(k) * A000027(k) = Sum_{k<=n} A007955(k) * k, where A007955(m) = product of divisors of m.
  • A174937 (program): a(n) = Sum_{d|n} d^tau(d).
  • A174938 (program): a(n) = Sum_{k<=n} A007955(k) * A007955(n-k+1), where A007955(m) = product of divisors of m.
  • A174939 (program): a(n) = Sum_{k<=n} A007955(k) * A007955(k) = Sum_{k<=n} A007955(k)^2, where A007955(m) = product of divisors of m.
  • A174941 (program): a(n) = Sum_{d|n} A007955(d) * A008683(d) = Sum_{d|n} A007955(d) * mu(d), where A007955(m) = product of divisors of m.
  • A174942 (program): a(n) = Sum_{k<=n} A007955(k) * A008683(n-k+1) = Sum_{k<=n} A007955(k) * mu(n-k+1), where A007955(m) = product of divisors of m.
  • A174943 (program): a(n) = Sum_{k<=n} A007955(k) * A008683(k) = Sum_{k<=n} A007955(k) * mu(k), where A007955(m) = product of divisors of m.
  • A174944 (program): Greatest number k such that sum of the n-th powers of the digits of k is greater than k.
  • A174947 (program): Triangle read by rows: R(n,k)=(prime(n)+1) mod prime(k).
  • A174956 (program): 0 unless n is the k-th semiprime when a(n) = k.
  • A174959 (program): G.f.: x^3*(2*x-1) / ((1-x)*(1-x-x^2)*(1-2*x^2)).
  • A174961 (program): Number of non-unitary divisors of a nonsquarefree number n.
  • A174962 (program): a(n) = n^n*(3+n)/2.
  • A174964 (program): Determinant of the symmetric n X n matrix M_n where M_n(j,k) = n^2+1 for j = k, M_n(j,k) = n for abs(j-k) = 1, M_n(j,k) = 0 otherwise.
  • A174966 (program): A symmetrical triangle sequence: q=1;t(n,m,q)=If[q == 1, Binomial[n, m] + Eulerian[n + 1, m] - Binomial[n, m]*Eulerian[n + 1, m], (q - 1) + Binomial[n, m]^q + Eulerian[n + 1, m]^q - q*Binomial[n, m]*Eulerian[n + 1, m]]
  • A174968 (program): Decimal expansion of (1 + sqrt(2))/2.
  • A174969 (program): Composites of form n^2 + n + 1.
  • A174971 (program): Periodic sequence: Repeat 3, -3.
  • A174973 (program): Numbers whose divisors increase by a factor of 2 or less.
  • A174980 (program): Stern’s diatomic series type ([0,1], 1).
  • A174981 (program): Numerators of the L-tree, left-to-right enumeration.
  • A174988 (program): Expansion of -x*(x-1)*(3*x+1) / (9*x^4-8*x^2+1).
  • A174989 (program): Partial sums of A003602.
  • A174994 (program): Repeat (8*n+4)^2.
  • A174996 (program): Triangle read by rows: R(n,k)=(prime(n)-1) mod prime(k).
  • A174997 (program): Integer part of the greatest eigenvalues of the matrix n X n whose elements are the Fibonacci numbers F(n) (A000045) such that n X n = ((F(0),F(1),…,F(n-1)),(F(n),F(n+1),…,F(2n-1)),…,(F(n(n-1)),F(n(n-1)+1),…,F(n^2-1))), for n=1,2,…
  • A175001 (program): Number of stable n-celled patterns (“still lifes”) in the Move (a.k.a. Morley; B368/S245) cellular automaton.
  • A175004 (program): Interspersion related to the Wythoff Array.
  • A175005 (program): Expansion of x/(1 - 4*x + 3*x^2 - 2*x^3).
  • A175006 (program): Row sums of triangle A175009.
  • A175013 (program): Sum of digits of n-th semiprime (or biprime).
  • A175014 (program): y-values in the solution to x^2-55*y^2=1.
  • A175015 (program): y-values in the solution to x^2-57*y^2=1.
  • A175027 (program): Replace prime with its index!
  • A175028 (program): a(n)=n+1 if n is prime, otherwise a(n)=n-1.
  • A175029 (program): a(n)=2*n if n is prime, otherwise a(n)=3*n.
  • A175030 (program): a(n)=3*n if n is prime, otherwise a(n)=2*n.
  • A175032 (program): a(n) is the difference between the n-th triangular number and the next perfect square.
  • A175033 (program): Numbers n such that (ceiling(sqrt(n*n/2)))^2 - n*n/2 = 17/2.
  • A175034 (program): Offsets i such that i + n*(n+1)/2 is never a perfect square for any n>0.
  • A175035 (program): Offsets i such that i + n*(n+1)/2 is a perfect square for some positive integer n.
  • A175036 (program): 2^(n-1) mod prime(n).
  • A175040 (program): Product of the n-th block of identical consecutive values of A072000.
  • A175044 (program): Lengths of runs of consecutive values in A168389(n).
  • A175046 (program): Write n in binary, then increase each run of 0’s by one 0, and increase each run of 1’s by one 1. a(n) is the decimal equivalent of the result.
  • A175047 (program): Write n in binary, then increase each run of 0’s by one 0. a(n) is the decimal equivalent of the result.
  • A175048 (program): Write n in binary, then increase each run of 1’s by one 1. a(n) is the decimal equivalent of the result.
  • A175049 (program): y-values in the solution to x^2-59*y^2=1.
  • A175054 (program): A positive integer n is included if there is no run of 0’s in the binary representation of n that is only one digit long.
  • A175055 (program): a(n) = decimal equivalent of {A033015(n) written in binary, and each run of 0’s reduced in length by one digit, and each run of 1’s reduced in length by one digit}.
  • A175056 (program): Inverse permutation to A175055.
  • A175067 (program): a(n) is the sum of perfect divisors of n, where a perfect divisor of n is a divisor d such that d^k = n for some k >= 1.
  • A175068 (program): a(n) = product of perfect divisors of n.
  • A175069 (program): a(n) = product of perfect divisors of n / n.
  • A175070 (program): a(n) is the sum of perfect divisors of n - n, where a perfect divisor of n is a divisor d such that d^k = n for some k >= 1.
  • A175071 (program): Natural numbers m with result 1 under iterations of {r mod (max prime p < r)} starting at r = m.
  • A175072 (program): Natural numbers m with result 2 under iterations of {r mod (max prime p < r)} starting at r = m.
  • A175073 (program): Primes q with result 1 under iterations of {r mod (max prime p < r)} starting at r = q.
  • A175074 (program): Nonprimes b with result 1 under iterations of {r mod (max prime p < r)} starting at r = b.
  • A175076 (program): Composites c which end at 2 under iterations of {r mod (max prime p < r)} starting at r = c.
  • A175077 (program): Final number reached by iterating r -> A049711(r) starting at r = n.
  • A175078 (program): Number of iterations of {r mod (max prime p < r)} needed to reach 1 or 2 starting at r = n.
  • A175081 (program): Values taken by the sum of perfect divisors of n (A175067) sorted into ascending order.
  • A175082 (program): Possible values for sum of perfect divisors of n.
  • A175083 (program): Number of numbers whose sum of perfect divisors is equal to n.
  • A175084 (program): Possible values for product of perfect divisors of n.
  • A175087 (program): Number of numbers whose product of perfect divisors is equal to n.
  • A175088 (program): Numbers m with result 1 under iterations of {r mod (max prime p <= r)} starting at r = m.
  • A175089 (program): Numbers m with result 0 under iterations of {r mod (max prime p <= r)} starting at r = m.
  • A175090 (program): Composites c with result 0 under iterations of {r mod (max prime p <= r)} starting at r = c.
  • A175109 (program): a(n) = ((2*n+1)^3+(-1)^n)/2.
  • A175110 (program): a(n) = ((2*n+1)^4+1)/2.
  • A175111 (program): ((2*n+1)^5+(-1)^n)/2.
  • A175112 (program): First differences of A175111.
  • A175113 (program): a(n) = ((2*n + 1)^6 + 1)/2.
  • A175114 (program): First differences of A175113.
  • A175126 (program): a(0) = a(1) = 0, for n >= 2, a(n) = number of steps of iteration of {r - (smallest prime divisor of r)} needed to reach 0 starting at r = n.
  • A175128 (program): a(n) = the number of natural numbers m with n steps of iterations of {r - (smallest prime divisor of r)} needed to reach 0 starting at r = m .
  • A175131 (program): 2^(n-1) mod semiprime(n).
  • A175134 (program): Define a(n) as the number of ways to achieve n from the following procedure. Let R={r(k)} and S={s(k)} each be some permutation of (1,2,3,…,j) for some nonnegative integer j (with R and S being empty sets if j=0). Define (b(0),b(1),…,b(j)) as follows. b(0)=1. b(m) = b(m-1)*r(m) + s(m), for 1<= m <= j. Does b(j) = n? If so, add 1 to the count. Calculate the b(j)’s by taking j over all nonnegative integers, and taking R and S over all permutations for a given j. The total count equals a(n).
  • A175139 (program): a(1)= 1. a(n) = smallest integer > a(n-1) such that the partial sums of A175140 are avoided. Or, the first difference of A131937.
  • A175140 (program): a(1)= 2. a(n) = smallest integer > a(n-1) such that the partial sums of A175139 are avoided. Or, the first difference of A131938.
  • A175144 (program): a(n) = d(p(n)-1) + d(p(n)+1), where p(n) is the n-th prime, and where d(m) is the number of divisors of m.
  • A175150 (program): a(1)=0. If d(n)>d(n-1), then a(n)=a(n-1)+1. If d(n)<d(n-1), then a(n)=a(n-1)-1. If d(n)=d(n-1), then a(n)=a(n-1). (d(n) is the number of divisors of n.)
  • A175151 (program): a(n) = Sum_{i=1..n} ((i+1)^i - 1)/i.
  • A175152 (program): Numbers n such that 11n-1 and 11n+1 are twin primes.
  • A175153 (program): Numbers n such that 13*n-1, 13*n+1 are twin primes.
  • A175154 (program): a(n) = prime index of A048059(n).
  • A175156 (program): 2^(n-1) mod composite(n).
  • A175157 (program): Numbers n such that 19*n-1, 19*n+1 are twin primes.
  • A175161 (program): a(n) = 8*(2^n + 1).
  • A175162 (program): a(n) = 16*(2^n + 1).
  • A175163 (program): a(n) = 32*(2^n + 1).
  • A175164 (program): a(n) = 16*(2^n - 1).
  • A175165 (program): a(n) = 32*(2^n - 1).
  • A175166 (program): a(n) = 64*(2^n - 1).
  • A175167 (program): a(n) = Sum_{j=1..floor(n/2)} binomial(n+j-1,j-1).
  • A175168 (program): Numbers n such that 2^(n-1) mod n is a prime number.
  • A175181 (program): Pisano period length of the 2-Fibonacci numbers A000129.
  • A175182 (program): Pisano period length of the 3-Fibonacci numbers A006190.
  • A175183 (program): Pisano period length of the 4-Fibonacci numbers A001076.
  • A175184 (program): Pisano period length of the 5-Fibonacci numbers, A052918 preceded by 0.
  • A175185 (program): Pisano period length of the 6-Fibonacci numbers A005668.
  • A175186 (program): a(1)=0. For 1<= n <= 2^m, m>=0, a(n+ 2^m) = a(n)+n.
  • A175187 (program): a(n) = A175186(n)+n.
  • A175188 (program): Smallest composite numbers of the form k*10^k + 1
  • A175191 (program): a(n) = the smallest positive integer such that (the n-th prime)+2*a(n) is composite.
  • A175192 (program): a(n) = characteristic function of numbers k such that A000203(m) = k has solution, where A000203(m) = sums of divisors of m.
  • A175212 (program): Numbers n such that A000975(n-1)/n is an integer. Also numbers n such that arithmetic mean of the first n Jacobsthal numbers is an integer.
  • A175213 (program): a(n)= a(r)+a(s) ; (r+s)<=n ; r=(floor(sqrt(n-1)))^2 ; s=n-(floor(sqrt(n)))^2.
  • A175216 (program): The first nonprimes after the primes.
  • A175217 (program): The second nonprimes after the primes.
  • A175219 (program): The fourth nonprimes after the primes.
  • A175220 (program): The fifth nonprimes after the primes.
  • A175221 (program): a(n) = prime(n) + 4.
  • A175222 (program): a(n) = prime(n) + 5.
  • A175223 (program): a(n) = prime(n) + 7.
  • A175224 (program): a(n) = prime(n) + 8.
  • A175225 (program): a(n) = prime(n) + 10.
  • A175228 (program): Remaining sequence of step 3 of sieve from A175227.
  • A175229 (program): Delete sequence of step 4 of sieve from A175227.
  • A175230 (program): Remaining sequence of step 4 of sieve from A175227.
  • A175237 (program): 2*(10^n - 7).
  • A175239 (program): Number of AP divisors of n.
  • A175242 (program): a(n) = the number of divisors of n that are palindromes when written in binary.
  • A175247 (program): Primes (A000040) with noncomposite (A008578) subscripts.
  • A175248 (program): Noncomposites (A008578) with noncomposite (A008578) subscripts.
  • A175249 (program): Noncomposites (A008578) with nonprime (A018252) subscripts.
  • A175250 (program): Nonprimes (A018252) with noncomposite (A008578) subscripts.
  • A175251 (program): Composites (A002808) with nonprime (A018252) subscripts.
  • A175253 (program): a(n) = characteristic function of numbers k such that A000203(m) = k has no solution for any m, where A000203(m) = sum of divisors of m.
  • A175254 (program): a(n) = Sum_{k<=n} A000203(k)*(n-k+1), where A000203(m) is the sum of divisors of m.
  • A175255 (program): Squares in A111153.
  • A175258 (program): Numbers n with property that n^2+41 is prime.
  • A175262 (program): Those positive integers that when written in binary contain an odd number of digits, the middle digit being a 1.
  • A175281 (program): Numbers n with property that 6n+1 is term in A005471.
  • A175282 (program): Positive numbers n with property that n^2+3n+9 is prime (A005471).
  • A175283 (program): Numbers k with the property that k and k^2 + 3k+9 are primes.
  • A175286 (program): Pisano period of the Jacobsthal sequence A001045 modulo n.
  • A175287 (program): Partial sums of ceiling(n^2/4).
  • A175297 (program): Convert n to binary. AND each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.
  • A175298 (program): Smallest number >=n whose binary representation is palindromic and has a 1 whenever the binary representation of n has a 1.
  • A175299 (program): a(n) = the smallest positive integer such that A175298(a(n)) = the n-th positive integer that is a palindrome when written in binary.
  • A175304 (program): A positive integer n is included if d(n+d(n)) = d(n), where d(n) is the number of divisors of n.
  • A175308 (program): Numbers n such that (Sum_{i=0..n} F(i)^2) / (n+1) is an integer, where F(i) i-th Fibonacci number.
  • A175312 (program): Maximum value on Lower Shuffle Part of Kimberling’s Expulsion Array (A035486).
  • A175317 (program): a(n) = Sum_{d|n} A007955(d) where A007955(m) = product of divisors of m.
  • A175318 (program): a(n) = Sum_{k<=n} A007955(k), where A007955(m) = product of divisors of m.
  • A175322 (program): a(n) = A053141(n)*A001109(n+1) = Sum_{k=A053141(n)+1..A001109(n+1)-1} k.
  • A175329 (program): a(n) = bitwise OR of prime(n) and prime(n+1).
  • A175330 (program): a(n) = bitwise AND of prime(n) and prime(n+1).
  • A175332 (program): Numbers whose binary expansion is of the form 11+0*
  • A175337 (program): Fixed point of morphism 0 -> 00110, 1 -> 00111
  • A175346 (program): a(n) = Sum_{k=1..n^2} d(k), d(k) = number of divisors of k (A000005).
  • A175348 (program): Last digit of p^p, where p is the n-th prime.
  • A175352 (program): Numbers such that arithmetic mean of all prime factors is not an integer.
  • A175360 (program): Partial sums of A000132.
  • A175361 (program): Partial sums of A000141.
  • A175362 (program): Number of integer pairs (x,y) satisfying |x|^3 + |y|^3 = n, -n <= x,y <= n.
  • A175363 (program): Partial sums of A175362.
  • A175364 (program): A175363(n^2).
  • A175378 (program): G.f. x^4*(2*x^2-1)/( (x^2-1)*(x^2+x-1)*(2*x^3-2*x^2+2*x-1) ).
  • A175381 (program): A positive integer of n is included if all positive integers that, when written in binary, occur as substrings in binary n divide n.
  • A175382 (program): Positive integers n for which there is at least one positive integer k whose binary expansion occurs as a substring in the binary expansion of n but does not divide n.
  • A175385 (program): a(n) = numerator of sum{i=1..n} binomial(2n-i-1,i-1)/i.
  • A175386 (program): a(n) = denominator of sum((1/i)*C(2n-i-1,i-1),i=1..n).
  • A175387 (program): a(n) = A004001(n)-floor(A004001(n)/2).
  • A175391 (program): Perfect squares having a square number of divisors.
  • A175395 (program): a(n) = 2*Fibonacci(n)^2.
  • A175406 (program): The greatest integer k such that (1+1/n)^k <= 2.
  • A175408 (program): a(n) + a(n - 1) is alternatively a cube or a square.
  • A175409 (program): Successive numbers of consecutive positive terms to add when rearranging the alternating harmonic series to sum to log[7/3].
  • A175410 (program): a(n) = (b(m)-1)*b(m) = Sum_{n=b(m)+1,…,c(m)}n, b=A046174, c=A046175, m=n+1.
  • A175411 (program): a(n) = Sum_{i=(n*n-n+2)/2..(n*n+n)/2} i!.
  • A175430 (program): a(n) = (n-1)! * (n+1)!.
  • A175431 (program): Numbers m such that sigma(m) is not a nontrivial power, i.e., sigma(m) = A000203(n) is not equal a^b where a and b are greater than 1.
  • A175432 (program): a(n) = the greatest number k such that sigma(n) = m^k for any m >= 1 (sigma = A000203).
  • A175433 (program): a(n) = the smallest number m such that sigma(n) = m^k for any k >= 1 (sigma = A000203).
  • A175434 (program): (Digit sum of 2^n) mod n.
  • A175435 (program): (Digit sum of 3^n) mod n.
  • A175441 (program): Denominators of the harmonic means H(n) of the first n positive integers.
  • A175442 (program): a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=3.
  • A175445 (program): a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=9.
  • A175446 (program): a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=11.
  • A175448 (program): a(n)>a(n-1), a(n) = smallest prime such that a(n)+a(n-1) is multiple of m, a(1)=2, m=15.
  • A175452 (program): a(n) = smallest prime such that a(n)+2 is multiple of 2n+1.
  • A175454 (program): a(n) = number of divisors of n(n+1) that divide neither n nor n+1.
  • A175456 (program): (Digit sum of 5^n) mod n.
  • A175457 (program): (Digit sum of 6^n) mod n.
  • A175461 (program): Semiprimes of form 8n+5.
  • A175462 (program): Number of divisors of integers of form 5 + 8n.
  • A175463 (program): Numbers k such that 8*k + 5 is semiprime.
  • A175467 (program): Write n in binary. Place a 0 between every pair of adjacent 1’s, and place a 1 between every pair of adjacent 0’s. a(n) is the decimal equivalent of the result.
  • A175478 (program): Decimal expansion of (log(3))^2.
  • A175482 (program): a(n) = lesser prime factor of A175461(n).
  • A175483 (program): a(n) = larger prime factor of A175461(n).
  • A175484 (program): a(n) = (1/2)*(A175482(n)+A175483(n)).
  • A175485 (program): Numerators of averages of squares of the first n positive integers.
  • A175493 (program): a(n) = Product_{k=1..n} k^d(k), where d(k) = number of divisors of k.
  • A175495 (program): Positive integers k such that k < 2^d(k), where d(k) is the number of divisors of k.
  • A175504 (program): a(n) = n ^ (phi(n) - 1), phi(n) = A000010(n) = Euler totient function.
  • A175505 (program): Numerator of A053818(n)/A023896(n) = antiharmonic mean of numbers k such that gcd(k,n) = 1, 1 <= k < n.
  • A175506 (program): Denominators of the antiharmonic means B of numbers k such that gcd(k, n) = 1 for numbers n >= 1 and k < n.
  • A175510 (program): (2*n)-th twin prime minus 2*(n-th twin prime).
  • A175511 (program): n-th even semiprime minus n-th semiprime.
  • A175512 (program): (Digit sum of 7^n) mod n.
  • A175515 (program): 1,2,3 together with the semiprimes A001358.
  • A175520 (program): Number of distinct transpositions of digits (zeros and units) in n-th semiprime written in base 2.
  • A175523 (program): a(n)=a(n-1)+ p, where p is the least prime whose first digit equals the first digit of a(n-1) and p>=a(n-1)
  • A175527 (program): Digit sum of 13^n.
  • A175528 (program): (Digit sum of 13^n) mod n.
  • A175539 (program): a(1)=1, then a(n) = smallest number whose square is larger than 2*(a(n-1))^2.
  • A175540 (program): a(n) = A067076(n) + n.
  • A175541 (program): A007505 in binary.
  • A175543 (program): Nonnegative integers that, when written in binary, are palindromes with a middle run of 0’s.
  • A175544 (program): Positive integers that, when written in binary, are palindromes with a middle run of 1’s.
  • A175548 (program): Binary weight of sigma(n).
  • A175549 (program): Number of triples (a, b, c) with gcd(a, b, c) = 1 and -n <= a,b,c <= n.
  • A175553 (program): Product of first k triangular numbers divided by the sum of first k triangular numbers is an integer.
  • A175558 (program): a(n) = 167^n.
  • A175559 (program): Digit sum of 167^n.
  • A175560 (program): (Digit sum of 167^n) mod n.
  • A175567 (program): (n!)^2 modulo n(n+1)/2.
  • A175571 (program): Decimal expansion of the Dirichlet beta function of 5.
  • A175574 (program): Decimal expansion of sqrt(Pi) / (Gamma(3/4))^2 .
  • A175575 (program): Decimal expansion of (Gamma(3/4))^2 / Pi^(3/2) .
  • A175591 (program): a(n) = (sigma(n-th Zumkeller number)/2) - (n-th Zumkeller number).
  • A175594 (program): Numbers having no primitive root.
  • A175596 (program): Partial products of A007425.
  • A175597 (program): Minimal run length in binary representation of n.
  • A175599 (program): The difference between maximal run length and minimal run length in binary representation of n.
  • A175600 (program): Primes of form 4k+1 where k is a Pythagorean prime.
  • A175601 (program): 7*(10^n-9).
  • A175602 (program): 8*(10^n-3).
  • A175603 (program): a(n) = 8*(10^n-5).
  • A175604 (program): a(n) = 8*(10^n-7).
  • A175605 (program): a(n) = concatenation of n^3 with itself.
  • A175608 (program): Characteristic function of squarefree triangular integers: 1 if n(n+1)/2 is squarefree else 0.
  • A175609 (program): The difference between maximal run length and minimal run length in binary representation of n-th prime.
  • A175612 (program): Pairs of cousin semiprimes (m, m+4).
  • A175614 (program): a(1)=1, a(2)=5, then a(n)=a(n-2)+4, if n odd else a(n)=prime(primepi(a(n-2)+4)).
  • A175624 (program): n! modulo n(n+1)(n+2)/3.
  • A175627 (program): a(1) = 1; a(n) is the smallest square > 2*a(n-1).
  • A175628 (program): a(2*n+1) = A005563(n). a(2*n) = A061037(n+1).
  • A175629 (program): Legendre symbol (n,7).
  • A175630 (program): a(n) = n-th pentagonal number mod (n+2).
  • A175631 (program): a(n) = (n-th pentagonal number) modulo (n-th triangular number).
  • A175632 (program): Maximal run length of primes of the form A025584(n), A025584(n)+2, A025584(n)+4, …
  • A175633 (program): Numbers x such that x^2 - 28*y^2 = 1 for some integer y.
  • A175634 (program): Chen semiprimes: semiprimes m such that m+4 is either a prime or a semiprime.
  • A175648 (program): Semiprimes m such that m+4 is also semiprime.
  • A175649 (program): a(n) = sopf(n) + sopf(n+1).
  • A175654 (program): Eight bishops and one elephant on a 3 X 3 chessboard. G.f.: (1 - x - x^2)/(1 - 3*x - x^2 + 6*x^3).
  • A175655 (program): Eight bishops and one elephant on a 3 X 3 chessboard. G.f.: (1+x-5*x^2)/(1-3*x-x^2+6*x^3).
  • A175656 (program): Eight bishops and one elephant on a 3 X 3 chessboard. G.f.: (1-3*x^2)/(1-3*x+4*x^3).
  • A175657 (program): Eight bishops and one elephant on a 3 X 3 chessboard: a(n) = 3*2^n - 2*F(n+1), with F(n) = A000045(n).
  • A175658 (program): Eight bishops and one elephant on a 3 X 3 chessboard: a(n) = 2*Pell(n+1)+2*Pell(n)-2^n, with Pell = A000129.
  • A175659 (program): Eight bishops and one elephant on a 3 X 3 chessboard: a(n)= (3^(n+1)-Jacobsthal(n+1))-(3^n-Jacobsthal(n)), with Jacobsthal=A001045.
  • A175660 (program): Eight bishops and one elephant on a 3 X 3 chessboard. a(n) = 2^(n+2) - 3*F(n+2).
  • A175661 (program): Eight bishops and one elephant on a 3 X 3 chessboard: a(n) = 2^(n+2)-3*F(n+1), with F(n) = A000045(n).
  • A175664 (program): Greater of twin semiprimes.
  • A175665 (program): The product of maximal run and minimal run lengths in the binary representation of n.
  • A175666 (program): Sum of Sophie Germain prime p and corresponding safe prime q=2p+1.
  • A175668 (program): First differences of A175648.
  • A175672 (program): y-values in the solution to x^2 - 28*y^2=1.
  • A175673 (program): Number of n-digit terms in A179955.
  • A175676 (program): a(n) = binomial(n,3) mod n.
  • A175677 (program): Binomial(n,4) mod n.
  • A175678 (program): Numbers m such that arithmetic mean Ad(m) of divisors of m and arithmetic mean Ah(m) of numbers h < m such that gcd(h,m) = 1 both integer.
  • A175679 (program): Numbers m such that arithmetic mean Ad(m) of divisors of m and arithmetic mean Ak(m) of numbers 1 <= k <= m are both integer.
  • A175680 (program): Semiprimes that are not Chen semiprimes A175634.
  • A175686 (program): a(n) = binomial(n-j-1,j) + binomial(n-j,j-1) with j= floor((n-1)/2).
  • A175699 (program): a(n) = n ^ phi(n-1), phi(n) = A000010(n) = Euler totient function.
  • A175700 (program): a(n) = n ^ phi(n+1), phi(n) = A000010(n) = Euler totient function.
  • A175701 (program): a(n) = n ^ (phi(n)+1), phi(n) = A000010(n) = Euler totient function.
  • A175702 (program): Convolution square of the Liouville sequence A008836.
  • A175708 (program): n-th semiprime minus n.
  • A175712 (program): The third column of the Lucas Fibonacci sum of binomials A175685.
  • A175713 (program): Expansion of 1/(1 - x - 4*x^2 + 4*x^3 - 2*x^4).
  • A175714 (program): Expansion of -1/((1 - x)*(1 - x^2 + 4*x^3)).
  • A175715 (program): Expansion of 1/(1 - x - x^2 - 3*x^4 + 4*x^5 - 2*x^6).
  • A175716 (program): The total number of elements(ordered pairs) in all equivalence relations on {1,2,…,n}
  • A175717 (program): First differences of A175628.
  • A175722 (program): a(n) = -a(n-1) + a(n-2) - F(-n) + 1, a(0) = 1, a(1) = -1, where F() = Fibonacci numbers A000045.
  • A175723 (program): a(1)=a(2)=1; thereafter a(n) = gpf(a(n-1)+a(n-2)), where gpf = “greatest prime factor”.
  • A175724 (program): Partial sums of floor(n^2/12).
  • A175729 (program): Numbers n such that the sum of the prime factors with multiplicity of n divides n-1.
  • A175732 (program): a(n) = gcd(phi(n), psi(n)).
  • A175733 (program): a(n) is the smallest n-digit number with 3 divisors.
  • A175742 (program): Numbers with 32 divisors.
  • A175743 (program): Numbers with 33 divisors.
  • A175746 (program): Numbers with 36 divisors.
  • A175749 (program): Numbers with 40 divisors.
  • A175753 (program): Numbers with 46 divisors.
  • A175754 (program): Numbers with 48 divisors.
  • A175757 (program): Triangular array read by rows: T(n,k) is the number of blocks of size k in all set partitions of {1,2,…,n}.
  • A175770 (program): In the sequence of prime numbers, replace all the ‘3’ digits with ‘1’ and vice versa.
  • A175771 (program): a(n) = ((n^2 + 1)^n - 1)/n^3.
  • A175774 (program): 7*(10^n-5)
  • A175775 (program): 7*(10^n-3).
  • A175776 (program): Partial sums of floor(n^2/15).
  • A175777 (program): Partial sums of floor(n^2/16).
  • A175779 (program): Triangle T(n,m) read by rows: numerator of 1/(n-m)^2 - 1/n^2.
  • A175780 (program): Partial sums of floor(n^2/24).
  • A175781 (program): a(n) = n^(1/k) with the smallest k>1 such that n is a k-th power, taking k=1 if no such k>1 exists.
  • A175784 (program): Numerators of k/(10+k)+1 for k = 2*n-1.
  • A175787 (program): Primes together with 4.
  • A175790 (program): Expansion of 1/((1 - x^3 - x^4)*(1 + x)).
  • A175792 (program): a(n) = Sum_{k=1..n} (-1)^A000796(k), excess of the number of even over odd digits in the first n digits of Pi.
  • A175793 (program): Excess of the number of even over the number of odd digits in the first n digits of the decimal expansion of E.
  • A175798 (program): Expansion of ( -3+x+4*x^2-3*x^3+3*x^5-x^7-3*x^4+x^6 ) / ( (1+x) *(x^5-x^4-x^3+x^2-1) *(x-1)^2 ).
  • A175803 (program): a(n) = 2^(prime(n)-2) mod prime(n+2).
  • A175804 (program): Square array A(n,k), n>=0, k>=0, read by antidiagonals: A(n,k) is the n-th term of the k-th differences of partition numbers A000041.
  • A175805 (program): a(n) = 21*2^n.
  • A175806 (program): a(n) = 27*2^n.
  • A175812 (program): Partial sums of ceiling(n^2/6).
  • A175818 (program): Concatenate all previous terms in base 2 and add 1.
  • A175822 (program): Partial sums of ceiling(n^2/7).
  • A175824 (program): Maximum unsigned integer that can be stored in n bytes.
  • A175825 (program): Maximum signed integer that can be stored in n bytes.
  • A175826 (program): Partial sums of ceiling(n^2/8).
  • A175827 (program): Partial sums of ceiling(n^2/10).
  • A175828 (program): a(n) = (n*(6*n+1)+(n+2)*(-1)^n)/2.
  • A175829 (program): Partial sums of ceiling(n^2/11).
  • A175831 (program): Partial sums of ceiling(n^2/12).
  • A175833 (program): Periodic sequence: repeat 4,7,11.
  • A175836 (program): a(n) = Product_{i=1..n} psi(i) where psi is the Dedekind psi function (A001615).
  • A175837 (program): (2n-1)-abundant numbers
  • A175840 (program): Mirror image of Nicomachus’ table: T(n,k) = 3^(n-k)*2^k for n>=0 and 0<=k<=n.
  • A175842 (program): Partial sums of ceiling(n^2/14).
  • A175844 (program): Parse the base-2 expansion of 1/n using the Ziv-Lempel encoding as described in A106182; sequence gives the eventual period of the differences of the sequence of lengths of the successive phrases.
  • A175846 (program): Partial sums of ceiling(n^2/15).
  • A175848 (program): Partial sums of ceiling(n^2/16).
  • A175851 (program): a(n) = 1 for noncomposite n, a(n) = n - previousprime(n) + 1 for composite n.
  • A175852 (program): a(n) = the highest power of 5 with n decimal digits.
  • A175856 (program): a(n) = n for n = noncomposites, a(n) = previous term - 1 for n = composites.
  • A175864 (program): Partial sums of ceiling(n^2/19).
  • A175865 (program): Numbers k with property that 2^(k-1) == 1 (mod k) and 2^((3*k-1)/2) - 2^((k-1)/2) + 1 == 0 (mod k).
  • A175868 (program): Partial sums of ceiling(n^2/20).
  • A175869 (program): Partial sums of ceiling(n^2/23).
  • A175870 (program): Partial sums of ceiling(n^2/24).
  • A175879 (program): Numbers arising from certain regular binary expansions.
  • A175880 (program): a(1)=1, a(2)=2. If n >= 3: if n/2 is in the sequence, a(n)=0, otherwise a(n)=n.
  • A175882 (program): Number of groupoids of order n with no identity element.
  • A175884 (program): Numbers that are congruent to {0, 2, 4, 7, 9} mod 12.
  • A175885 (program): Numbers that are congruent to {1, 10} mod 11.
  • A175886 (program): Numbers that are congruent to {1, 12} mod 13.
  • A175887 (program): Numbers that are congruent to {1, 14} mod 15.
  • A175898 (program): Expansion of (1+3*x+9*x^2+9*x^3+9*x^4+3*x^5+x^6) /( (1+x)^2 * (1-x)^5 ).
  • A175899 (program): a(n) = a(n-2) + a(n-3) + 2*a(n-4), with a(1) = 0, a(2) = 2, a(3) = 3, a(4) = 10.
  • A175908 (program): 3*sum(k=1..n, floor(k^2/n)) - n^2.
  • A175917 (program): Convert n to binary. NOR each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.
  • A175918 (program): Convert n to binary. NAND each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.
  • A175919 (program): Convert n to binary. XOR each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.
  • A175920 (program): Convert n to binary. XNOR each respective digit of binary n and binary A030101(n), where A030101(n) is the reversal of the order of the digits in the binary representation of n (given in decimal). a(n) is the decimal value of the result.
  • A175921 (program): Period 5: repeat [1, 2, 2, -1, 1].
  • A175922 (program): Period 5: repeat [1, 1, 2, -1, 2].
  • A175923 (program): Index of the first occurrence of p(n)-1 consecutive zeros in the sequence of Bell numbers reduced modulo the n-th prime p(n).
  • A175925 (program): a(n) = (2*n+1)*(n+1)!.
  • A175926 (program): Sum of divisors of cubes.
  • A175944 (program): 1 appears once, n-th prime p appears p times.
  • A175945 (program): Start with the binary expansion of n; list the lengths of the runs of ones and interpret this list as lengths of runs of alternating ones and zeros in binary.
  • A175946 (program): List the run lengths of n’s binary runs of zeros, then interpret this list as lengths of runs of alternating ones and zeros in binary.
  • A175953 (program): Let a(1)=1; for n>1 a(n)=nextprime(a(n-1)+(a(n-1)+1)/4).
  • A175961 (program): n-th nonprime number appears n-th nonprime numbers times.
  • A175965 (program): Lexicographically earliest sequence with first differences as increasing sequence of noncomposites A008578.
  • A175966 (program): Complement of A175965(n), where A175965(n) = the lexicographically earliest sequence with first differences as increasing sequence of noncomposites A008578.
  • A175967 (program): Lexicographically earliest sequence with first differences as increasing sequence of nonprimes A018252.
  • A175968 (program): Complement of A175967(n), where A175967(n) = the lexicographically earliest sequence with first differences as increasing sequence of nonprimes A018252(n).
  • A175969 (program): Complement of A014284(n), where A014284(n) = the lexicographically earliest sequence with first differences as increasing sequence of primes A000040.
  • A175970 (program): Complement of A051349(n), where A051349(n) = the lexicographically earliest sequence with first differences as increasing sequence of composites A002808(n).
  • A175971 (program): Denominators of 1/16-1/m^2 for some m>0, which are of the form (8*k+4)^2, sorted by increasing m.
  • A175976 (program): a(n) = 4^n-3*n+1.
  • A175990 (program): Irregular triangle t(n,m) = binomial(n-m-1,m+1) read by rows.
  • A175991 (program): a(n) = binomial(binomial(binomial(n, 2), 3), 4)/5.
  • A175992 (program): Triangle T(n,k) read by rows. If n=k then 0, else if k divides n then 1 else 0.
  • A176003 (program): a(n) = 3*(n-th noncomposite number) - 2.
  • A176004 (program): (n-th prime > 3) minus (n-th semiprime).
  • A176006 (program): The number of branching configurations of RNA (see Sankoff, 1985) with n or fewer hairpins.
  • A176010 (program): Positive numbers k such that k^2 == 2 (mod 97).
  • A176014 (program): Decimal expansion of (3+sqrt(21))/6.
  • A176015 (program): Decimal expansion of (5 + 3*sqrt(5))/10.
  • A176016 (program): Decimal expansion of (3+sqrt(15))/6.
  • A176017 (program): Decimal expansion of (7+sqrt(77))/14.
  • A176018 (program): a(n) = binomial(A000460(n), 3).
  • A176019 (program): Decimal expansion of (3+sqrt(13))/6.
  • A176020 (program): Decimal expansion of (3+sqrt(15))/3.
  • A176027 (program): Binomial transform of A005563.
  • A176029 (program): a(n)= n^Omega(n).
  • A176031 (program): a(n) = n^rad(n)
  • A176032 (program): Absolute values of A106044-A056892.
  • A176034 (program): Difference between product of two distinct primes and next perfect square.
  • A176035 (program): Difference between product of two distinct primes and previous perfect square.
  • A176036 (program): Absolute values of A176035(n)-A176034(n).
  • A176037 (program): a(n) = n!*(n+1)!*(n+2)!.
  • A176040 (program): Periodic sequence: Repeat 3, 1.
  • A176043 (program): a(n) = (2*n-1)*(n-1)^(n-1).
  • A176044 (program): n-th-prime without last digit.
  • A176045 (program): Numbers n such that n-1 and 2*n-1 are both prime.
  • A176050 (program): Det(M) where M is an n X n antisymmetric matrix with M(i,j) = n for i < j.
  • A176051 (program): Decimal expansion of (2+sqrt(6))/2.
  • A176052 (program): Decimal expansion of (5+sqrt(35))/5.
  • A176053 (program): Decimal expansion of (3+2*sqrt(3))/3.
  • A176054 (program): Decimal expansion of (7+3*sqrt(7))/7.
  • A176055 (program): Decimal expansion of (2+sqrt(5))/2.
  • A176056 (program): Decimal expansion of (3+sqrt(11))/3.
  • A176057 (program): Decimal expansion of (5+sqrt(30))/5.
  • A176058 (program): Decimal expansion of (3+sqrt(15))/2.
  • A176059 (program): Periodic sequence: Repeat 3, 2.
  • A176060 (program): a(n) = n*(n+1)*(3*n^2+5*n+4)/12.
  • A176065 (program): Numbers n such that n-th semiprime-2 is prime.
  • A176067 (program): Binary analog of A098755 and A098756: Binary representation of least available nonnegative integer with bit values alternating for entire sequence.
  • A176069 (program): Products of two distinct primes of the form n^2+n+1.
  • A176070 (program): Products of two distinct primes of the form n^3+n^2+n+1.
  • A176078 (program): Triangle, read by rows, T(n, k) = (2*n)!/((n-k)! * k!)^2 - (2*n)!/(n!)^2 + 1.
  • A176079 (program): Triangle T(n,k) read by rows: If k divides n then k-1, otherwise -1.
  • A176080 (program): Triangle, read by rows, T(n, k) = Sum_{j=0..k} (n+k)!/((n-j)!*(k-j)!*j!).
  • A176083 (program): a(n) = 2^(2n-2) mod prime(2n).
  • A176085 (program): a(n) = A136431(n,n).
  • A176092 (program): Triangle, read by rows, T(n, k) = Sum_{j=0..k} (-1)^j*(n+k)!/((n-j)!*(k-j)!*j!).
  • A176095 (program): a(n) = n - phi(2*n), where phi() is the Euler totient A000010().
  • A176097 (program): Degree of the hyperdeterminant of the cubic format (k+1) X (k+1) X (k+1).
  • A176098 (program): a(n) = prime(n)*(nonnegative noncomposite(n)).
  • A176099 (program): Prime(n) + A158611(n).
  • A176100 (program): Even numbers that are not semiprimes, or, twice the nonprimes.
  • A176102 (program): Decimal expansion of (3+2*sqrt(3))/2.
  • A176103 (program): Decimal expansion of (15+sqrt(285))/10.
  • A176104 (program): Decimal expansion of sqrt(285).
  • A176105 (program): Decimal expansion of (3+sqrt(11))/2.
  • A176106 (program): Decimal expansion of (21+5*sqrt(21))/14.
  • A176107 (program): Decimal expansion of (6+sqrt(42))/4.
  • A176108 (program): Decimal expansion of (9+sqrt(93))/6.
  • A176109 (program): Decimal expansion of (15+sqrt(255))/10.
  • A176110 (program): Decimal expansion of sqrt(255).
  • A176114 (program): Numbers n such that 30*n-1, 30*n+1 are twin primes.
  • A176115 (program): Numbers n such that 2310*n-1, 2310*n+1 are twin primes, (2310=2*3*5*7*11).
  • A176120 (program): Triangle read by rows: Sum_{j=0..k} binomial(n, j)*binomial(k, j)*j!.
  • A176121 (program): Triangle, read by rows, T(n,k) = binomial(n+k+1, n+1) * Sum_{j=0..k} j!*binomial(n,j)*binomial(k, j).
  • A176122 (program): Triangle, read by rows, T(n,k) = Sum_{j=1..k} binomial(n-1, j-1)*binomial(k, j - 1)*(j-1)!.
  • A176123 (program): Irregular triangle, read by rows, T(n, k) = binomial(n-(k-1),k-1), 1 <= k <= floor(n/2-1).
  • A176126 (program): Numerator of -A127276(n)/A001788(n).
  • A176128 (program): a(n) = (n*n!)^2.
  • A176133 (program): Pythagorean primes p (primes of form 4*k + 1) such that 6*p -+ 1 are twin primes.
  • A176137 (program): Number of partitions of n into distinct Catalan numbers, cf. A000108.
  • A176144 (program): a(2n) = A164555(n). a(2n+1) = A027641(n).
  • A176145 (program): a(n) = n*(n-3)*(n^2-7*n+14)/8.
  • A176146 (program): a(n) = n-th-semiprime without last digit.
  • A176147 (program): a(n) = n^sopf(n), where sopf(n) is the sum of the distinct primes dividing n (A008472).
  • A176158 (program): A polynomial coefficient sequence:p(x,n,m)=(1 + 2*Binomial[n, m]*x)^n
  • A176159 (program): A polynomial coefficient sequence:p(x,n,m)=(1 + Binomial[n, m]*x)^n
  • A176160 (program): A polynomial coefficient sequence:p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n
  • A176166 (program): Highest exponents of triangular numbers.
  • A176172 (program): 3rd prime-factor of n-th product of 4 distinct primes.
  • A176173 (program): 4th|largest prime-factor of n-th product of 4 distinct primes.
  • A176174 (program): Starting with 1, multiply the n-th term by 10, then subtract the sum of all terms up to and including the n-th, to make the (n+1)th term.
  • A176175 (program): Numbers k such that (2^(k-1) mod k) = number of prime divisors of k (counted with multiplicity).
  • A176176 (program): Numbers k such that 2^(k-1) == 4^(k-1) (mod k).
  • A176177 (program): a(n) = 2*n*3^(n-1) - (3^n-1)/2.
  • A176184 (program): a(2n) = A027641(n). a(2n+1) = A164555(n).
  • A176189 (program): Natural numbers whose squares have only 0’s and 1’s in base 3.
  • A176190 (program): A sequence of polynomial coefficients:p(x,n,m)=(1 + (Binomial[n, m]*Binomial[n + 1, m]/(m + 1))*x)^n
  • A176191 (program): Numbers n such that semiprime(n)-1 is prime, where semiprime(n) is A001358.
  • A176193 (program): The positions of semiprimes in A002808.
  • A176195 (program): Largest prime factor of A174562(n).
  • A176198 (program): A symmetrical triangle of polynomial coefficients:q=2;p(x,n,q)=(1 - x)^(n + 1)*Sum[((q*k + 1)^n + (q*k + q - 1)^n)*x^k, {k, 0, Infinity}]
  • A176200 (program): A symmetrical triangle T(n, m) = 2*Eulerian(n+1, m) -1, read by rows.
  • A176201 (program): G.f. satisfies A(x)/A(x^2) = (1 + 9x + 9x^2 + 9x^3 + …).
  • A176203 (program): Triangle read by rows: T(n, k) = 16*binomial(n, k) - 15.
  • A176204 (program): Triangle T(n, k) = 4 * A008292(n+1, k) - 3, read by rows.
  • A176209 (program): Sums of at least 2 squares s’, for s >= 4.
  • A176213 (program): Decimal expansion of 2+sqrt(6).
  • A176214 (program): Decimal expansion of (6+4*sqrt(3))/3.
  • A176215 (program): Decimal expansion of (10+2*sqrt(30))/5.
  • A176216 (program): Decimal expansion of (6+sqrt(42))/3.
  • A176217 (program): Decimal expansion of (14+4*sqrt(14))/7.
  • A176218 (program): Decimal expansion of (4 + 3*sqrt(2))/2.
  • A176219 (program): Decimal expansion of (6+2*sqrt(10))/3.
  • A176220 (program): Decimal expansion of (10+sqrt(110))/5.
  • A176221 (program): Decimal expansion of sqrt(110).
  • A176222 (program): a(n) = (n^2 - 3*n + 1 + (-1)^n)/2.
  • A176224 (program): A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=2.
  • A176225 (program): A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=3.
  • A176226 (program): A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=5.
  • A176227 (program): A symmetrical triangle sequence: T(n, k) = q^k + q^(n-k) - q^n, with q=4.
  • A176228 (program): Triangle read by rows: T(n,k) = binomial(n,k) + Fibonacci(n) + 1.
  • A176230 (program): Exponential Riordan array [1/sqrt(1-2x), x/(1-2x)].
  • A176231 (program): Coefficient array of orthogonal polynomials whose moment sequence is the double factorial numbers A001147.
  • A176232 (program): Determinant of the n X n matrix with rows (1!,-1,0,…,0), (1, 2!,-1,0,…,0), (0,1,3!,-1,0,…,0), …, (0,0,…,1,n!).
  • A176233 (program): Determinant of n X n matrix with rows (n^2,-1,0,…,0), (1,n^2,-1, 0,…,0), (0,1,n^2,-1,0,…,0), …,(0,0,…,1,n^2).
  • A176235 (program): Numbers n such that one of nonprime(n)-1 or nonprime(n)+1 is prime.
  • A176237 (program): Binary expansion of n contains at least one 1-bit at even position and one 1-bit at odd position.
  • A176238 (program): Natural numbers n such that d(d(n)+1) > 2
  • A176239 (program): Shifted signed Catalan triangle T(n,k) = (-1)^*(n+k+1)*A009766(n,k-n+1) read by rows.
  • A176246 (program): a(n) = A001223(n+1) - 1.
  • A176255 (program): Numbers of the form 4k-1 with least prime divisor of the form 4m+1.
  • A176256 (program): Numbers of the form 4k+1 with least prime divisor of the form 4m-1.
  • A176257 (program): Numbers of the form 4k-1 with greatest prime divisor of the form 4m+1.
  • A176258 (program): Numbers of the form 4k+1 with greatest prime divisor of the form 4m-1.
  • A176260 (program): Periodic sequence: Repeat 5, 1.
  • A176262 (program): Numbers of the form 3k+1 with greatest prime divisor of the form 3m-1.
  • A176270 (program): Triangle T(n,m) = 1 + m*(m-n) read by rows, 0 <= m <= n.
  • A176271 (program): The odd numbers as a triangle read by rows.
  • A176274 (program): Numbers of the form 3k-1 with greatest prime divisor of the form 3m+1
  • A176275 (program): Numbers of the form 6k+1 with the least prime divisor of the form 6m-1
  • A176278 (program): Numbers of the form 6k-1 with the least prime divisor of the form 6m+1.
  • A176280 (program): Diagonal sums of number triangle A046521.
  • A176281 (program): Hankel transform of A176280.
  • A176282 (program): Triangle T(n,k) = 1 + A000330(n) - A000330(k) - A000330(n-k), read by rows.
  • A176283 (program): Triangle T(n,k) = 1 + A000537(n) - A000537(k) - A000537(n-k), read by rows.
  • A176284 (program): Triangle T(n,k) = 1 + 3*n*k*(n-k) read by rows.
  • A176286 (program): Triangle T(n,k) = 1 + 2*k*(n-k)*(k^2 -n*k +2*n^2) read by rows.
  • A176287 (program): Diagonal sums of number triangle A092392.
  • A176288 (program): Hankel transform of A176287.
  • A176289 (program): Denominators of the rational sequence with e.g.f. (x/2)*(1+exp(-x))/(1-exp(-x)).
  • A176290 (program): Hankel transform of A105872.
  • A176291 (program): A symmetrical triangle based on Narayana numbers and Eulerian numbers of type B: T(n, k) = 2 + A060187(n, k) - 2*binomial(n, k)*binomial(n+1, k)/(k+1).
  • A176293 (program): Triangle T(n,k) = 1 + 2*k*(n-k)*(n-1)^2, read by rows.
  • A176296 (program): Irregular triangle read by rows: eigenvalues of Laplacian of parity’s landscape graph.
  • A176297 (program): Numbers with at least one 3 in their prime signature.
  • A176301 (program): Numbers k such that the k-th semiprime + 2 is prime.
  • A176302 (program): a(n) = floor(abs( (i+n)^n )) where “i” is the Imaginary unit.
  • A176303 (program): a(n) = abs(2^n-127).
  • A176304 (program): a(n) = (-1)^n * n * a(n-1) - 1, with a(0)=0.
  • A176310 (program): G.f.: exp( Sum_{n>=1} sigma(n*2^n)*x^n/n ).
  • A176311 (program): a(n) = sigma(n*2^n).
  • A176314 (program): Sum of remainders of mod(n, k), for 1 <= k <= sqrt(n).
  • A176317 (program): Decimal expansion of (5+sqrt(35))/2.
  • A176318 (program): Decimal expansion of (15 + sqrt(285))/6.
  • A176319 (program): Decimal expansion of (5+sqrt(30))/2.
  • A176320 (program): Decimal expansion of (15 + sqrt(255))/6.
  • A176321 (program): Decimal expansion of (35 + sqrt(1365))/14.
  • A176322 (program): Decimal expansion of sqrt(1365).
  • A176323 (program): Decimal expansion of (10+sqrt(110))/4.
  • A176324 (program): Decimal expansion of (15+7*sqrt(5))/6.
  • A176325 (program): Decimal expansion of (5+3*sqrt(3))/2.
  • A176326 (program): a(3n) is the sequence 7, 6, 5, 4, …; a(3n+1) is the sequence 9, 11, 13, 15, …; a(3n+2) is the sequence 11, 8, 5, …
  • A176327 (program): Numerators of the rational sequence with e.g.f. (x/2)*(1+exp(-x))/(1-exp(-x)).
  • A176332 (program): Row sums of triangle A176331.
  • A176333 (program): Expansion of (1-3*x)/(1-4*x+9*x^2).
  • A176335 (program): Central coefficients T(2n,n) of number triangle A176331.
  • A176337 (program): a(n) = 1 + (1-2^n)*a(n-1) for n > 0, a(0)=0.
  • A176338 (program): a(n) = 1 + (1-3^n)*a(n-1) for n >=1, a(0) = 0.
  • A176342 (program): Phi(A166546(n)).
  • A176343 (program): a(n) = Fibonacci(n)*a(n-1) + 1, a(0) = 0.
  • A176345 (program): Sum of gcd(k,n) from k = 1 to n over “regular” integers only (an integer k is regular if there is an x such that k^2 x == k (mod n))
  • A176346 (program): A dual remainder symmetrical triangle sequence T(n, m) = 1 + 2*(n+1) - (m+1)*floor((n+1)/(m+1)) - (n-m+1)*floor((n+1)/( n-m+1)), read by rows.
  • A176347 (program): n-th semiprime minus sum of its prime factors.
  • A176348 (program): Triangle, read by rows: T(n, k) = binomial(n, k)*(1 + 2*(n+1) - (k+1)*floor((n+1)/(k+1)) - (n-k+1)* floor((n+1)/(n-k+1))).
  • A176355 (program): Periodic sequence: Repeat 6, 1.
  • A176358 (program): Partial sums of A002503.
  • A176360 (program): a(n) = quadrant of unit circle corresponding to n radians.
  • A176361 (program): G.f.: exp( Sum_{n>=1} sigma(n*2^(n-1))*x^n/n ).
  • A176362 (program): a(n) = sigma(n*2^(n-1)).
  • A176363 (program): Non-semiprime numbers of order 2.
  • A176365 (program): Numerator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx.
  • A176366 (program): Denominator of (1/Pi)*Integral_{0..infinity} (sin x / x)^(2*n) dx.
  • A176367 (program): y-values in the solution to x^2 - 62*y^2 = 1.
  • A176368 (program): x-values in the solution to x^2 - 65*y^2 = 1.
  • A176369 (program): y-values in the solution to x^2 - 65*y^2 = 1.
  • A176370 (program): x-values in the solution to x^2 - 66*y^2 = 1.
  • A176372 (program): y-values in the solution to x^2 - 66*y^2 = 1.
  • A176377 (program): x-values in the solution to x^2-70*y^2=1.
  • A176378 (program): y-values in the solution to x^2-70*y^2=1.
  • A176393 (program): a(n) = A176100(n) + 1 = 2*A141468(n) + 1.
  • A176394 (program): Decimal expansion of 3+2*sqrt(3).
  • A176395 (program): Decimal expansion of 3+sqrt(11).
  • A176396 (program): Decimal expansion of (6+sqrt(42))/2.
  • A176397 (program): Decimal expansion of (15+sqrt(255))/5.
  • A176398 (program): Decimal expansion of 3+sqrt(10).
  • A176399 (program): Decimal expansion of (21+sqrt(483))/7.
  • A176400 (program): Decimal expansion of sqrt(483).
  • A176401 (program): Decimal expansion of (6+sqrt(39))/2.
  • A176402 (program): Decimal expansion of (9+sqrt(87))/3.
  • A176403 (program): Decimal expansion of (15+4*sqrt(15))/5.
  • A176404 (program): Semiprimes == -+1 (mod 8).
  • A176405 (program): Fixed point of morphism 0->0100110, 1->0110110
  • A176406 (program): Odd semiprimes minus 2.
  • A176408 (program): a(n) = (n+1)*(a(n-1) +a(n-2)) n>1, a(0)=1,a(1)=0
  • A176409 (program): Multiples of 3 or 7.
  • A176413 (program): a(n) = 19*3^n.
  • A176414 (program): Expansion of (7+8*x)/(1+2*x).
  • A176415 (program): Periodic sequence: repeat 7,1.
  • A176416 (program): Fixed point of morphism 0->0PPMM00, P->0PPMM0P, M=0PPMM0M (where P=+1, M=-1)
  • A176423 (program): Numbers that are the sum of at least three distinct positive integers in arithmetic progression.
  • A176434 (program): Decimal expansion of (7+3*sqrt(7))/2.
  • A176435 (program): Decimal expansion of (21+5*sqrt(21))/6.
  • A176436 (program): Decimal expansion of (7+2*sqrt(14))/2.
  • A176437 (program): Decimal expansion of (35+sqrt(1365))/10.
  • A176438 (program): Decimal expansion of (21+sqrt(483))/6.
  • A176439 (program): Decimal expansion of (7+sqrt(53))/2.
  • A176440 (program): Decimal expansion of (14+sqrt(210))/4.
  • A176441 (program): Decimal expansion of sqrt(210).
  • A176442 (program): Decimal expansion of (21+sqrt(469))/6.
  • A176443 (program): Decimal expansion of sqrt(469).
  • A176444 (program): Decimal expansion of (35+sqrt(1295))/10.
  • A176445 (program): Decimal expansion of sqrt(1295).
  • A176447 (program): a(2n) = -n, a(2n+1) = 2n+1.
  • A176448 (program): a(n) = 7*2^n - 2.
  • A176449 (program): a(n) = 9*2^n - 2.
  • A176451 (program): Number of primes between two consecutive nonprimes in A037143.
  • A176453 (program): Decimal expansion of 4+2*sqrt(5).
  • A176454 (program): Decimal expansion of (12+2*sqrt(42))/3.
  • A176455 (program): Decimal expansion of (20+2*sqrt(110))/5.
  • A176456 (program): Decimal expansion of (12+2*sqrt(39))/3.
  • A176457 (program): Decimal expansion of (28+2*sqrt(210))/7.
  • A176458 (program): Decimal expansion of 4+sqrt(17).
  • A176459 (program): Decimal expansion of (12+2*sqrt(38))/3.
  • A176460 (program): Decimal expansion of (20+2*sqrt(105))/5.
  • A176461 (program): Decimal expansion of sqrt(105).
  • A176464 (program): The positions of primes in A065516.
  • A176470 (program): Primes of the form 5*x^2 - 3*y^2, where x and y are consecutive numbers.
  • A176476 (program): Partial sums of A012814.
  • A176479 (program): a(n) = (n+1)*A001003(n).
  • A176484 (program): Triangle t(n,m) read by rows: t(n,n)= 1, t(n,m) = (-1)^(n+m)*(m+1), 0<=m<n.
  • A176487 (program): Triangle t(n,m) = binomial(n,m) + A008292(n+1,m+1)-1 read by rows.
  • A176488 (program): Triangle T(n,k) = A008292(n+1,k+1) + A176487(n,k) - 1, 0<=k<=n.
  • A176489 (program): Triangle T(n,k) = A176487(n,k)+A176488(n,k)-1 read by rows 0<=k<=n.
  • A176490 (program): Triangle T(n,k) = A008292(n+1,k+1) + A060187(n+1,k+1)- 1 read along rows 0<=k<=n.
  • A176491 (program): Triangle T(n,k) = binomial(n,k) + A176490(n,k) - 1 read along rows 0<=k<=n.
  • A176492 (program): Triangle T(n,k) = A176492(n,k) + A008292(n+1,k+1) - 1 read along rows 0<=k<=n.
  • A176493 (program): A091137(n)/(n+1).
  • A176496 (program): a(n) = Sum_{k=1..n} 2^nonprime(k).
  • A176504 (program): a(n) = m + k where prime(m)*prime(k) = semiprime(n).
  • A176506 (program): Difference between the prime indices of the two factors of the n-th semiprime.
  • A176513 (program): a(n+5) = a(n+3) + a(n+2) + a(n), with a(1) = a(2) = a(3) = a(4) = a(5) = 1.
  • A176514 (program): Period 6: repeat [3, 1, 1, 3, 2, 1].
  • A176515 (program): Decimal expansion of (9+3*sqrt(11))/2.
  • A176516 (program): Decimal expansion of (9+sqrt(93))/2.
  • A176517 (program): Decimal expansion of (9+3*sqrt(10))/2.
  • A176518 (program): Decimal expansion of 3*(15+7*sqrt(5))/10.
  • A176519 (program): Decimal expansion of (9+sqrt(87))/2.
  • A176520 (program): Decimal expansion of (63+3*sqrt(469))/14.
  • A176521 (program): Decimal expansion of (18+3*sqrt(38))/4.
  • A176522 (program): Decimal expansion of (9+sqrt(85))/2.
  • A176523 (program): Decimal expansion of (45+3*sqrt(235))/10.
  • A176524 (program): Decimal expansion of sqrt(235).
  • A176525 (program): Fermi-Dirac semiprimes: products of two distinct terms of A050376
  • A176529 (program): Decimal expansion of 5+sqrt(30).
  • A176530 (program): Decimal expansion of (15+sqrt(255))/3.
  • A176531 (program): Decimal expansion of (10+sqrt(110))/2.
  • A176532 (program): Decimal expansion of 5+3*sqrt(3).
  • A176533 (program): Decimal expansion of (15+4*sqrt(15))/3.
  • A176534 (program): Decimal expansion of (35+sqrt(1295))/7.
  • A176535 (program): Decimal expansion of (10 + sqrt(105))/2.
  • A176536 (program): Decimal expansion of (15 + sqrt(235))/3.
  • A176537 (program): Decimal expansion of 5 + sqrt(26).
  • A176539 (program): Indices of nonprime numbers in the products of two noncomposite numbers.
  • A176540 (program): 1 together with the semiprimes.
  • A176542 (program): Numbers n such that there are only a finite nonzero number of sets of n consecutive triangular numbers that sum to a square.
  • A176545 (program): Numbers n>0 such that 2*n^2+14*n+5 is prime.
  • A176546 (program): Bernoulli numerators A000367 with an additional 1 inserted to represent B_1.
  • A176547 (program): Numbers n such that 2*n^2 + 6*n + 1 is prime.
  • A176549 (program): Primes of the form 2*n^2+6*n+1.
  • A176551 (program): Products of 2 primes of the form 3*k-+1.
  • A176557 (program): Primes of the form 7*x^2 - 5*y^2, where x and y are successive natural numbers.
  • A176560 (program): A symmetrical triangle recursion:q=5;t(n,m,0)=Binomial[n,m];t(n,m,1)=Narayana(n,m);t(n,m,2)=Eulerian(n+1,m);t(n,m,q)=t(n,m,g-2)+t(n,m,q-3)
  • A176561 (program): A symmetrical triangle recursion:q=6;t(n,m,0)=Binomial[n,m];t(n,m,1)=Narayana(n,m);t(n,m,2)=Eulerian(n+1,m);t(n,m,q)=t(n,m,g-2)+t(n,m,q-3)
  • A176563 (program): Period 4: repeat [1, -3, 1, 1].
  • A176566 (program): Triangle T(n, k) = binomial(n*(n+1)/2 + k, k), read by rows.
  • A176569 (program): a(n) = (-1)^n + (n-th prime of the form 3k-+1).
  • A176570 (program): a(n)=n-th semiprime if n-th semiprime odd and n-th semiprime/2 if n-th semiprime even.
  • A176580 (program): n^3+Largest square, (Largest square <= n^3).
  • A176581 (program): n^3+Smallest square, (Smallest square >= n^3).
  • A176582 (program): n^2+Largest cube, (Largest cube <= n^2).
  • A176583 (program): n^2+Smallest cube, (Smallest cube >= n^2).
  • A176587 (program): Numbers such that arithmetic mean of distinct prime factors is not an integer.
  • A176591 (program): Bernoulli denominators A141056(n), with the exception a(1)=1.
  • A176592 (program): List of pairs n,11*n
  • A176593 (program): List of pairs n,13*n.
  • A176597 (program): Double primes: concatenation of the n-th prime with itself.
  • A176608 (program): Primes of the form x^2 + 5*y^2, where x and y=x+1 are consecutive natural numbers.
  • A176615 (program): Number of edges in the graph on n vertices, labeled 1 to n, where two vertices are joined just if their labels sum to a perfect square.
  • A176616 (program): Primes of the form x^2 + 7*y^2, where x and y=x+1 are consecutive natural numbers.
  • A176617 (program): Primes of the form 14*k^2 + 26*k + 13.
  • A176620 (program): Primes p for which the factorization of p! over distinct terms of A050376 does not contain 2.
  • A176621 (program): a(n) = 2 + Sum_{k=0..n-1} A176513(4*k+1).
  • A176622 (program): Primes of the form x^2 + 17*y^2, where x and y=x+1 are consecutive natural numbers.
  • A176624 (program): a(n) = prime(n) + n*(-1)^n.
  • A176625 (program): T(n,k) = 1 + 3*k*(k - n), triangle read by rows (n >= 0, 0 <= k <= n).
  • A176627 (program): Triangle T(n, k) = 12^(k*(n-k)), read by rows.
  • A176628 (program): a(n) = prime(n) - n*(-1)^prime(n).
  • A176629 (program): a(n) = n-th semiprime - (-1)^(n-th semiprime).
  • A176631 (program): Triangle T(n, k) = 22^(k*(n-k)), read by rows.
  • A176632 (program): a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 2; a(0) = 77, a(1) = 897, a(2) = 3333.
  • A176633 (program): a(n) = 6*a(n-1)-8*a(n-2) for n > 2; a(0) = 83, a(1) = 708, a(2) = 2952.
  • A176634 (program): a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 2; a(0) = 89, a(1) = 519, a(2) = 2063.
  • A176635 (program): a(n) = 6*a(n-1)-8*a(n-2) for n > 1; a(0) = 57, a(1) = 242.
  • A176636 (program): Periodic sequence: Repeat 57, 71.
  • A176639 (program): Triangle T(n, k) = 15^(k*(n-k)), read by rows.
  • A176640 (program): Partial sums of A005985.
  • A176641 (program): Triangle T(n, k) = 28^(k*(n-k)), read by rows.
  • A176642 (program): Triangle T(n, k) = 8^(k*(n-k)), read by rows.
  • A176643 (program): Triangle T(n, k) = 21^(k*(n-k)), read by rows.
  • A176644 (program): Triangle T(n, k) = 40^(k*(n-k)), read by rows.
  • A176646 (program): a(n) is the number of convex pentagons in an n-triangular net.
  • A176656 (program): The positions of single (or isolated or non-twin) primes in A000040.
  • A176662 (program): a(0)=2, a(1)=7, and a(n) = (3*n+1)*2^(n-1) if n > 1.
  • A176672 (program): a(2*n) = 1 + 6*n, a(2*n+1) = A165367(n).
  • A176677 (program): Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=1, k=0 and l=-1.
  • A176686 (program): Numbers n such that n^2-1 are products of 3 distinct primes.
  • A176687 (program): Numbers k such that k^2-1 is the product of 4 distinct primes.
  • A176688 (program): Partial sums of A058681.
  • A176690 (program): Partial sums of A048200.
  • A176691 (program): a(n) = 2^n + 2*n + 1.
  • A176693 (program): Union of squares and the even numbers.
  • A176695 (program): Primes of the form x^2 + 29*(x+1)^2.
  • A176697 (program): G.f. satisfies: A(x) = 1 + x^2 + x*A(x)^2.
  • A176702 (program): Triangle T(n,k) read by rows. A051731(n,k)-A051731(n,k+1).
  • A176704 (program): Number of twin primes between non-twin prime(n) and non-twin prime(n+1).
  • A176705 (program): Number of semiprimes between single (or isolated or non-twin) prime(n) and single (or isolated or non-twin) prime(n+1).
  • A176708 (program): Partial sums of A094820.
  • A176710 (program): Mix A001021, 2*A001021.
  • A176711 (program): a(n) = 16n^4 + 64n^3 + 104n^2 + 80n + 21.
  • A176712 (program): a(n) = 16*n^4 + 256*n^3 + 1160*n^2 + 1088*n + 285.
  • A176718 (program): Partial sums of A004207.
  • A176730 (program): Denominators of coefficients of a series, called f, related to Airy functions.
  • A176731 (program): Denominators of coefficients of a series, called g, related to Airy functions.
  • A176732 (program): a(n) = (n+5)*a(n-1) + (n-1)*a(n-2), a(-1)=0, a(0)=1.
  • A176733 (program): a(n) = (n+6)*a(n-1) + (n-1)*a(n-2), a(-1)=0, a(0)=1.
  • A176734 (program): a(n) = (n+7)*a(n-1) + (n-1)*a(n-2), a(-1)=0, a(0)=1.
  • A176735 (program): a(n) = (n+8)*a(n-1) + (n-1)*a(n-2), a(-1)=0, a(0)=1.
  • A176736 (program): a(n) = (n+9)*a(n-1) + (n-1)*a(n-2), a(-1)=0, a(0)=1.
  • A176737 (program): Expansion of 1 / (1-4*x^2-3*x^3). (4,3)-Padovan sequence.
  • A176738 (program): Expansion of 1 / ((1+x)*(1-x-4*x^2)). (5,4)-Padovan sequence.
  • A176739 (program): Expansion of 1/(1-2*x^2-4*x^3). (2,4)-Padovan sequence.
  • A176742 (program): Expansion of (1 - x^2) / (1 + x^2) in powers of x.
  • A176743 (program): a(n) = gcd(A000217(n+1), A002378(n+2)).
  • A176758 (program): a(n) = Sum_{k=0..floor((n-1)/2)} (3^k-1)*binomial(n, 2*k+1).
  • A176774 (program): Smallest polygonality of n = smallest integer m>=3 such that n is m-gonal number.
  • A176775 (program): Index of n as m-gonal number for the smallest possible m (=A176774(n)).
  • A176776 (program): a(n) = 2^n-n*(n-2).
  • A176777 (program): 2^n-n*(n-3).
  • A176778 (program): 2^n-n*(n+2).
  • A176780 (program): a(n) = n^4 + 6n^3 + 14n^2 + 15n + 6.
  • A176783 (program): Primes of the form 13*n^2+3*n+1
  • A176785 (program): Sequence with e.g.f. g(x) = -(1/2)*sqrt(2*exp(-2*x)-1) + 1/2.
  • A176787 (program): a(n) = (0!-1!+2!-3!….(-1)^(n-1)*(n-1)!) mod n.
  • A176788 (program): a(n) = (0!! + 1!! + 2!! + 3!! + … + (n-1)!!) mod n.
  • A176793 (program): A symmetrical triangle:q=2;f(n,m,q)=Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];t(n,m,q)=1 - (f(n, k, q) + f(n, 2*n - k, q) - (f(n, 1, q) + f(n, 2*n - 1, q)))
  • A176794 (program): A symmetrical triangle sequence:q=3;f(n,m,q)=Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];t(n,m,q)=1 - (f(n, k, q) + f(n, 2*n - k, q) - (f(n, 1, q) + f(n, 2*n - 1, q)))
  • A176798 (program): Triangle read by rows: T(n,m)=1 + n*(2*m + 1 + n)/2, 0<=m<=n.
  • A176805 (program): a(n) = 3^n + 3*n + 1.
  • A176806 (program): Consider asymmetric 1-D random walk with set of possible jumps {-1,+1,+2}. Sequence gives number of paths of length n ending at origin.
  • A176808 (program): Triangle read by rows: T(n,m)=Floor[(n - 1)/m], 1<=m<=n.
  • A176810 (program): Semiprimes of the form 2 * (greater of twin primes).
  • A176812 (program): Expansion of 3*(1+x)/(1-2*x-5*x^2).
  • A176814 (program): The number of iterations needed to reach 1 under the map n-> n-bigomega(n)).
  • A176816 (program): The number of steps to reach 0 under the map x -> x-tau(sigma(x)), starting at n.
  • A176818 (program): a(n) = (3^(2*n+1) + 2^(n+2))/7.
  • A176819 (program): Distances between terms in A085986.
  • A176823 (program): a(n)=Mod(n^(n+1),(n+1)^n).
  • A176824 (program): a(n) = (n+1)^n mod n^n.
  • A176835 (program): Number of positive integers k for which k^2 - n*k is a square.
  • A176839 (program): The number of iterations to reach 1 under the map x -> x-tau(phi(x)), starting at n.
  • A176840 (program): Variant of A176546 with the sign of the second term switched.
  • A176841 (program): a(n) is the number of iterations of f(n) = n-phi(tau(n)) needed to reach 1.
  • A176844 (program): The number of iterations of the map n -> n - bigomega(sigma(n)) until reaching 1.
  • A176845 (program): Numbers k such that A147846(k) + A147846(k+1) is a square.
  • A176846 (program): Number of iterations of the map n-> n - sigma(bigomega(n)) needed to reach 1.
  • A176847 (program): The odd non-semiprime numbers.
  • A176848 (program): Number of compositions of n into floor(j/3) kinds of j’s for all j>=1.
  • A176849 (program): Triangle read by rows which contains the (6n)-th row of the Pascal triangle in row n.
  • A176850 (program): a(n,k) is the number of ways to choose integers i,j from {0,1,…,k} such that the inequalities |i-j| <= n <= i+j are satisfied.
  • A176852 (program): Complement to A176845.
  • A176860 (program): Triangle, read by rows, T(n, k) = (-1)^k * (n-k+1)^(n+2) * binomial(n+1, k).
  • A176864 (program): Numbers k such that A053186(k) is prime.
  • A176865 (program): Numbers n such that n-LargestCube is prime, (LargestCube <= n).
  • A176880 (program): Expansion of 1/(1 - 3*x + x^2 - 2*x^3 + 2*x^4).
  • A176888 (program): Unsafe primes minus 1.
  • A176889 (program): a(2*k-1)=1, a(2*k)=2*k^2 (definition by T. M. Apostol, see References).
  • A176890 (program): Triangle T(n,k) read by rows. Signed subsequence of A051731.
  • A176891 (program): Triangle T(n,k) = k if k<n and k|n, = 0 otherwise, 1 <= k <= n; read by rows.
  • A176892 (program): Decimal representation of the reverted binary representation of n followed by digits substitution 0->2, 1->3.
  • A176893 (program): a(n) = 2^(number of zeros in binary expansion of n) * 3^(numbers of ones in binary expansion of n).
  • A176894 (program): Increase each digit in the binary representation of n by 2.
  • A176895 (program): Period 4: repeat [1, 4, 2, 4].
  • A176896 (program): Semiprimes s such that (s-1)/2 is also semiprime.
  • A176897 (program): Primes p such that (p+1)/2 is not prime.
  • A176898 (program): a(n) = binomial(6*n, 3*n)*binomial(3*n, n)/(2*(2*n+1)*binomial(2*n, n)).
  • A176900 (program): a(n) = sin((2*n+5)*Pi/6)*(n+1)*2^(n+1).
  • A176902 (program): Primes p such that p-1 and p+1 are both non-semiprime.
  • A176906 (program): Decimal expansion of (15+sqrt(230))/5.
  • A176907 (program): Decimal expansion of (9+sqrt(145))/16.
  • A176908 (program): Decimal expansion of (7+sqrt(145))/16.
  • A176909 (program): Decimal expansion of sqrt(230).
  • A176910 (program): Decimal expansion of sqrt(145).
  • A176915 (program): Average of n-th twin prime pair minus total number of prime factors of average of n-th twin prime pair.
  • A176916 (program): 5^n + 5n + 1.
  • A176918 (program): Triangle read by rows, a signed variant of A077049 * A128407; as infinite lower triangular matrices
  • A176919 (program): Triangle by columns: (1, 2, 3, …) in each column interleaved with (0, 1, 2, …) zeros. Columns > 1 shifted down twice.
  • A176923 (program): Squares of A057148 taken as decimal numbers.
  • A176961 (program): a(n) = (3*2^(n+1) - 8 - (-2)^n)/6.
  • A176963 (program): a(n) = (10*4^n - 3*(-4)^n - 22)/30.
  • A176965 (program): a(n) = 2^(n-1) - (2^n*(-1)^n + 2)/3.
  • A176968 (program): Expansion of x*( 1+2*x-x^2-6*x^3 ) / ( 1-9*x^2+12*x^4 ).
  • A176969 (program): Numbers n such that n^2 + 13^2 is prime.
  • A176971 (program): Expansion of (1+x)/(1+x-x^3) in powers of x.
  • A176972 (program): a(n) = 7^n + 7*n + 1.
  • A176974 (program): First exponent n to generate maximum remainder when (a + 1)^n + (a - 1)^n is divided by a^2 for variable n and a>2.
  • A176976 (program): Decimal expansion of (4+sqrt(65))/7.
  • A176977 (program): Decimal expansion of (3+sqrt(37))/7.
  • A176979 (program): Decimal expansion of (15+sqrt(365))/10.
  • A176980 (program): Decimal expansion of sqrt(365).
  • A176981 (program): Expansion of 1+(1-2*x)/(-1+2*x+x^2).
  • A176991 (program): Triangle t(n,m) = binomial(n+m,m) - binomial(n-m,m), 1<=m<=n, read by rows.
  • A176992 (program): Triangle T(n,m) = binomial(2n-k+1, n+1) read by rows, 0 <= k <= n.
  • A176995 (program): Numbers that can be written as (m + sum of digits of m) for some m.
  • A176997 (program): Integers n such that 2^(n-1) == 1 (mod n).
  • A177002 (program): Period 4: repeat [1, 2, 4, 2].
  • A177003 (program): Decimal expansion of (7+sqrt(93))/6.
  • A177009 (program): a(n) = n^n - A002275(n).
  • A177010 (program): G.f.: ((1-q)^2+(1+q)*sqrt(1-6*q+q^2))/2.
  • A177018 (program): a(n) is the smallest integer >= a(n-1) such that a(n) + A067076(n) + n-1 is an odd prime.
  • A177019 (program): a(n) = (3*10^(2*n)+3*10^n+1), (n>=0).
  • A177022 (program): Decimal expansion of 49/36.
  • A177023 (program): a(n) = 2^(2*n) mod (2*n+1).
  • A177025 (program): Number of ways to represent n as a polygonal number.
  • A177029 (program): Numbers that have exactly two different representations as polygonal numbers.
  • A177033 (program): Decimal expansion of (2+sqrt(14))/4.
  • A177036 (program): Decimal expansion of (4+sqrt(37))/7.
  • A177037 (program): Decimal expansion of (9+2*sqrt(39))/15.
  • A177040 (program): Irregular triangle t(n,m) = binomial(m+1,n-m) read by rows floor((n+1)/2) <= m <= n.
  • A177042 (program): Eulerian version of the Catalan numbers, a(n) = A008292(2*n+1,n+1)/(n+1).
  • A177043 (program): Central MacMahon numbers: a(n)=A060187(2*n+1, n+1).
  • A177044 (program): a(n) = 103*(n-1)-a(n-1) with n>1, a(1)=38.
  • A177046 (program): a(n) = 127*(n-1)-a(n-1) with n>1, a(1)=16.
  • A177049 (program): Numerator of (3n+1)*(3n+2)/4.
  • A177056 (program): Decimal expansion of 7^3/6^3.
  • A177057 (program): Decimal expansion of 7/6.
  • A177058 (program): a(n) = n^3 - 3n^2 + 3.
  • A177059 (program): a(n) = 25*n^2 + 25*n + 6.
  • A177060 (program): (7*n+2)*(7*n+5)=49*n^2+49*n+10
  • A177065 (program): a(n) = (8*n+3)*(8*n+5).
  • A177066 (program): Determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(2i-1,2j-1) for 1 <= i,j <= n.
  • A177068 (program): 10^n+n^10
  • A177069 (program): 11^n + n^11.
  • A177071 (program): (7n + 3)(7n + 4).
  • A177072 (program): (9*n+2)*(9*n+7).
  • A177073 (program): (9*n+4)*(9*n+5).
  • A177074 (program): 3*(10^n-5).
  • A177075 (program): n^5 - n^3 - 2n^2 + 1.
  • A177077 (program): Primes of the form 5*x^2 - 2*y^2, where x and y are successive natural numbers.
  • A177079 (program): 5*(10^n-3)
  • A177080 (program): a(n) = 5*(10^n-7).
  • A177082 (program): a(n) = 2*n*A071148(n).
  • A177083 (program): A006093(k)-fold repetition of A001248(k), k=1,2,3,..
  • A177089 (program): Numbers n >= 0 such that n^3-n-1 is not prime.
  • A177090 (program): a(n) = a(n-1) + 12*100^(n-1), with a(0)=0.
  • A177091 (program): Numbers n such that n^4-n-1 is not prime.
  • A177092 (program): Primes p such that 11*p + 2 is also prime.
  • A177095 (program): 9^n - 8.
  • A177096 (program): 5*(10^n-2).
  • A177097 (program): a(n) = 6*(10^n-5).
  • A177098 (program): 6*(10^n-7)
  • A177099 (program): a(n) = 81*n^2 + 2*n.
  • A177100 (program): Partial sums of round(n^2/9).
  • A177102 (program): Beatty sequence for sqrt(10).
  • A177105 (program): Primes of the form 2*n^3-1.
  • A177107 (program): 3*(10^n-7).
  • A177108 (program): a(n) = 4*(10^n-3).
  • A177109 (program): a(n) = 4*(10^n-5).
  • A177112 (program): 4*(10^n-7).
  • A177114 (program): 4*(10^n-9).
  • A177116 (program): Partial sums of round(n^2/11).
  • A177121 (program): Square array T(n,k) read by antidiagonals up: T(n,k) = 1 if n=1; otherwise if n divides k then T(n,k) = -n+1; otherwise T(n,k) = 1.
  • A177138 (program): Numbers of the form (n!*(n+1))/2 with n or (n+1) prime.
  • A177139 (program): Numbers n such that (3*n-4, 3*n-2) is a twin prime pair.
  • A177143 (program): Pasquale’s sequence: a(n) = 2a(n-1) + (-1)^n*floor(n/2), with a(1)=1.
  • A177145 (program): E.g.f.: arcsin(x).
  • A177146 (program): n-th derivative of arctan(x) at x = 1, n >= 4.
  • A177151 (program): a(n) = least k such that 1 + 1/4 + 1/9 + … + 1/k^2 exceeds (Pi^2)*(n-1)/(6*n).
  • A177152 (program): Positions in A177151 of runs of length 1.
  • A177154 (program): Fractional part of the conversion from degrees Centigrade (or Celsius) to Fahrenheit.
  • A177155 (program): G.f.: exp( Integral (theta_3(x)^8-1)/(16x) dx ), where theta_3(x) = 1 + Sum_{n>=1} 2*x^(n^2) is a Jacobi theta function.
  • A177156 (program): Decimal expansion of (9+sqrt(221))/14.
  • A177157 (program): Decimal expansion of sqrt(221).
  • A177176 (program): Partial sums of round(n^2/13).
  • A177187 (program): Union of A057080 and A001090
  • A177189 (program): Partial sums of round(n^2/16).
  • A177191 (program): Determinant of the n X n matrix whose element (r,c) is n for r = c, is -n for c>r, and 1 for c< r.
  • A177205 (program): Partial sums of round(n^2/17).
  • A177206 (program): a(n) = 2*binomial(n+4, 4) + n + 4.
  • A177207 (program): Triangle read by rows: R(n,k)=2^(n-k) mod n.
  • A177208 (program): Numerators of exponential transform of 1/n.
  • A177209 (program): Denominators of exponential transform of 1/n.
  • A177219 (program): a(1) = 1; a(2n) = -a(n); a(2n+1) = -a(n) + a(n+1).
  • A177221 (program): Numbers k that are the products of two distinct primes such that 2*k + 1 is also the product of two distinct primes.
  • A177227 (program): Triangle T(n,m) read by rows: equals -binomial(n,m) in general, but 2 if n=m or m=0.
  • A177228 (program): A combinatorial differential triangle sequence:q=3;t=1/q;f(t,n)=d^n/dt^n*(t/(1+t); c(t.n,m)=(1/(1+t)*f(n,t)/(f(t,m)*f(t,(n-m))
  • A177229 (program): A combinatorial differential triangle sequence:q=4;t=1/q;f(t,n)=d^n/dt^n*(t/(1+t); c(t.n,m)=(1/(1+t)*f(n,t)/(f(t,m)*f(t,(n-m))
  • A177234 (program): a(n) = binomial(n^2, n)/(n+1).
  • A177235 (program): The number of non-divisors k of n, 1 < k < n, for which floor(n/k) is odd.
  • A177236 (program): a(n) = A049820(n) - A177235(n).
  • A177237 (program): Partial sums of round(n^2/19).
  • A177239 (program): Partial sums of round(n^2/20).
  • A177249 (program): Number of permutations of [n] having no adjacent transpositions, that is, no cycles of the form (i, i+1).
  • A177255 (program): a(n) = Sum_{j=1..n} j*B(j-1), where B(k) = A000110(k) are the Bell numbers.
  • A177257 (program): a(n) = Sum((binomial(n,j)-j-1)*B(j), j=0..n-1), where B(j)=A000110(j) are the Bell numbers.
  • A177258 (program): Number of derangements of {1,2,…,n} having no adjacent transpositions.
  • A177262 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} starting with exactly k consecutive integers (1<=k<=n).
  • A177265 (program): Number of permutations of {1,2,…,n} having exactly one string of consecutive fixed points (including singletons).
  • A177272 (program): Decimal expansion of sqrt(193).
  • A177274 (program): Periodic sequence: Repeat 1, 2, 3, 4, 5, 6, 7, 8, 9.
  • A177276 (program): Triangle T(n,k) with the coefficient [x^k] of the polynomial (1+x^2)^n + 2*n*x*(1+x^2)^(n-1) in row n, column k, 0<=k<=2n.
  • A177277 (program): Partial sums of round(n^2/28).
  • A177282 (program): Number of permutations of 2 copies of 1..n with all adjacent differences <= 1 in absolute value.
  • A177316 (program): Number of permutations of n copies of 1..4 with all adjacent differences <= 1 in absolute value.
  • A177322 (program): Number of permutations of n copies of 1..4 with all adjacent differences <= 2 in absolute value.
  • A177332 (program): Partial sums of round(n^2/29).
  • A177334 (program): Largest factor in the factorization of n! over distinct terms of A050376.
  • A177337 (program): Partial sums of round(n^2/36).
  • A177339 (program): Partial sums of round(n^2/44).
  • A177342 (program): a(n) = (4*n^3-3*n^2+5*n-3)/3.
  • A177346 (program): Decimal expansion of (1+sqrt(10))/3.
  • A177347 (program): Decimal expansion of (5+sqrt(85))/10.
  • A177349 (program): Primes p for which no m! has a prime power factorization of the form 2^p*…*p^1*…
  • A177353 (program): n! (mod n^2+1).
  • A177354 (program): a(n) is the moment of order n for the density measure 24*x^4*exp(-x)/( (x^4*exp(-x)*Ei(x) - x^3 - x^2 - 2*x - 6)^2 + Pi^2*x^8*exp(-2*x) ) over the interval 0..infinity.
  • A177356 (program): a(n) is the index of the first 0 term in the rumor sequence with initial 0th term 1 and parameters b = 2 and n.
  • A177357 (program): Number of positive squares <= prime(n) - 3.
  • A177369 (program): Expansion of g.f.: (1+4*x-4*x^2)/(1-3*x-4*x^2+4*x^3)
  • A177370 (program): (1+7*x-6*x^2)/(1-4*x-8*x^2+6*x^3)
  • A177373 (program): a(n) = 2*n*a(n-1) if the parity of the ratio a(n-1)/a(n-2) is odd, otherwise (for even parity) a(n) = (2n-1)*a(n-1).
  • A177398 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2n)-sigma(n))^2 * x^n/n ).
  • A177400 (program): a(n) = binomial(n*2^n, n).
  • A177410 (program): a(n) = binomial((n+1)*2^n, n)/(n+1).
  • A177411 (program): a(n) = binomial((n+1)*2^(n+1), n)/(n+1).
  • A177424 (program): Exponent of the highest power of 2 dividing binomial(n^2,n).
  • A177425 (program): Integers with multiple and strictly distinct powers.
  • A177427 (program): Numerators of the Inverse Akiyama-Tanigawa transform of the aerated even-indexed Bernoulli numbers 1, 0, 1/6, 0, -1/30, 0, 1/42, …
  • A177428 (program): Triangle T(n,m)= A141686(n,m)*(m-1)! read by rows, n>=1, 1<=m<=n.
  • A177429 (program): Triangle read by rows: T(n,m)=A060187(1+n,1+m) *n! / (n-m)!
  • A177444 (program): Triangle by columns, (1, 1, 0, 1, 0, 0, 0, …); shifted down twice for columns > 0.
  • A177445 (program): Partial sums of A120562
  • A177452 (program): Partial sums of A002055.
  • A177453 (program): Partial sums of A001863.
  • A177454 (program): ( binomial(2*p,p) - 2)/p where p = prime(n).
  • A177456 (program): a(n) = binomial(n^2,n+1)/n.
  • A177485 (program): G.f.: (1+x+x^3+x^5)/( (1-x^2+x^3)*(1-x-x^3) ).
  • A177492 (program): Products of squares of 2 or more distinct primes.
  • A177493 (program): Products of cubes of 2 or more distinct primes.
  • A177499 (program): Period 4: repeat [1, 16, 4, 16].
  • A177500 (program): Divisors of 8064.
  • A177687 (program): Number of distinct transpositions of digits (zeros and units) in n-th prime written in base 2.
  • A177690 (program): Denominators of the Inverse Akiyama-Tanigawa transform of the aerated even-indexed Bernoulli numbers 1, 0, 1/6, 0, -1/30, 0, 1/42, …
  • A177691 (program): The odd values of PrimePi(.), with repetition.
  • A177692 (program): The even values of PrimePi(.), with repetition.
  • A177698 (program): Expansion of e.g.f.: sin(arctan(x)).
  • A177699 (program): E.g.f.: log(1+x)*sinh(x).
  • A177700 (program): The n-th derivative of log(1+x)*tanh(x) evaluated at x = 0.
  • A177702 (program): Period 3: repeat [1, 1, 2].
  • A177703 (program): Decimal expansion of (2+sqrt(10))/3.
  • A177704 (program): Period 4: repeat [1, 1, 1, 2].
  • A177705 (program): Decimal expansion of (3+2*sqrt(6))/5.
  • A177706 (program): Period 5: repeat [1, 1, 1, 1, 2].
  • A177707 (program): Decimal expansion of (5+sqrt(65))/8.
  • A177711 (program): Natural numbers which are not sums of one or more distinct primorials.
  • A177712 (program): Even numbers that have a nontrivial odd divisor.
  • A177713 (program): Sums of two or more positive consecutive odd numbers.
  • A177716 (program): The k-th prime repeated A073124(k) times, k = 1,2,3….
  • A177718 (program): a(n) = |(number of 1’s in binary representation of prime(n)) - (number of 0’s in binary representation of prime(n))|.
  • A177727 (program): a(0)=1; a(n) = a(n-1) * Fibonacci(3+n) * Fibonacci(1+n) / (Fibonacci(n))^2, n > 1.
  • A177728 (program): Expansion of (1 + 14*x) / ((1 - x)*(1 - 2*x)*(1 - 4*x)*(1 - 8*x)*(1 - 16*x)).
  • A177730 (program): Expansion of (6*x + 1) / ((x - 1)*(2*x - 1)*(4*x - 1)*(8*x - 1)).
  • A177735 (program): a(0)=1, a(n)=A002445(n)/6 for n>=1.
  • A177737 (program): Partial sums of A046878.
  • A177744 (program): Number of conjugacy classes in PSL_2(q) as q runs through the primes and prime powers.
  • A177747 (program): Convolution of A008805 (triangular numbers repeated) with itself.
  • A177754 (program): Partial sums of A047994.
  • A177755 (program): Number of ways to place 2 nonattacking bishops on an n X n toroidal board.
  • A177756 (program): Number of ways to place 3 nonattacking bishops on an n X n toroidal board.
  • A177767 (program): Triangle read by rows: T(n,k) = binomial(n - 1, k - 1), 1 <= k <= n, and T(n,0) = A153881(n+1), n >= 0.
  • A177769 (program): a(n) = 111*n.
  • A177771 (program): Factorial of (prime(n) - 1).
  • A177783 (program): Wolstenholme quotient of prime p=A000040(n), i.e., such integer m<p that harmonic number H(p-1) == m*p^2 (mod p^3).
  • A177784 (program): a(n) = binomial(n^2, n) / ( n*(n+1) ).
  • A177785 (program): a(n) = a(n-1)^2 - a(n-2) for n > 2; a(1)=3, a(2)=0.
  • A177787 (program): Number of paths from (0,0) to (n+2,n) using only up and right steps and avoiding two or more consecutive moves up or three or more consecutive moves right.
  • A177788 (program): binomial(n^2,n+1)/(n-1).
  • A177790 (program): Number of paths from (0,0) to (n,n) avoiding 3 or more consecutive east steps and 3 or more consecutive north steps.
  • A177795 (program): Number of length n binary words that have at least one maximal run of 1’s having length two.
  • A177808 (program): Triangle T(n,m) = binomial(4*n, 4*m), 0 <= m <= n, read by rows.
  • A177809 (program): Symmetrical sequence:Binomial(n,5*m)
  • A177810 (program): Triangle binomial(6*n,6*m), 0 <= m <= n, read by rows.
  • A177811 (program): Sub-triangle of Eulerian numbers A008292, taking every 4th term of every 4th row.
  • A177823 (program): Triangle of Eulerian numbers squared: A008292(n,m)^2 read by rows.
  • A177824 (program): a(n) = (Fibonacci(n)*Fibonacci(n+7)) mod 7.
  • A177825 (program): Expansion of 1/((1 + x^3 - x^4)*(1 - x)).
  • A177826 (program): Sub-triangle of A060187: even-indexed entries of even-indexed rows.
  • A177837 (program): Binomial(n^3,n) / (n^2 * (n^2+n+1) ), or binomial(n^3-2,n-2).
  • A177840 (program): Consider the n pairs (1,2), …, (2n-1,2n); a(n) is the number of permutations of [ 2n ] with no two fixed points for any pair.
  • A177841 (program): Decimal expansion of (5+sqrt(221))/14.
  • A177842 (program): Period 27: repeat 1, 81, 81, 3, 81, 81, 9, 81, 81, 3, 81, 81, 3, 81, 81, 9, 81, 81, 3, 81, 81, 1, 81, 81, 9, 81, 81.
  • A177851 (program): Triangle read by rows: T(n, m) = binomial(n + m - 3, m - 1)*(2 * m + n - 2) / m, for n>=1 and 1<=m<=n.
  • A177852 (program): prime(n)-A177687(n).
  • A177853 (program): Partial sums of A018805.
  • A177863 (program): Product modulo p of the quadratic nonresidues of p, where p = prime(n).
  • A177864 (program): a(n) is the smallest nontrivial quadratic residue modulo prime(n), for n >= 3.
  • A177868 (program): a(n) = number of 2-digit primes with digit sum n, where n runs through the non-multiples of 3 in the range [2..17].
  • A177869 (program): Integers divisible by their number of digits in binary.
  • A177870 (program): Decimal expansion of 3*Pi/4.
  • A177877 (program): Triangle in which row n is derived from (1,2,3,…,n) dot (n,n-1,…,1) with additive carryovers.
  • A177878 (program): Triangle in which row n is generated from (1,2,3,…,n) dot (n, n-1,…,1) with subtractive carryovers.
  • A177880 (program): Numbers k such that not all exponents in the prime power factorization of k are in A005836.
  • A177881 (program): Partial sums of round(3^n/10).
  • A177882 (program): Trisection of A001317.
  • A177883 (program): Period 6: repeat [4, 5, 7, 2, 1, 8].
  • A177885 (program): a(n) = (1-n)^(n-1).
  • A177888 (program): P_n(k) with P_0(z) = z+1 and P_n(z) = z + P_(n-1)(z)*(P_(n-1)(z)-z) for n>1; square array P_n(k), n>=0, k>=0, read by antidiagonals.
  • A177890 (program): 15-gonal (or pentadecagonal) pyramidal numbers: a(n) = n*(n+1)*(13*n-10)/6.
  • A177891 (program): Numbers n such that sum of proper (or aliquot) divisors of n is a semiprime.
  • A177892 (program): The number of distinct prime factors in Lucas-Lehmer number A003010(n).
  • A177897 (program): Triangle of octanomial coefficients read by rows: n-th row is obtained by expanding ((1+x)*(1+x^2)*(1+x^4))^n ] mod 2 and converting to decimal.
  • A177926 (program): a(n) = ((n-th-prime - 1)!)^2
  • A177935 (program): Decimal expansion of sqrt(107).
  • A177936 (program): Decimal expansion of sqrt(179).
  • A177939 (program): Array t(n,m)=(n*m)!/(n + m - 1)! read by antidiagonals.
  • A177940 (program): Decimal expansion of 190/89.
  • A177944 (program): Array T(n,m) = 1/Beta(n+1, m+1) - n - m read by antidiagonals.
  • A177946 (program): a(n) = prime(n)! / n!.
  • A177947 (program): A symmetrical triangle sequence based on the beta function inverse and the spotlight tile A051601 as antidiagonal: t(n,m) = 1/Integrate[(-1 + t)^n/t^(m + n + 2), {t, 1, Infinity}] - (-2 Binomial[m + n, m] + Binomial[2 + m + n, 1 + m]).
  • A177949 (program): First string of 43 consecutive composite numbers.
  • A177951 (program): PrimePi(A066903(n)), the index of A066903(n) in the primes.
  • A177954 (program): Triangle read by rows, A070909 * Pascal’s triangle.
  • A177957 (program): Decimal expansion of (12+3*sqrt(35))/19.
  • A177959 (program): n-th prime minus number of 0’s in binary representation of n-th prime.
  • A177961 (program): a(1)=2. Otherwise the average of the smallest prime divisors of 2n-1 and 2n+1.
  • A177962 (program): Number of distinct transpositions of prime factors of n-th composite number.
  • A177964 (program): Indices m for which A177961(m) = 4.
  • A177965 (program): Indices m for which A177961(m) - m = 1.
  • A177970 (program): Array T(n,m) = A177944(2*n,2*m) read by antidiagonals.
  • A177978 (program): Triangle T(n,k) read by rows: A051731(n,k) - A051731(n-1,k).
  • A177979 (program): Smallest number k such that A002313(n) divides k^2+1.
  • A177980 (program): Iterate (n + lpf(n)) / 2 until a prime is reached, where lpf equals the least prime factor. a(n) is that terminating prime.
  • A177983 (program): a(1)=3. Otherwise the average of the least prime divisors of 2n-1 and 2n+3.
  • A177984 (program): A symmetrical triangle of polynomial coefficients:p(x,n)=If[n == 0, 1, (1 - x)^(n + 1)*Sum[((2*k + 1)^n + (k + 1)^n + k^n)*x^k, {k, 0, Infinity}]/2]
  • A177985 (program): A177983(n) - A177961(n).
  • A177990 (program): Triangle read by rows, variant of A070909, a cellular automaton
  • A177991 (program): Triangle read by rows, A070909 * A177990
  • A177992 (program): Triangle read by rows, A007318 * A177990.
  • A177993 (program): Triangle read by rows, A177990 * A007318.
  • A177994 (program): Triangle read by rows, A177990 * A070909
  • A178027 (program): Multiples of 5291.
  • A178030 (program): Array read by antidiagonals: T(0,m)=2, T(1,m)=1, T(n,m)=A000032(n) and recursively T(n,m)=( T(n-1,m)^2 + (4*m + 1)*(-1)^n) / T(n-2, m), n>=0, m>=1.
  • A178040 (program): Decimal expansion of sqrt(211).
  • A178050 (program): n=x^2+17, n and n+2 are prime.
  • A178058 (program): Number of 1’s in the Gray code for binomial(n,m).
  • A178061 (program): Number of distinct cycles without repeated edges on the multigraph consisting of two vertices joined by n edges.
  • A178064 (program): Number of 0’s in binary representation of n-th semiprime.
  • A178065 (program): Number of 1’s in binary representation of n-th semiprime.
  • A178067 (program): Triangle read by rows: T(n,k) = (n^2 + k)*(n - k + 1)/2.
  • A178069 (program): a(n) = 12345679 * A001651(n).
  • A178073 (program): Partial sums of sequence A177342.
  • A178075 (program): A (1,2) Somos-4 sequence.
  • A178077 (program): A (4,-8) Somos-4 sequence.
  • A178079 (program): A (1,-1) Somos-4 sequence.
  • A178081 (program): A (1,1) Somos-4 sequence.
  • A178094 (program): a(1)=a(2)=1; thereafter a(n) = lpf(a(n-1)+a(n-2)), where lpf = “least prime factor”.
  • A178095 (program): a(1)=a(2)=a(3)=1; thereafter a(n) = lpf(a(n-1)+a(n-2)+a(n-3)), where lpf = “least prime factor”.
  • A178096 (program): Cube of n is equal to sum of four positive distinct squares; n^3=a^2+b^2+c^2+d^2; a>b>c>d>0.)
  • A178111 (program): Number triangle T(n,k)=(-1)^((n-k)/2)*C(floor(n/2),floor(k/2))*(1+(-1)^(n-k))/2.
  • A178112 (program): Number triangle T(n,k)=C(floor(n/2),floor(k/2))*(1+(-1)^(n-k))/2.
  • A178113 (program): Transform of C(n+1,floor((n+1)/2)) by A178112.
  • A178114 (program): Expansion of (sqrt(1-2x+7x^2-6x^3+5x^4)-(1-x+x^2))/(2x^2(1-x+x^2)).
  • A178115 (program): a(n)=(-1)^C(n+1,2)*(F(n+1)*(1+(-1)^n)/2+F(n+2)*(1-(-1)^n)/2).
  • A178122 (program): Triangle T(n,m) = A060187(n+1,m+1) + 2*binomial(n,m) - 2, read by rows.
  • A178129 (program): Partial sums of A050508.
  • A178131 (program): Decimal expansion of (11+3*sqrt(21))/17.
  • A178138 (program): Apply partial sum operator 4 times to primes.
  • A178141 (program): Period 6: repeat [4, -1, 2, -4, 1, 2].
  • A178142 (program): Sum over the divisors d = 2 and/or 3 of n.
  • A178143 (program): Sum of squares d^2 over the divisors d=2 and/or d=3 of n.
  • A178144 (program): Sum of divisors d of n which are d=2, 3 or 5.
  • A178146 (program): a(n) is the number of distinct divisors d of n of the form d=2,3 or 5
  • A178147 (program): Sum of squares d^2 of distinct divisors of n, d in {2, 3, 5}.
  • A178149 (program): Decimal expansion of (15+sqrt(1365))/30.
  • A178159 (program): Modified variant of A006645, the self-convolution of the Pell series.
  • A178166 (program): 10^a(n) Pascal triangle, where a(n) = A007318(n).
  • A178167 (program): Binomial transform of odd primes.
  • A178168 (program): Product of the numbers in the Collatz (3x+1) trajectory of n, including n.
  • A178178 (program): Primes of the form A177353(n) + 1 sorted with respect to increasing n.
  • A178181 (program): Minute with hour hand overlap problem on analog clock.
  • A178182 (program): Minimal polynomials of sin(2Pi/n) are mapped to those of cos(2Pi/a(n)).
  • A178184 (program): Sum 2^((k^2+3k)/2) from k=1 to n
  • A178185 (program): Numerators of sum (1/2)^((k^2+3k)/2) from k=1 to n.
  • A178186 (program): Sum 3^((k^2+3k)/2) from k=1 to n.
  • A178187 (program): Numerators of sum (1/3)^((k^2+3k)/2) from k=1 to n.
  • A178205 (program): a(n) = a(n-1) + 10*a(n-3) for n > 2; a(0) = a(1) = a(2) = 1.
  • A178207 (program): a(n) = 4*n - 2*A000120(n) + 1 where A000120(n) = number of nonzero digits in the binary representation of n.
  • A178208 (program): Number of ways to choose three points in an (n X n)-grid (or geoplane).
  • A178211 (program): prime(n)^2 mod n.
  • A178212 (program): Nonsquarefree numbers divisible by exactly three distinct primes.
  • A178218 (program): Numbers of the form 2k^2-2k+1 or 2k^2-1.
  • A178219 (program): a(0)=a(1)=a(2)=0, a(3)=1; thereafter a(n) = 4a(n-3)-5a(n-4).
  • A178222 (program): Partial sums of floor(3^n/4).
  • A178225 (program): Characteristic function of A006995 (binary palindromes).
  • A178226 (program): Characteristic function of A154809 (numbers that are not binary palindromes)
  • A178231 (program): Decimal expansion of sqrt(181).
  • A178233 (program): Decimal expansion of (11+sqrt(229))/18.
  • A178236 (program): Decimal expansion of (7+sqrt(229))/18.
  • A178238 (program): Triangle read by rows: partial column sums of the triangle of natural numbers (written sequentially by rows).
  • A178242 (program): Numerator of n*(5+n)/((n+1)*(n+4)).
  • A178243 (program): a(2n) = a(n), a(2n+1) = 10*a(n) + a(n+1).
  • A178244 (program): Number of distinct transpositions of binary digits (0’s and 1’s) in n.
  • A178248 (program): a(n) = 12^n + 1.
  • A178252 (program): Triangle T(n,m) read by rows: the numerator of the coefficient [x^m] of the umbral inverse Bernoulli polynomials B^{-1}(n,x), 0 <= m <= n.
  • A178255 (program): Decimal expansion of (3+sqrt(17))/2.
  • A178294 (program): Number of collinear point triples in a 4 X 4 X 4 X… n-dimensional cubic grid
  • A178295 (program): Number of collinear point 4-tuples in a 5 X 5 X 5 X… n-dimensional cubic grid
  • A178296 (program): Number of collinear point 5-tuples in a 6 X 6 X 6 X… n-dimensional cubic grid
  • A178300 (program): Triangle T(n,k) = binomial(n+k-1,n) read by rows, 1 <= k <= n.
  • A178301 (program): Triangle T(n,k) = binomial(n,k)*binomial(n+k+1,n+1) read by rows, 0 <= k <= n.
  • A178305 (program): a(0)=1, a(1)=a(2)=1 and a(3k)=a(k), a(3k+1) = a(3k+2) = 2a(k) for k >= 1.
  • A178310 (program): Decimal expansion of sqrt(157).
  • A178312 (program): a(n) = n * T(ceiling(n/2)), where T are the triangular numbers, A000217.
  • A178313 (program): Absolute difference between prime factors of n-th semiprime mod n.
  • A178320 (program): INVERT transform of A008805 (triangular numbers repeated).
  • A178325 (program): G.f.: A(x) = Sum_{n>=0} x^n/(1-x)^(n^2).
  • A178331 (program): Decimal expansion of (17+2*sqrt(210))/29.
  • A178333 (program): Characteristic function of mountain numbers.
  • A178334 (program): Number of mountain numbers <= n.
  • A178335 (program): Integers for which the decimal expansion of the reciprocal contains the repeating digits 1,4,2,8,5,7 (corresponding to the decimal expansion of 1/7)
  • A178338 (program): Numbers k such that the sum of decimal digits of k does not divide k+1.
  • A178340 (program): Triangle T(n,m) read by rows: denominator of the coefficient [x^m] of the umbral inverse Bernoulli polynomial B^{-1}(n,x).
  • A178343 (program): Triangle T(n,m)= binomial(n, m)/Beta(m + 1, n - m + 1) read by rows.
  • A178348 (program): a(n) = Sum_{k=0..n} 1100^k.
  • A178349 (program): Partial sums of sum_{n=0…infinity} 1010^n.
  • A178359 (program): Rounded up arithmetic mean of digits of n appended to n, cf. A004427.
  • A178361 (program): Numbers with rounded up arithmetic mean of digits = 1.
  • A178362 (program): Numbers with rounded up arithmetic mean of digits = 2.
  • A178363 (program): Numbers with rounded up arithmetic mean of digits = 3.
  • A178364 (program): Numbers with rounded up arithmetic mean of digits = 4.
  • A178365 (program): Numbers with rounded up arithmetic mean of digits = 5.
  • A178366 (program): Numbers with rounded up arithmetic mean of digits = 6.
  • A178367 (program): Numbers with rounded up arithmetic mean of digits = 7.
  • A178368 (program): Numbers with rounded up arithmetic mean of digits = 8.
  • A178369 (program): Numbers with rounded up arithmetic mean of digits = 9.
  • A178370 (program): The trisection A178242(3n+2).
  • A178376 (program): A (-1,-2) Somos-4 sequence associated to the elliptic curve y^2 +y = x^3 +3*x^2 +x.
  • A178381 (program): Number of paths of length n starting at initial node of the path graph P_9.
  • A178384 (program): A (-1,1) Somos-4 sequence associated with the elliptic curve y^2 + y = x^3 + x.
  • A178389 (program): Multiples of 3 in A175461.
  • A178390 (program): a(n) = (n^2+1)^2+1.
  • A178391 (program): a(n) = (n^3+1)^3+1.
  • A178392 (program): a(n) = (n^2-1)^2-1.
  • A178393 (program): a(n) = (n^3-1)^3-1.
  • A178395 (program): Triangle T(n,m) read by rows: the numerator of the coefficient [x^m] of the inverse Euler polynomial E^{-1}(n,x), 0 <= m <= n.
  • A178396 (program): a(1)=1, a(n) = a(n-1)*1000 + 11^(n-1) for n>=2.
  • A178397 (program): Partial sums of round(7^n/10).
  • A178398 (program): a(n) = p(p+1)^2, where p is the n-th prime.
  • A178400 (program): Sums of two primes, an array by antidiagonals.
  • A178407 (program): a(n+1) = a(n)*1000 + 101^n with a(0) = 0.
  • A178411 (program): a(1)=2, a(2)=1; for n>=3, a(n) is defined by recursion: Sum_{d|n}((-1)^(n/d))*a(d) = -1.
  • A178414 (program): Least odd number in the Collatz (3x+1) preimage of odd numbers not a multiple of 3.
  • A178417 (program): A (-1,1) Somos-4 sequence associated to the elliptic curve y^2 + x*y + y = x^3 + x^2 + x.
  • A178420 (program): Partial sums of floor(2^n/3).
  • A178440 (program): Convolution square of A058187, the tetrahedral series with repeats.
  • A178441 (program): INVERT transform of A058187, the tetrahedral numbers with repeats
  • A178445 (program): Prime(n)^2 mod n^2.
  • A178448 (program): Dirichlet inverse of A001160, sigma_5.
  • A178450 (program): Dirichlet inverse of A034448 (unitary sigma).
  • A178452 (program): Partial sums of floor(2^n/5).
  • A178453 (program): Numerator of n!*Sum((-1)^k/k!, k=0..n)/(n-1)^n.
  • A178454 (program): Denominator of n!*Sum((-1)^k/k!, k=0..n)/(n-1)^n.
  • A178455 (program): Partial sums of floor(2^n/7).
  • A178457 (program): Partial sums of floor(2^n/23).
  • A178459 (program): Partial sums of floor(2^n/31).
  • A178460 (program): Partial sums of floor(2^n/127).
  • A178464 (program): Minimal number of lines that must be removed from an n X n square array of cells in order to break all rectangles.
  • A178465 (program): Expansion of -2*x^2*(-3-2*x+x^2-x^3-2*x^4+x^5) / ( (1+x)^2*(x-1)^4 ).
  • A178472 (program): Number of compositions (ordered partitions) of n where the gcd of the part sizes is not 1.
  • A178474 (program): Triangle T(n,m) read by rows: the denominator of the coefficient [x^m] of the inverse Euler polynomial E^{-1}(n,x), 0<=m<=n.
  • A178475 (program): Permutations of 12345: Numbers having each of the decimal digits 1,…,5 exactly once, and no other digit.
  • A178476 (program): Permutations of 123456: Numbers having each of the decimal digits 1,…,6 exactly once, and no other digit.
  • A178477 (program): Permutations of 1234567: Numbers having each of the decimal digits 1,…,7 exactly once, and no other digit.
  • A178478 (program): Permutations of 12345678: Numbers having each of the decimal digits 1..8 exactly once, and no other digit.
  • A178482 (program): Phi-antipalindromic numbers.
  • A178485 (program): (A178475(n)-6)/9.
  • A178486 (program): (A178476(n)-3)/9.
  • A178487 (program): a(n) = floor(n^(1/5)): integer part of fifth root of n.
  • A178489 (program): a(n) = floor(n^(1/6)): integer part of sixth root of n.
  • A178490 (program): Primes of the form 2*p^k-1, where p is prime and k >= 1.
  • A178493 (program): Numbers of powers of phi in base-phi expansion of phi-antipalindromic numbers (A178482).
  • A178500 (program): a(n) = 10^n * signum(n).
  • A178501 (program): Zero followed by powers of ten.
  • A178503 (program): n minus totally additive with a(p)=PrimePi(p), where PrimePi(n)=A000720(n).
  • A178510 (program): a(n+1) = a(n)*100 + 21^n, with a(1)=1.
  • A178511 (program): a(n) = (1/119)*(100^n -(-19)^n).
  • A178512 (program): Reversed decimal expansions of A178510.
  • A178513 (program): Partial sums of 80^n
  • A178518 (program): Triangle read by rows: T(n,k) is the number of permutations p of {1,2,…,n} having genus 0 and such that p(1)=k (see first comment for definition of genus).
  • A178521 (program): The cost of all leaves in the Fibonacci tree of order n.
  • A178522 (program): Triangle read by rows: T(n,k) is the number of nodes at level k in the Fibonacci tree of order n (n>=0, 0<=k<=n-1).
  • A178523 (program): The path length of the Fibonacci tree of order n.
  • A178524 (program): Triangle read by rows: T(n,k) is the number of leaves at level k in the Fibonacci tree of order n (n>=0, 0<=k<=n-1).
  • A178525 (program): The sum of the costs of all nodes in the Fibonacci tree of order n.
  • A178526 (program): Triangle read by rows: T(n,k) is the number of nodes of cost k in the Fibonacci tree of order n.
  • A178529 (program): Self-convolution square-root of A008977, where A008977(n) = (4n)!/(n!)^4.
  • A178532 (program): Partial sums of problimes (third definition, A003068).
  • A178536 (program): First column of A178535.
  • A178537 (program): (2n+1)^(2n+1) mod 2^(2n+1).
  • A178543 (program): Partial sums of round(3^n/5).
  • A178547 (program): Composite numbers; start sequence with composite number and end with prime, length of successive sequences are strictly increasing.
  • A178549 (program): a(n) is a composite number at the start of an interval of consecutive integers, ending in a prime, and non-overlapping with and at least as long as the interval addressed by a(n-1).
  • A178550 (program): Primes with exactly one digit 1.
  • A178569 (program): a(2*n) = 10*a(n), a(2*n+1) = a(n) + a(n+1).
  • A178572 (program): Numbers with ordered partitions that have periods of length 5.
  • A178574 (program): a(n) = 2*n*(9*n-1).
  • A178575 (program): Number of permutations of {1,2,…,3n} whose cycle lengths are all divisible by 3.
  • A178577 (program): Partial sums of round(5^n/9).
  • A178590 (program): a(2n) = 3*a(n), a(2n+1) = a(n) + a(n+1).
  • A178591 (program): Decimal expansion of (9 + sqrt(165))/14.
  • A178592 (program): Decimal expansion of sqrt(165).
  • A178593 (program): Decimal expansion of (7 + 5*sqrt(29))/26.
  • A178596 (program): Records in A039996.
  • A178598 (program): a(n) is the smallest integer such that the geometric mean of the first n terms is >= n.
  • A178599 (program): a(n) is the smallest multiple of a(n-1) that is greater than n^n.
  • A178600 (program): Expansion of the polynomial (1+x^3)*(1+x^11).
  • A178601 (program): a(n) = s(s(n)), where s(n) = sigma(n)-n = A001065(n).
  • A178608 (program): Primes of the form (2*k^3 + 3*k^2 + k - 12)/6.
  • A178610 (program): n-th semiprime minus difference between the prime indices of the two factors of n-th semiprime.
  • A178611 (program): n-th semiprime minus sum of prime indices of the two factors of n-th semiprime.
  • A178614 (program): a(n) = prime(n)!/(n+1)!.
  • A178617 (program): a(n) = n^4 - (n+1)^3.
  • A178620 (program): Sum of binary digits ( = sum of ternary digits ) of terms in A037301.
  • A178621 (program): A (1, 2) Somos-4 sequence associated to the elliptic curve E: y^2 + x*y - y = x^3 - x.
  • A178622 (program): A (1, -2) Somos-4 sequence associated to the elliptic curve E: y^2 - 3*x*y - y = x^3 - x.
  • A178623 (program): Triangle T(n,m) read by rows: T(n,0)= prime(n); T(n,m)=1 if m>=1.
  • A178625 (program): A (1,-1) Somos-4 sequence associated to the elliptic curve E : y^2 + x*y - y = x^3 + 3*x^2 - x.
  • A178626 (program): Convolution of Pell(n) and 10^n.
  • A178627 (program): A (1,1) Somos-4 sequence associated to the elliptic curve E: y^2 + x*y - y = x^3 - x^2 + x and point (0,0).
  • A178628 (program): A (1,1) Somos-4 sequence associated to the elliptic curve E: y^2 - x*y - y = x^3 + x^2 + x.
  • A178630 (program): a(n) = 18 * ((10^n - 1)/9)^2.
  • A178631 (program): a(n) = 27 * ((10^n - 1)/9)^2.
  • A178632 (program): a(n) = 45 * ((10^n - 1)/9)^2.
  • A178633 (program): a(n) = 54*( (10^n - 1)/9 )^2.
  • A178634 (program): a(n) = 63 * ((10^n - 1)/9)^2.
  • A178635 (program): a(n) = 72 * ((10^n - 1)/9)^2.
  • A178637 (program): a(n) = sum of divisors d of n such that d is not equal to p^k where p = prime, k >=1.
  • A178638 (program): a(n) is the number of divisors d of n such that d^k is not equal to n for any k >= 1.
  • A178640 (program): Triangle T(n,k) with the coefficient [x^k] of the series (-1)^(n+1) * (x-1)^(n+1) * Sum_{j>=0} (5+8*j)^n*x^j in row n, column k.
  • A178643 (program): Square array read by antidiagonals.Convolution of a(n)= 2*a(n-1)-a(n-2) and 10^n.
  • A178645 (program): a(n) = sum of divisors d of n such that d^k is not equal to n for any k >= 1.
  • A178646 (program): a(n) = product of divisors d of n such that d^k is not equal to n for any k >= 1.
  • A178649 (program): a(n) = product of nonsquarefree divisors of n.
  • A178650 (program): Triangle read by rows A051731 * A070909
  • A178655 (program): Triangle which contains the first differences of the Catalan triangle A001263 constructed along rows.
  • A178659 (program): Numbers n such that n^2 +- (n-1)^2 are primes.
  • A178664 (program): 2^n concatenated with itself.
  • A178667 (program): Irregular triangle: T(n,k) is the coefficient [x^k] of the series (-1)^n *(x-1)^(n+2) *sum_{j=0..infinity} x^j /Beta(n+1,2*j+1), k=0..1+n/2, where Beta() is the usual Gamma-function ratio.
  • A178668 (program): Maximal prime divisor of the average of the twin prime pairs, different from 2 and 3. In case of maximal prime divisor is 2 or 3, then a(n)=1.
  • A178669 (program): The number of permutations of [n] with 2 cycles of length 2
  • A178671 (program): a(n) = 5^n - 5.
  • A178672 (program): a(n) = 6^n - 6.
  • A178674 (program): a(n) = 3^n + 3.
  • A178675 (program): a(n) = 4^n + 4.
  • A178676 (program): a(n) = 5^n + 5.
  • A178681 (program): a(n) = 6^n + 6.
  • A178686 (program): Expansion of the polynomial (1+x^3)*(1+x^5)*(1+x^7)*(1+x^9).
  • A178687 (program): Expansion of the polynomial (1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)*(1+x^11).
  • A178690 (program): Expansion of (exp(3*x)-1)*(exp(2*x)-1)*(exp(x)-1).
  • A178691 (program): Expansion of the polynomial (1+x^3)*(1+x^5)*(1+x^7)*(1+x^9)*(1+x^11)*(1+x^13).
  • A178693 (program): Numerators of coefficients of Maclaurin series for 2 - sqrt(1 - x - x^2).
  • A178694 (program): Numerators of coefficients of Maclaurin series for (1-x-x^2)^(-1/2).
  • A178703 (program): Partial sums of round(3^n/7).
  • A178704 (program): Partial sums of floor(3^n/7).
  • A178706 (program): Partial sums of floor(3^n/5).
  • A178710 (program): Partial sums of floor(4^n/7).
  • A178711 (program): Partial sums of floor(5^n/7).
  • A178719 (program): Partial sums of (1/5)*floor(6^n/7).
  • A178729 (program): a(n) = n XOR 3n, where XOR is bitwise XOR.
  • A178730 (program): Partial sums of floor(7^n/8)/6.
  • A178731 (program): a(n) = n XOR 5n, where XOR is bitwise XOR.
  • A178732 (program): a(n) = n XOR 6n, where XOR is bitwise XOR.
  • A178733 (program): a(n) = n XOR 7n, where XOR is bitwise XOR.
  • A178734 (program): a(n) = n XOR 8n, where XOR is bitwise XOR.
  • A178735 (program): a(n) = n XOR 9n, where XOR is bitwise XOR.
  • A178736 (program): a(n) = n XOR 10n, where XOR is bitwise XOR.
  • A178737 (program): Coefficients in expansion of Jacobi theta_1’’‘(0).
  • A178740 (program): Product of the 5th power of a prime (A050997) and a different prime (p^5*q).
  • A178741 (program): a(1)=2. For a(n)+1, differences must be strictly increasing and consecutive terms are relatively prime
  • A178742 (program): Partial sums of floor(2^n/9).
  • A178743 (program): a(n) = A000041(n) mod 10.
  • A178744 (program): Partial sums of floor(4^n/9).
  • A178746 (program): Binary counter with intermittent bits. Starting at zero the counter attempts to increment by 1 at each step but each bit in the counter alternately accepts and rejects requests to toggle.
  • A178748 (program): Total number of ‘1’ bits in the terms of ‘rows’ of A178746.
  • A178750 (program): Partial sums of floor(5^n/9).
  • A178752 (program): a(n) gives the number of conjugacy classes in the permutation group generated by transposition (1 2) and double n-cycle (1 3 5 7 … 2n-1)(2 4 6 8 … 2n). This group is a semidirect product formed by a cyclic group acting on an elementary abelian 2-group of rank n by cyclically permuting the factors.
  • A178753 (program): a(n) = n XOR floor(Log_2(n))+1, where XOR is bitwise XOR.
  • A178754 (program): a(n) = n XOR floor(Log_2(n)), where XOR is bitwise XOR.
  • A178756 (program): Rectangular array T(n,k) = binomial(n,2)*k*n^(k-1) read by antidiagonals.
  • A178757 (program): Smallest k such that k*n has an odd number of 1’s in its base-2 expansion.
  • A178759 (program): Expansion of e.g.f. 3*x*exp(x)*(exp(x)-1)^2.
  • A178763 (program): Product of primitive prime factors of Fibonacci(n).
  • A178765 (program): a(n) = 17*a(n-1) + a(n-2), with a(-1) = 0 and a(0) = 1.
  • A178766 (program): Values of gcd(Fibonacci(n), Fibonacci(n+1)+1) sorted with no repeats.
  • A178769 (program): a(n) = (5*10^n + 13)/9.
  • A178774 (program): a(2n) = 3*a(n), a(2n+1) = a(n) + a(n-1), with a(0)=a(1)=1.
  • A178775 (program): Smallest prime factors of zerofull restricted pandigital numbers.
  • A178778 (program): Partial sums of walks of length n+1 on a tetrahedron A001998.
  • A178781 (program): Expansion of the polynomial (x^9-1)*(x^7-1)*(x^6-1)*(x^5-1)*(x^4-1)*(x^3-1)*(x-1) in increasing powers of x.
  • A178789 (program): 4^(n-1) + 2: Number of acute angles after n iterations of the Koch snowflake construction.
  • A178790 (program): The arithmetic mean of (2*k+1)*A_k (k=0,…,n-1), where A_0,A_1,… are Apery numbers given by A005259.
  • A178792 (program): Dot product of the rows of triangle A046899 with vector (1,2,4,8,…) (= A000079).
  • A178801 (program): Write n! partition(n) times.
  • A178804 (program): When dealing cards into 3 piles (Left, Center, Right), the number of cards in the n-th card’s pile, if dealing in a pattern L, C, R, C, L, C, R, C, L, C, … [as any thoughtful six-year-old will try to do when sharing a pile of candy among 3 people].
  • A178809 (program): Decimal expansion of the area of the regular 12-gon (dodecagon) of edge length 1.
  • A178815 (program): First base of a nonzero Fermat quotient mod the n-th prime.
  • A178816 (program): Decimal expansion of the area of the regular 10-gon (decagon) of edge length 1.
  • A178820 (program): Triangle read by rows: T(n,k) = C(n+3,3) * C(n,k), 0 <= k <= n.
  • A178821 (program): Triangle read by rows: T(n,k) = binomial(n+4,4) * binomial(n,k), 0 <= k <= n.
  • A178822 (program): Triangle read by rows: T(n,k) = C(n+5,5) * C(n,k), 0 <= k <= n.
  • A178824 (program): a(n) = Sum_{k=0..n} binomial(n,k)^4/(n+1).
  • A178826 (program): Partial sums of floor(7^n/9).
  • A178827 (program): Partial sums of floor(8^n/9)/7.
  • A178828 (program): Partial sums of floor(3^n/10)/2.
  • A178829 (program): Partial sums of (1/2)*floor(7^n/10).
  • A178831 (program): Rectangular array T(n,k) = binomial(n+1,2)*(n^k - (n-1)^k) read by antidiagonals.
  • A178832 (program): Number of minima of the 1-D Griewank function in [-n, n].
  • A178837 (program): Indices k such that the sums of the digits of Fibonacci(k) are prime numbers.
  • A178838 (program): Indices n such that the sums of the squares of the digits of Fibonacci(n) are prime.
  • A178841 (program): The number of pure inverting compositions of n.
  • A178842 (program): a(n) = binomial((n-1)^2, n).
  • A178844 (program): First nonzero Fermat quotient mod the n-th prime.
  • A178851 (program): The number of length n sequences on {0,1,2}(ternary sequences) that contain a prime number of 2’s.
  • A178853 (program): “Josephus problem”: n persons stand in a circle and eliminate every seventh person counting clockwise until only person a(n) is remaining.
  • A178855 (program): Partial sums of A033485.
  • A178858 (program): Divisors of 5040.
  • A178859 (program): Divisors of 7560.
  • A178860 (program): Divisors of 10080.
  • A178861 (program): Divisors of 15120.
  • A178862 (program): Divisors of 20160.
  • A178863 (program): Divisors of 25200.
  • A178864 (program): Divisors of 27720.
  • A178869 (program): a(n) = 9*a(n-1) - 10*a(n-2); a(0)=0, a(1)=1.
  • A178872 (program): Partial sums of round(4^n/7).
  • A178873 (program): Partial sums of round(5^n/7).
  • A178874 (program): Partial sums of round(5^n/8).
  • A178875 (program): Partial sums of round(4^n/9).
  • A178877 (program): Divisors of 1260.
  • A178878 (program): Divisors of 1680.
  • A178881 (program): Sum of all pairs of greater common divisors for (i,j) where 1 <= i < j <= n.
  • A178885 (program): Partial sums of Berstel sequence (A007420).
  • A178890 (program): a(n) = n OR 3n, where OR is bitwise OR.
  • A178891 (program): a(n) = n OR 4n, where OR is bitwise OR.
  • A178892 (program): a(n) = n OR 5n, where OR is bitwise OR.
  • A178893 (program): a(n) = n OR 6n, where OR is bitwise OR.
  • A178894 (program): a(n) = n OR 7n, where OR is bitwise OR.
  • A178895 (program): a(n) = n OR 8n, where OR is bitwise OR.
  • A178896 (program): a(n) = n OR 9n, where OR is bitwise OR.
  • A178897 (program): a(n) = n OR 10n, where OR is bitwise OR.
  • A178901 (program): a(1)=2; for n > 1, a(n) is the largest number <= 2*a(n-1) divisible by n.
  • A178902 (program): Expansion of q^(-1/24) * eta(q^2)^13 / (eta(q)^5 * eta(q^4)^5) in powers of q.
  • A178906 (program): a(n) = 111*a(n-1) - 100*a(n-2) with a(0)=0 and a(1)=1.
  • A178907 (program): n-th prime + n-th problime (third definition).
  • A178914 (program): 10’s complement of nonnegative numbers.
  • A178915 (program): Rearrangement of natural numbers so that every partial sum is composite.
  • A178916 (program): Triangular array a(n,k) read by rows: nextprime(k*n!)-k*n!. For 1<=k<=n.
  • A178920 (program): Expansion of e.g.f. A(x), where A(x)=exp(x*A(x)+x^2*A(x)^2)
  • A178922 (program): a(n) = (n+1)^n - n^(n-1) for n > 0, a(0) = 1.
  • A178924 (program): Sum_{k>0} (n mod k) * 2^(n-k).
  • A178931 (program): This sequence S is generated by the following rules: 2 is in S, and if n is in S, then floor[(3n-1)/2] and 3n are in S.
  • A178933 (program): Generating function exp( sum(n>=1, sigma(n)^3*x^n/n ) ).
  • A178934 (program): a(n) = floor((3*4^n + 2*3^n)/5).
  • A178935 (program): a(n) = floor((3*4^n - 2*3^n)/5).
  • A178936 (program): Floor((2*3^n+3*2^n)/5).
  • A178945 (program): Expansion of x*(1-x)^2/( (1-2*x^2)*(1-2*x)^2).
  • A178946 (program): a(n) = n*(n+1)*(2*n+1)/6 - n*floor(n/2).
  • A178947 (program): Expansion of x*(1+2*x+8*x^2+3*x^4+4*x^3) / ( (1+x)^2*(x-1)^4 ).
  • A178949 (program): E.g.f. satisfies: A(x) = exp(x^2*A(x)) where A(x) = Sum_{n>=0} a(n)*x^(2n)/(2n)!.
  • A178960 (program): Numbers n such that n! contains every digit at least once.
  • A178965 (program): a(n) = numerator of Sum_{k>=1} floor(n/k)/2^k.
  • A178969 (program): Last nonzero decimal digit of (10^10^n)!
  • A178970 (program): 2^(2n-1) mod (2n+1).
  • A178972 (program): Number of ways to place 2 nonattacking amazons (superqueens) on an n X n toroidal board.
  • A178977 (program): a(n) = (3*n+2)*(3*n+5)/2.
  • A178978 (program): a(n) = A144448(n+1)/8.
  • A178982 (program): Partial sums of floor(Fibonacci(n)/2).
  • A178984 (program): a(n) is the smallest prime p that makes prime(n) + 1 - p a prime.
  • A178987 (program): a(n) = n*(n-3)*2^(n-2).
  • A178989 (program): a(n) = (k^k + k!) / (k*(k + 1)), where k = prime(n) - 1.
  • A178999 (program): Number of n-node simple graphs that are not determined by their resistance distance multisets.
  • A179000 (program): Array T(n,k) read by antidiagonals: coefficient [x^k] of (1 + n*Sum_{i>=1} x^i)^2, k >= 0.
  • A179001 (program): Partial sums of floor(Fibonacci(n)/3).
  • A179002 (program): Primes p such that 2^(2p-1) mod (2p+1) is prime.
  • A179003 (program): Numbers n such that 2^(2n-1) mod (2n+1) is prime.
  • A179005 (program): Indices of nonprime repunits: nonnegative numbers n such that 11…111 = (10^n - 1)/9 is composite.
  • A179006 (program): Partial sums of floor(Fibonacci(n)/4).
  • A179007 (program): Sum of 3 consecutive composite odd numbers.
  • A179010 (program): The number of isomorphism classes of commutative quandles of order n.
  • A179016 (program): The infinite trunk of binary beanstalk: The only infinite sequence such that a(n-1) = a(n) - number of 1’s in binary representation of a(n).
  • A179017 (program): Odd numbers c such that c(c^2-1)/4 is squarefree.
  • A179018 (program): Partial sums of ceiling(Fibonacci(n)/2).
  • A179019 (program): a(n) = (A179017(n)+1)/2.
  • A179020 (program): Doubled Thue-Morse sequence: the A010059 sequence replacing 0 with 0,0 and 1 with 1,1.
  • A179022 (program): Decimal expansion of 3*sqrt(39)/4.
  • A179023 (program): a(n) = n(F(n+2) - 1) where F(n) is defined by A000045.
  • A179041 (program): Partial sums of ceiling(Fibonacci(n)/3).
  • A179042 (program): Partial sums of ceiling(Fibonacci(n)/4).
  • A179044 (program): Decimal expansion of (5/18)Pi. Decimal expansion of, asymptotically, the probability that the evolution of a random graph ever simultaneously has two complex components.
  • A179047 (program): Decimal expansion of 9*sqrt(3)/4, the area of an equilateral triangle of side length 3.
  • A179048 (program): Decimal expansion of 25*sqrt(3)/4, the area of the equilateral triangle of side 5.
  • A179050 (program): Decimal expansion of 5/(2*sqrt(5+2*sqrt(5))), area of regular pentagram with base edge length 1.
  • A179053 (program): Partial sums of ceiling(Fibonacci(n)/11).
  • A179054 (program): a(n) = (1^k + 2^k + … + n^k) modulo (n+2), where k is any odd integer greater than or equal to 3.
  • A179058 (program): Number of non-attacking placements of 3 rooks on an n X n board.
  • A179059 (program): Number of non-attacking placements of 4 rooks on an n X n board.
  • A179060 (program): Number of non-attacking placements of 5 rooks on an n X n board.
  • A179061 (program): Number of non-attacking placements of 6 rooks on an n X n board.
  • A179062 (program): Number of non-attacking placements of 7 rooks on an n X n board.
  • A179063 (program): Number of non-attacking placements of 8 rooks on an n X n board.
  • A179064 (program): Number of non-attacking placements of 9 rooks on an n X n board.
  • A179065 (program): Number of non-attacking placements of 10 rooks on an n X n board.
  • A179070 (program): a(1)=a(2)=a(3)=1, a(4)=3; thereafter a(n) = a(n-1) + a(n-3).
  • A179075 (program): Concatenation of the first n numbers in base n.
  • A179076 (program): Number of primes of the form k^2 + 1 less than n.
  • A179077 (program): a(n) is the residue ((2^p - 2)/p) mod p, where p is the n-th prime.
  • A179078 (program): a(n)=((3^p - 3)/p) mod p where p is n-th prime
  • A179081 (program): Parity of sum of digits of n.
  • A179082 (program): Even numbers having an even sum of digits in their decimal representation.
  • A179083 (program): Even numbers having an odd sum of digits in their decimal representation.
  • A179084 (program): Odd numbers having an even sum of digits in their decimal representation.
  • A179085 (program): Odd numbers having an odd sum of digits in their decimal representation.
  • A179088 (program): Positive integers of the form (2*m^2+1)/11.
  • A179089 (program): a(n) = (1/n^2) * Sum_{k=0..n-1} (2k+1)*T_k^2(-3)^(n-1-k), where T_0, T_1, … are central trinomial coefficients given by A002426.
  • A179094 (program): Fill an n X n array with various permutations of the integers 1, 2, 3, 4… n^2. Define the organization number of the n X n array to be the following: Start at 1, count the rectilinear steps to reach 2, then the rectilinear steps to reach 3, etc. Add them up. The array that has the maximum organization number would be the “most disorganized.” This sequence is the sequence showing the most disorganized number for n X n arrays starting at 1 X 1.
  • A179095 (program): Rectified 5-cell numbers: the coefficient of x^{2n-2} in (1+x+x^2+ … + x^{n-1})^5.
  • A179096 (program): Rectified hexateron (5-simplex) numbers: the coefficient of x^(2n-2) in (1+x+x^2+…+x^(n-1))^6.
  • A179102 (program): A variation on A119505 that gives a limited digit set {2, 3, 4, 6, 7, 8, 9}.
  • A179103 (program): A variation on A119505 that gives a limited digit set {2, 3, 4, 6, 8}.
  • A179104 (program): A variation on A119505 that gives a limited digit set {2, 3, 4, 5, 6, 7, 8, 9}.
  • A179111 (program): Partial sums of round(Fibonacci(n)/11).
  • A179118 (program): Number of Collatz steps to reach 1 starting with 2^n + 1.
  • A179123 (program): a(n) red and b(n) blue balls in an urn; draw 6 balls without replacement; Probability(6 red balls)=Probability(4 red and 2 blue balls); binomial(a(n),6)=binomial(a(n),4)*binomial(b(n),2);
  • A179125 (program): a(n) = A000037(n)^3.
  • A179126 (program): Positive integers m for which the torsion subgroup of the elliptic curve y^2 = x^3 + m has order 3.
  • A179131 (program): Numerators of A178381(4*n+1)/A178381(4*n)
  • A179132 (program): Denominators of A178381(4*n+1)/A178381(4*n)
  • A179133 (program): Denominators of A178381(4*n+3)/A178381(4*n+2).
  • A179134 (program): a(n) = (F(2*n-1) + F(2*n+2)) * (5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).
  • A179135 (program): a(n) = (3-sqrt(5))*((3+sqrt(5))/10)^(-n)/2+(3+sqrt(5))*((3-sqrt(5))/10)^(-n)/2.
  • A179167 (program): a(n) red and b(n) blue balls in an urn; draw 3 balls without replacement; Probability(3 red balls) = Probability(1 red and 2 blue balls); binomial(a(n),3) = binomial(a(n),1)*binomial(b(n),2).
  • A179178 (program): The number of equal-sized equilateral triangles visible (when viewed from above) in successive Genealodrons formed from 2^n -1 same size equilateral triangles.
  • A179179 (program): a(n) = phi(n) - omega(n) = A000010(n) - A001221(n).
  • A179180 (program): Partial sums of A007895.
  • A179182 (program): Natural numbers n such that n+1 or 2n+1 is prime.
  • A179184 (program): Number of connected 2-regular simple graphs with n vertices.
  • A179190 (program): Coefficient [x^n] of the Maclaurin series for 2 - sqrt(1 - 4*x - 4*x^2).
  • A179191 (program): Expansion of o.g.f. (1/2)*(-1 + 1/sqrt(1 - 4*x - 4*x^2)).
  • A179194 (program): Bases n in which 1/(n-2) is non-terminating and has period n-3.
  • A179207 (program): a(n) = n - 1 + ceiling((-3 + n^2)/2) if n > 1 with a(1)=1, complement of A182835.
  • A179209 (program): n such that 2^(2n-1) mod (2n+1) = 2.
  • A179211 (program): Number of squarefree numbers between n and 2*n (inclusive).
  • A179212 (program): First differences of A179211.
  • A179213 (program): Sum of squarefree numbers between n and 2*n (inclusive).
  • A179215 (program): Product of squarefree numbers less than n+1.
  • A179229 (program): a(n)=number of Abelian groups of order 2n which are not isomorphic to any Galois field GF(k) of that order.
  • A179231 (program): Primes of the form 250n + 1.
  • A179237 (program): a(0) = 1, a(1) = 2; a(n+1) = 6*a(n) + a(n-1) for n>1.
  • A179238 (program): Numerators in convergents to infinitely repeating period 3 palindromic continued fraction [1,2,1,…].
  • A179241 (program): Powers of sqrt(5) - 1 rounded down.
  • A179242 (program): Numbers that have two terms in their Zeckendorf representation.
  • A179243 (program): Numbers that have three terms in their Zeckendorf representation.
  • A179244 (program): Numbers that have 4 terms in their Zeckendorf representation.
  • A179245 (program): Numbers that have 5 terms in their Zeckendorf representation.
  • A179246 (program): Numbers that have 6 terms in their Zeckendorf representation.
  • A179247 (program): Numbers that have 7 terms in their Zeckendorf representation.
  • A179248 (program): Numbers that have 8 terms in their Zeckendorf representation.
  • A179251 (program): Numbers that have 11 terms in their Zeckendorf representation.
  • A179252 (program): Numbers that have 12 terms in their Zeckendorf representation.
  • A179257 (program): Number of permutations of length n which avoid the patterns 321 and 1324.
  • A179259 (program): Arises in covering a graph by forests and a matching.
  • A179260 (program): Decimal expansion of the connective constant of the honeycomb lattice.
  • A179262 (program): a(n) = 2*prime(n)^2 - 1.
  • A179272 (program): Sharp upper bound on Rosgen overlap number n-vertex graph with n => 14, formula abused here for nonnegative integers.
  • A179273 (program): Primes in A179272.
  • A179276 (program): Largest 3-smooth number <= n.
  • A179278 (program): Largest nonprime integer not less than n.
  • A179280 (program): E.g.f. equals the real part of the series F(x) = 1 + x*F(x)^i where i=sqrt(-1).
  • A179281 (program): E.g.f. equals the imaginary part of the series F(x) = 1 + x*F(x)^i where i=sqrt(-1).
  • A179290 (program): Decimal expansion of length of edge of a regular icosahedron with radius of circumscribed sphere = 1.
  • A179297 (program): a(n) = n^2 - (n-1)^2 - (n-2)^2 - … - 1^2.
  • A179298 (program): a(n)=n^3-(n-1)^3-(n-2)^3-…-1.
  • A179312 (program): Largest semiprime dividing n, or 0 if no semiprime divides n.
  • A179327 (program): G.f.: Product_{n>=1} 1/(1-x^n)^((n-1)!).
  • A179329 (program): Number of iterations of (n + lpf(n)) / 2 required to reach a prime, where lpf equals the least prime factor.
  • A179337 (program): Positive integers of the form (6*m^2 + 1)/11.
  • A179338 (program): Positive integers of the form (10*m^2+1)/11.
  • A179339 (program): Positive integers of the form (30*m^2+1)/11.
  • A179370 (program): Positive integers of the form (7*m^2+1)/11.
  • A179382 (program): a(n) is the smallest period of pseudo-arithmetic progression with initial term 1 and difference 2n-1.
  • A179383 (program): a(n) = 2*k(n)-1 where k(n) is the sequence of positions of records in A179382.
  • A179384 (program): Nonprimes in A040976.
  • A179394 (program): a(n) = prime(n)^2 mod prime(n+2).
  • A179395 (program): a(n) = prime(n)^2 mod prime(n+3).
  • A179396 (program): a(n) = prime(n)^2 modulo prime(n+4).
  • A179397 (program): a(n) = prime(n)^2 mod prime(n-2).
  • A179398 (program): a(n) = prime(n)^2 mod prime(n-3).
  • A179399 (program): Prime(n)^2 mod prime(n-4).
  • A179403 (program): Number of ways to place 2 nonattacking kings on an n X n toroidal board.
  • A179431 (program): a(n) = binomial(3^(n-1), n).
  • A179432 (program): a(n) = C(2*3^(n-1), n).
  • A179436 (program): a(n) = (3*n+7)*(3*n+2)/2.
  • A179437 (program): |2n - prime(n)|.
  • A179441 (program): Number of solutions to a+b+c < d+e with each of a,b,c,d,e in {1..n+1}.
  • A179442 (program): a(n) = ((n-1)! * (n+1)!) / n.
  • A179445 (program): Nonprimes m such that 10m + 1 are primes.
  • A179446 (program): Primes p of form p = 10k + 1, where k is nonprime.
  • A179449 (program): Decimal expansion of the volume of great icosahedron with edge length 1.
  • A179452 (program): Decimal expansion of sqrt(5 + 2*sqrt(5))/2, the height of a regular pentagon and midradius of an icosidodecahedron with side length 1.
  • A179453 (program): Decimal expansion of the inradius of an icosidodecahedron with edge length 1.
  • A179458 (program): Numbers n such that ((2^(2n) - 1) mod 2n) - (2^(2n-1) mod 2n) = 1.
  • A179461 (program): Decimal expansion of sqrt(51)/7.
  • A179464 (program): a(n) = min(nextprime(n),nextsemiprime(n)).
  • A179474 (program): a(n) = position of A045392(n) in A042997.
  • A179475 (program): a(n) = A042997(n) mod 7.
  • A179477 (program): Antonym of A014824: each term is 10 times the previous term minus n.
  • A179478 (program): a(n) = sqrt(A073609(n+1)-A073609(n))
  • A179483 (program): A(k,3) where A(k,n) = Sum_{m=1..k} (-1)^(m+1) *binomial(n,m)*m^k.
  • A179504 (program): a(n) = sigma(2n,n) for n>0 with a(0)=1.
  • A179508 (program): a(n) is the unique integer such that Sum_{k=0..p-1} b(k)/(-n)^k == a(n) (mod p) for any prime p not dividing n, where b(0), b(1), b(2), … are Bell numbers given by A000110.
  • A179509 (program): Numbers that can be written uniquely as sum of a square and a nonnegative cube.
  • A179523 (program): Round (3/2)^n.
  • A179524 (program): a(n) = Sum_{k=0..n} (-4)^k*binomial(n,k)^2*binomial(n-k,k)^2.
  • A179526 (program): (3^k - 1)/2 appears 3^(k-1) times, k>0.
  • A179527 (program): Characteristic function of numbers in A083207.
  • A179528 (program): Number of terms of A083207 that are not greater than n.
  • A179532 (program): a(n) = 2^ceiling(n*(n+1)/3).
  • A179534 (program): Number of labeled split graphs on n vertices.
  • A179535 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(n-k,k)^2 * 81^k.
  • A179536 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2*binomial(n-k,k)^2*(-324)^k.
  • A179537 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2*binomial(n-k,k)^2*(-16)^k.
  • A179540 (program): a(0)=0, a(1)=1, a(n)=2*n*(a(n-1)+a(n-2)), n>1.
  • A179541 (program): a(n) is the least possible smallest period attainable by the action of a periodic sequence of binary operations <+>,<-> (see A179382,A179480), beginning with 2n-1<+>1 or 2n-1<->1
  • A179542 (program): Trajectory of 1 under the morphism 1->(1,2,3), 2->(1,2), 3->(1) related to the heptagon and A006356.
  • A179545 (program): The sum of the elements within a jump in a Sieve of Eratosthenes table.
  • A179546 (program): a(n) = p^2*(p + 3)/2, where p = prime(n).
  • A179552 (program): Decimal expansion of the volume of pentagonal pyramid with edge length 1.
  • A179555 (program): a(1)=10; a(n) = a(n-1)*10 - 1.
  • A179556 (program): a(1) = 10; a(n) = a(n-1)*10 - 2^(n-2).
  • A179557 (program): a(1)=10; a(n)=a(n-1)*10 -/+ 1 (alternating)
  • A179558 (program): a(1)=10; a(n) = a(n-1)*10 - 5^(n-2).
  • A179571 (program): Number of permutations of 1..n+4 with the number moved left exceeding the number moved right by n.
  • A179572 (program): Number of permutations of 1..n+5 with the number moved left exceeding the number moved right by n
  • A179579 (program): Number of permutations of 1..n+4 with the number moved left exceeding the number moved right by n or more.
  • A179580 (program): Number of permutations of 1..n+5 with the number moved left exceeding the number moved right by n or more
  • A179587 (program): Decimal expansion of the volume of square cupola with edge length 1.
  • A179589 (program): Decimal expansion of the circumradius of square cupola with edge length 1.
  • A179590 (program): Decimal expansion of the volume of pentagonal cupola with edge length 1.
  • A179596 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + x)/(1 - 2*x - 11*x^2 - 6*x^3).
  • A179597 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 5*x + 2*x^2)/(1 - 2*x - 11*x^2 - 6*x^3).
  • A179598 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2*x)/(1 - 3*x - 8*x^2).
  • A179599 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 4*x)/(1 - 3*x - 8*x^2).
  • A179600 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + x)/(1 - 2*x - 10*x^2 - 4*x^3).
  • A179601 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1+4*x)/(1 - 2*x - 10*x^2 - 4*x^3).
  • A179602 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2*x)/(1 - 3*x - 7*x^2).
  • A179603 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 3*x)/(1 - 3*x - 7*x^2).
  • A179604 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + x)/(1 - 2*x - 9*x^2 - 2*x^3).
  • A179605 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 3*x - 2*x^2)/(1 - 2*x - 9*x^2 - 2*x^3).
  • A179606 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + x)/(1 - 3*x - 5*x^2).
  • A179607 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1 + 2*x - 4*x^2)/(1 - 2*x - 8*x^2).
  • A179608 (program): a(n) = (7 + (-1)^n + 6*n)*2^(n-3).
  • A179609 (program): a(n)=(5-(-1)^n-6*n)*2^(n-2)
  • A179610 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: 1/(1-3*x-5*x^2+4*x^3).
  • A179611 (program): Eight white kings and one red king on a 3 X 3 chessboard. G.f.: (1+2*x)/(1 - 2*x - 8*x^2 - 4*x^3).
  • A179614 (program): Composite numbers not divisible by any triangular number other than 1.
  • A179619 (program): a(1)=1, a(n+1) = 10*a(n)+2*n-1
  • A179620 (program): a(n) = largest k such that A002808(n+1) = A002808(n) + (A002808(n) mod k), or 0 if no such k exists.
  • A179626 (program): Distance between the n-th abundant number and the nearest prime below it.
  • A179627 (program): a(n) = length of Collatz sequence starting with n-th prime
  • A179628 (program): Sum of the numbers already killed in the first jump of a Sieve of Eratosthenes table.
  • A179635 (program): Median of the digits in n (rounding down).
  • A179636 (program): Median of the digits in n (rounding up).
  • A179639 (program): Decimal expansion of the volume of gyroelongated pentagonal pyramid with edge length 1.
  • A179641 (program): Decimal expansion of the volume of pentagonal dipyramid with edge length 1.
  • A179642 (program): Product of exactly 5 primes, 3 of which are distinct.
  • A179643 (program): Products of exactly 2 distinct squares of primes and a different prime (p^2 * q^2 * r).
  • A179644 (program): Product of the 4th power of a prime and 2 different distinct primes (p^4*q*r).
  • A179645 (program): a(n) = prime(n)^8.
  • A179648 (program): Expansion of (1/(1+4x-2x^2))*c(x/(1+4x-2x^2)), c(x) the g.f. of A000108.
  • A179650 (program): a(n) = (n-th prime) mod (n-th nonprime).
  • A179651 (program): Difference between consecutive practical numbers.
  • A179652 (program): (A175600(n)-5)/48 or A112559(n)/3.
  • A179654 (program): Sum of the numbers already removed (including the target number) in the first jump of a Sieve of Eratosthenes table.
  • A179655 (program): Digital root of n-th abundant number.
  • A179656 (program): prime(n) mod (digital root(prime(n))).
  • A179657 (program): Digital root of n-th practical number.
  • A179665 (program): a(n) = prime(n)^9.
  • A179688 (program): Numbers of the form p^3*q^3*r where p, q, and r are prime.
  • A179690 (program): Numbers of the form p^2*q^2*r*s where p, q, r, and s are distinct primes.
  • A179694 (program): Numbers of the form p^6*q^3 where p and q are distinct primes.
  • A179696 (program): Numbers with prime signature {7,1,1}, i.e., of form p^7*q*r with p, q and r prime.
  • A179741 (program): a(n) = (2*n+1)*(6*n-1).
  • A179742 (program): The number of syllables in each letter of the English alphabet.
  • A179743 (program): Triangle read by rows: antidiagonals of an array formed by sequences of the form a(0)=1, a(1) = (n+1); a(n+1), n>1 = 2*a(n).
  • A179744 (program): a(0) = 1, a(n) = 3*2^(n-1) - n for n>0.
  • A179746 (program): Numbers of the form p^4*q^2*r^2 where p, q, and r are distinct primes.
  • A179752 (program): Maximum depth of parenthesizations encoded by A014486, or correspondingly, maximum height for the equivalent general trees.
  • A179753 (program): Integers (2k)-1..0 followed by integers (2k)+1..0 and so on.
  • A179783 (program): a(n) = 2*n*(n+1)*(n+2)/3 + (-1)^n.
  • A179789 (program): Sum of the differences between the first prime and the next, inside in the first jump in a Sieve of Eratosthenes table.
  • A179802 (program): Digital root of A179545.
  • A179804 (program): Number of letter combinations on a standard telephone keypad represented by the digits in n
  • A179805 (program): a(0) = 1, a(1) = 3, a(2) = 6 and a(n) = 2*a(n-1) - a(n-2) for n > 3.
  • A179808 (program): Number of n X 3 arrays with every diagonal and antidiagonal of length L containing a permutation of 1..L.
  • A179816 (program): Sum of the prime numbers that are between 10*n and 10*(n+1).
  • A179819 (program): Monetary amounts in U.S. cents such that the smallest number of coins summing to the amount uses only denominations of 10 cents and above.
  • A179820 (program): a(n) = n-th triangular number mod (n+2).
  • A179823 (program): Denominators in the approximation of sqrt(2) satisfying the recurrence: a(n)= [a(n-1)*a(n-2)+2]/[a(n-1)+a(n-2)] with a(1)=a(2)=1.
  • A179824 (program): Chromatic polynomial of the star graph on 4 vertices (claw graph) and the path graph on 4 vertices.
  • A179837 (program): Triangle T(n,k) read by rows: the coefficient [x^k] of the product_{s=1..n} (x+16*cos(s*Pi/(2n+1))^4), 0<=k<=n.
  • A179848 (program): Expansion of series reversion of generating function for triangular numbers.
  • A179850 (program): Characteristic function of numbers that are congruent to {0, 1, 3, 4} mod 5.
  • A179851 (program): Expansion of q^(-1/4) * (eta(q^4) * eta(q^25) + eta(q) * eta(q^100))^2 / (eta(q^2) * eta(q^50)) in powers of q.
  • A179853 (program): E.g.f. A(x) = Sum_{n>=0} a(n)*x^(3n)/(3n)!.
  • A179854 (program): Number of 0’s (mod 3) in the binary expansion of n.
  • A179865 (program): Number of n-bit binary numbers containing one run of 0’s.
  • A179867 (program): “Recurrence function” for Thue-Morse infinite word A010060.
  • A179868 (program): (Number of 1’s in the binary expansion of n) mod 4.
  • A179870 (program): a(n) = ((n-1)! * (n+1)!) ^ 2.
  • A179871 (program): Numbers h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is integer.
  • A179872 (program): Numbers h such that antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 is not integer.
  • A179873 (program): Corresponding values of antiharmonic means B(h) to numbers h from A179871 (numbers h such that antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 is integer).
  • A179875 (program): Numbers h such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1.
  • A179876 (program): Numbers h such that h and h-1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1.
  • A179877 (program): Numbers h such that h and h+1 have same contraharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is integer (see A179882).
  • A179878 (program): Numbers h such that h and h-1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is integer (see A179882).
  • A179882 (program): a(n) is the corresponding value of contraharmonic mean B(h) of numbers k such that gcd(k, h) = 1 (k < h) for numbers h from A179877(n) and A179878(n).
  • A179883 (program): List of twin numbers (h, h+1) such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1.
  • A179884 (program): List of twin numbers (h, h+1) such that h and h+1 have same antiharmonic mean of the numbers k < h such that gcd(k, h) = 1 and simultaneously this mean is integer.
  • A179886 (program): Corresponding values of antiharmonic mean B(h) of the numbers k < h such that gcd(k, h) = 1 for numbers h from A179884.
  • A179888 (program): Starting with a(1)=2: if m is a term then also 4*m+1 and 4*m+2.
  • A179890 (program): Values of antiharmonic mean B(q) of the numbers k < q such that gcd(k, q) = 1 is integer for nonprimes q from A179887, where B(q) = A053818(q) / A023896(q) = A175505(q) / A175506(q).
  • A179892 (program): Numbers which are not the sum of three distinct members of twin primes.
  • A179893 (program): a(n) = 3/2 * (prime(n)-1).
  • A179894 (program): Given the series (1, 2, 1, 2, 1, 2, …), let (1 + 2x + x^2 + 2x^3 + …) * (1 + 2x^2 + x^3 + 2x^4 + …) = (1 + 2x + 3x^2 + 7x^3 + …)
  • A179896 (program): Sum of the numbers between k := n-th nonprime and 2k (like a jump in a Sieve of Eratosthenes).
  • A179897 (program): Numbers a_n with property that a(n) is arithmetic mean of sequence “n-times n^-1, once n^(2*n+1)” that has integer valued both arithmetic and geometric means even though some of the sequence members are (for n>1) non-integer.
  • A179899 (program): Integers of the form A179896(n)/A141468(n+1).
  • A179903 (program): (1, 3, 5, 7, 9, …) convolved with (1, 0, 3, 5, 7, 9, …).
  • A179904 (program): a(n) = A056520(n)+1 for n>0, a(0)=1.
  • A179905 (program): (1, 4, 7, 10, 13, …) convolved with (1, 0, 4, 7, 10, 13, …); given A016777 = (1, 4, 7, 10, 13, …).
  • A179906 (program): (1, 1, 2, 3, 5, 7, 11, …) convolved with (1, 0, 1, 2, 3, 5, 7, 11, …); given A000041 = (1, 1, 2, 3, 5, 7, …).
  • A179907 (program): Numerators in the approximation of sqrt(2) satisfying the recurrence: a(n)= [a(n-1)*a(n-2)+2]/[a(n-1)+a(n-2)] with a(1)=a(2)=1
  • A179927 (program): Triangle of centered orthotopic numbers
  • A179928 (program): Row sums of A179927, the triangle of centered orthotopic numbers.
  • A179929 (program): a(n) = 2^n*A(n, -1/2), A(n, x) the Eulerian polynomials.
  • A179930 (program): a(n) = gcd(n, A001157(n)).
  • A179931 (program): a(n) = gcd(sigma(n), sigma_2(n)).
  • A179934 (program): Expansion of x*(4+5*x-13*x^2-x^3+x^4) / ( (1-x)*(1-10*x^2+x^4) ).
  • A179935 (program): Squares where the number of decimal digits is also a square.
  • A179941 (program): Number of times n appears in a 100 X 100 multiplication table.
  • A179942 (program): Number of times n appears in a 1000 X 1000 multiplication table.
  • A179943 (program): Triangle read by rows, antidiagonals of an array (r,k), r=(0,1,2,…), generated from 2 X 2 matrices of the form [1,r; 1,(r+1)].
  • A179944 (program): Row sums of triangle A179943.
  • A179952 (program): Add 1 to all the divisors of n. a(n)=number of perfect squares in the set.
  • A179953 (program): a(n) is the least exponent k such that q^k >= n, where q is the greatest prime factor of n (= A006530(n)); a(1) = 1 by convention.
  • A179956 (program): a(n) is the smallest integer that contains a(n-1) but does not begin with a(n-1).
  • A179962 (program): Number of permutations of 1..2*n+4 with no adjacent elements within n in value.
  • A179970 (program): Numbers such that in base-4 representation all sums of two adjacent digits are odd.
  • A179976 (program): a(n) = 2^(2n+1) mod (2n+1).
  • A179980 (program): a(n)=10*a(n-1)+/- n
  • A179983 (program): Positive integers n such that, if k appears in n’s prime signature, k-1 appears at least as often as k (for any integer k > 1).
  • A179984 (program): Numerators of Integral_{x=0..1} cos(log(x))^n dx.
  • A179986 (program): Second 9-gonal (or nonagonal) numbers: a(n) = n*(7*n+5)/2.
  • A179991 (program): Nonhomogeneous three-term sequence a(n) = a(n-1) + a(n-2) + n.
  • A179992 (program): Extended three term Fibonacci sequence a(n)=a(n-1)+a(n-2)+n^2. a(1)=2; a(2)=5
  • A179995 (program): Generating function A(5,t)(1+t+t^2)/(1-t)^6, where A(5,t) is an Eulerian polynomial.
  • A179999 (program): Length of the n-th term in the modified Look and Say sequence A110393.
  • A180000 (program): a(n) = lcm{1,2,…,n} / swinging_factorial(n) = A003418(n) / A056040(n).
  • A180003 (program): a(n) blue and b(n)(A180002) red balls in an urn, draw 5 balls without replacement, Probability(5 red balls) = Probability(3 red and 2 blue balls).
  • A180004 (program): a(n) is the nearest integer to n*(27/26).
  • A180016 (program): Partial sums of number of n-step closed paths on hexagonal lattice A002898.
  • A180017 (program): Difference of sums of digits of n in ternary and in binary.
  • A180018 (program): Difference of sums of digits of n in decimal and in binary representation.
  • A180019 (program): Difference of sums of digits of n in decimal and in ternary representation.
  • A180027 (program): Partial sums of sigma_A100706(n).
  • A180028 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1 + 3*x)/(1 - 6*x - 3*x^2).
  • A180029 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1 + 2*x)/(1 - 6*x - 2*x^2).
  • A180030 (program): Number of n-move paths on a 3 X 3 chessboard of a queen starting or ending in a corner or side square.
  • A180031 (program): Number of n-move paths on a 3 X 3 chessboard of a queen starting or ending in the central square.
  • A180032 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1+x)/(1-5*x-7*x^2).
  • A180033 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1 + x)/(1 - 5*x - 5*x^2).
  • A180034 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1 - 2*x)/(1 - 6*x + 2*x^2).
  • A180035 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1+x)/(1-5*x-3*x^2).
  • A180036 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1 - 2*x)/(1 - 5*x - 3*x^2).
  • A180037 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1+x)/(1-5*x-2*x^2).
  • A180038 (program): Eight white queens and one red queen on a 3 X 3 chessboard. G.f.: (1 - 3*x)/(1 - 5*x - 2*x^2).
  • A180046 (program): a(n+1) = a(n-3) + a(n-2) - a(n-1) + a(n).
  • A180047 (program): Coefficient triangle of the numerators of the (n-th convergents to) the continued fraction w/(1 + w/(2 + w/3 + w/…
  • A180052 (program): Partial sums of A180039.
  • A180053 (program): a(1)=1, a(2)=101, a(n) = 1001*a(n-1) for n > 2.
  • A180054 (program): In binary expansion, number of 1’s in 3n is less than in n.
  • A180056 (program): The number of permutations of {1,2,…,2n} with n ascents.
  • A180060 (program): 2^(2^n mod n) mod n.
  • A180061 (program): Numbers n such that (2^(2^n mod n) mod n)=4.
  • A180063 (program): Pascal-like triangle with trigonometric properties, row sums = powers of 4; generated from shifted columns of triangle A180062.
  • A180064 (program): a(n) = n!/A056040(n).
  • A180082 (program): Semiprime centered cube numbers: m^3 + (m+1)^3.
  • A180085 (program): Eulerian polynomials at nonpositive integers, A_{n}(-n).
  • A180092 (program): Denominators of Integral_{x=0..1} cos(log(x))^n dx.
  • A180094 (program): Number of steps to reach 0 or 1, starting with n and applying the map k -> (number of 1’s in binary expansion of k) repeatedly.
  • A180101 (program): a(0)=0, a(1)=1; thereafter a(n) = largest prime factor of sum of all previous terms.
  • A180102 (program): a(1)=1; a(n)=percentage of sum of previous terms represented by n
  • A180103 (program): Floor( 100*(n-1)/n ).
  • A180104 (program): Floor( 100*n/(n-1) ).
  • A180107 (program): Partial sums of terms in A180101.
  • A180114 (program): Sigma(A001694(n)), sum of divisors of the powerful number A001694(n).
  • A180115 (program): A109613(n)-fold concatenation of A008619(n).
  • A180118 (program): a(n) = Sum_{k=1..n} (k+2)!/k! = Sum_{k=1..n} (k+2)*(k+1).
  • A180119 (program): a(n) = (n+2)! * Sum_{k = 1..n} 1/((k+1)*(k+2)).
  • A180122 (program): First of three “least, sum, least” self-generating sequences.
  • A180123 (program): Second of three “least, sum, least” self-generating sequences.
  • A180124 (program): Third of three “least, sum, least” self-generating sequences.
  • A180125 (program): Self-convolution of period-doubling sequence A035263
  • A180129 (program): Expansion of log(1/(1-Prime(x))) where Prime(x) = Sum{n>=1} A008578(n)*x^n.
  • A180140 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1+x+x^2)/(1-3*x-5*x^2).
  • A180141 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1 + x - 2*x^2)/(1 - 3*x - 6*x^2).
  • A180142 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1 + x - x^2)/(1 - 3*x - 3*x^2).
  • A180143 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1 + x^2)/(1 - 4*x + x^2 + 2*x^3).
  • A180144 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1 - 2*x^2)/(1 - 4*x + x^2 + 2*x^3).
  • A180145 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1 - 3*x^2)/(1 - 4*x - 3*x^2 + 6*x^3).
  • A180146 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: 1/(1 - 4*x - 3*x^2 + 6*x^3).
  • A180147 (program): Eight rooks and one berserker on a 3 X 3 chessboard. G.f.: (1 + 3*x)/(1 - 4*x - 3*x^2 + 6*x^3).
  • A180148 (program): a(n) = 3*a(n-1) + a(n-2) with a(0)=2 and a(1)=5.
  • A180153 (program): a(n) = 10*a(n-1) + A109242(n).
  • A180157 (program): Arithmetic mean of digits is not an integer.
  • A180158 (program): Number of ways are there to score a break of n points at snooker. Assuming an infinite number of reds are available, along with the usual six colors, and a break alternates red-color-red-…
  • A180165 (program): Triangle read by rows, derived from an array of sequences generated from (1 + x)/ (1 - r*x - r*x^2).
  • A180166 (program): Row sums of triangle A180165.
  • A180167 (program): a(0) = 1, a(1) = 7; a(n)= 6*a(n-1) + 6*a(n-2) for n>1.
  • A180168 (program): a(n) = 2*a(n-1) + 5*a(n-2), a(0) = 1, a(1) = 3.
  • A180170 (program): a(0) = 1, a(n) = n*a(n-1)*A014963(n).
  • A180172 (program): a(n) = gcd(prime(n)+2, n).
  • A180173 (program): a(n) = gcd(prime(n)-2, n).
  • A180175 (program): Diagonal sums of A164844.
  • A180177 (program): Triangle read by rows: T(n,k) is the number of compositions of n without 2’s and having k parts; 1<=k<=n.
  • A180184 (program): Irregular triangle read by rows: T(n,k) is the number of compositions of n with k parts, all >= 4, for n >= 4 and 1 <= k <= floor(n/4).
  • A180187 (program): Number of successions in all the permutations p of [n] such that p(1)=1 and having no 3-sequences. A succession of a permutation p is a position i such that p(i +1) - p(i) = 1.
  • A180188 (program): Triangle read by rows: T(n,k) is the number of permutations of [n] with k circular successions (0<=k<=n-1). A circular succession in a permutation p of [n] is either a pair p(i), p(i+1), where p(i+1)=p(i)+1 or the pair p(n), p(1) if p(1)=p(n)+1.
  • A180189 (program): Number of permutations of [n] having exactly 1 circular succession. A circular succession in a permutation p of [n] is either a pair p(i), p(i+1), where p(i+1)=p(i)+1 or the pair p(n), p(1) if p(1)=p(n)+1.
  • A180191 (program): Number of permutations of [n] having at least one succession. A succession of a permutation p is a position i such that p(i+1)-p(i) = 1.
  • A180195 (program): a(n)=(-1)^n*Sum((-1)^j*b(j), j=1..n), where b(n)=(n-1)!*(n^2 - n + 1) = A001564(n-1) (n>=1).
  • A180198 (program): A180200(A180200(n)).
  • A180199 (program): a(n) = A180201(A180201(n)).
  • A180200 (program): a(0)=0, a(1)=1; for n > 1, a(n) = 2*m + 1 - (n mod 2 + m mod 2) mod 2, where m = a(floor(n/2)).
  • A180201 (program): Inverse permutation to A180200.
  • A180203 (program): Differences between prime powers of primes, offsetting the prime and the power by only one. (For purposes of this sequence, 0 and 1 are treated as primes; see Formula.)
  • A180212 (program): Number of permutations of 0..(n-1) representable as consecutive sums of 9 adjacent elements of a sequence of n+8 nonnegative integers
  • A180217 (program): a(n) = (n-th prime modulo 3) + (n-th prime modulo 4).
  • A180218 (program): a(n) = (n+2)!*sum(1/k, k=1..n)
  • A180221 (program): Numbers that can be written as sum of one or more distinct elements of A000043. Numbers k for which sigma(A180162(k))=2^k, k>=2.
  • A180222 (program): a(n) = 4*a(n-1) + 8*a(n-2), with a(1)=0 and a(2)=1.
  • A180223 (program): a(n) = (11*n^2 - 7*n)/2.
  • A180226 (program): a(n) = 4*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.
  • A180231 (program): Prime partial sums of digits of decimal expansion of e.
  • A180232 (program): a(n) = n*(17*n - 13)/2.
  • A180234 (program): Demi-tribonacci numbers (rounding down): a(0)=a(1)=0, a(2)=2; a(n) = floor( (a(n-1)+a(n-2)+a(n-3))/2 )
  • A180235 (program): Demi-tribonacci numbers (rounding up): a(0)=a(1)=0, a(2)=2; a(n) = ceiling( (a(n-1)+a(n-2)+a(n-3))/2 )
  • A180246 (program): Triangle T(n,k) read by rows: T(n,k) = Sum_{j=0..k} (-1)^j *binomial(n+1,j)*(k+2-j)^n, 0 <= k < n.
  • A180250 (program): a(n) = 5*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.
  • A180251 (program): Decimal expansion of 6*(phi+1)/5, where phi is (1 + sqrt(5))/2.
  • A180253 (program): Call two divisors of n adjacent if the larger is a prime times the smaller. a(n) is the sum of elements of all pairs of adjacent divisors of n.
  • A180255 (program): a(n) = n^2 * a(n-1) + n, a(0)=0.
  • A180263 (program): Odd k such that (k^2 + 1)/2 is not prime.
  • A180266 (program): a(0) = 0; a(n) = C(2*n-2,n-1)*(n^2-2*n+2)/n for n >= 1.
  • A180270 (program): Integers of the form (k^12 - k^8 - k^4 + 1)/512.
  • A180272 (program): a(n) = binomial(n, A002024(n+1)-1) where A002024 is “n appears n times”.
  • A180275 (program): Primes of the form n^3+3*n+1.
  • A180276 (program): Primes of the form n^3 + 3*n - 1.
  • A180282 (program): Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to 2.
  • A180291 (program): Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to n-1.
  • A180292 (program): Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to n-2.
  • A180302 (program): Sequence of primes separated by [sequence of prime] elements. 2, [find 2nd prime after 2 = ] 5, find 3rd prime after 5 =] 13, [find 5th prime after 13 =] 61, …, etc.
  • A180304 (program): Sum of consecutive equal values of floor(sqrt(A000040(n))).
  • A180305 (program): G.f.: 1/(1 + x*d/dx log(eta(x))), where eta(x) is Dedekind’s eta(q) function without the q^(1/24) factor.
  • A180312 (program): Number of solutions to n = x + 4*y + 4*z in triangular numbers.
  • A180313 (program): A sequence a(n) such that a(n+1)^2 - a(n)^2 are perfect squares.
  • A180316 (program): Concatenation of n and A008954(n).
  • A180317 (program): Decimal expansion of the torsional rigidity constant for an equilateral triangular shaft.
  • A180318 (program): Expansion of a(-q) in powers of q where a(q) is a cubic AGM function.
  • A180319 (program): Total number of possible standard knight moves on an n X 2n chessboard, if the knight is placed anywhere
  • A180324 (program): Vassiliev invariant of fourth order for the torus knots
  • A180339 (program): Triangle by rows, A137710 * a diagonalized variant of A001906
  • A180350 (program): G.f.: Sum_{n>=0} a(n)*x^n/n!^5 = [ Sum_{n>=0} x^n/n!^5 ]^3.
  • A180353 (program): a(n) = n^n * prime(n).
  • A180354 (program): a(n) = n^4 + 4*n.
  • A180355 (program): n^5+5n
  • A180356 (program): n^6+6n
  • A180357 (program): a(n) = n^7 + 7*n.
  • A180358 (program): n^8+8n
  • A180359 (program): n^9+9n
  • A180363 (program): a(n) = Lucas(prime(n)).
  • A180364 (program): a(n) = sum_{k=0..n} C(n,k)*C(n+k,k)*(2*k+1)^2, where C(m,k) denotes the binomial coefficient m!/(k!*(m-k)!).
  • A180366 (program): Numbers n such that 0<A000203(n)-n-1<n.
  • A180392 (program): Number of permutations of 1..n with both permutation and its inverse having exactly 2 maxima
  • A180397 (program): T(n,m) = binomial(m!,n).
  • A180402 (program): a(n) = lcm(1,…,Fibonacci(n)).
  • A180408 (program): Nonzero digits not used in n.
  • A180409 (program): Unique digits used in n in numerical order (with 0 last)
  • A180410 (program): Unique digits used in n in numerical order.
  • A180413 (program): Total number of possible knight moves on an n X n X n chessboard, if the knight is placed anywhere.
  • A180415 (program): (n^3 - 3n^2 + 14n - 6)/6.
  • A180433 (program): Binary string formed from the binary expansion of Pi by exchanging 0’s and 1’s.
  • A180434 (program): Decimal expansion of constant (2 - Pi/2).
  • A180435 (program): a(n) = a(n-1)*2^n+n, a(0)=1.
  • A180444 (program): a(n) equals the number of bispecial Sturmian words of length n, that is words which are prefix to two words of length n+1, and likewise suffix. Note that prefix and suffix are not independent, unless the word is also palindromic: see A000010.
  • A180446 (program): Number of non-pentagonal numbers <= n.
  • A180447 (program): n appears 3n+1 times.
  • A180458 (program): Largest palindromic number <= n-th-prime.
  • A180459 (program): Sampling n numbers between 1 and a(n)-1, you are guaranteed to always find two subsets whose sums are equal.
  • A180470 (program): a(n) = -prime(n) + prime(n + prime(n)) - 1.
  • A180473 (program): Expansion of o.g.f. x*s(x)/(1-x*s(x)-x^2*s(x)^2), where s(x) is the o.g.f. of the little Schroeder numbers (A001003).
  • A180483 (program): Expansion of (3+3*x-25*x^2-3*x^3+2*x^4)/((1-x)*(1-10*x^2+x^4)).
  • A180486 (program): Numbers of the form ceiling(A179896(j)/A018252(j)) where A179896(j) mod A018252(j) <> 0.
  • A180488 (program): Partial sums of A006864.
  • A180491 (program): Product of remainders of n mod k, for k = 2,3,4,…,n-1.
  • A180492 (program): Product of remainders of prime(n) mod k, for k = 2,3,4,…,prime(n)-1
  • A180497 (program): a(n)=n^2-3*floor[n/sqrt(3)]^2
  • A180498 (program): a(n) = n^2 - 5*floor(n/sqrt(5))^2.
  • A180499 (program): n^3 + n-th cubefree number.
  • A180511 (program): Fermat quotients for base 4: (4^(p - 1) - 1)/p, where p = prime(n).
  • A180516 (program): Numbers of the form i*4^j-1 (i=1..3, j >= 0).
  • A180564 (program): Number of permutations of [n] having no isolated entries. An entry j of a permutation p is isolated if it is not preceded by j-1 and not followed by j+1. For example, the permutation 23178564 has 2 isolated entries: 1 and 4.
  • A180569 (program): The Wiener index of the P_3 X P_n grid, where P_m is the path graph on m nodes. The Wiener index of a connected graph is the sum of distances between all unordered pairs of nodes in the graph.
  • A180571 (program): The Wiener index of the graph \|/_\/_\/_…_\/_\|/ having n nodes on the horizontal path.
  • A180574 (program): Wiener index of the n-sunlet graph.
  • A180576 (program): Wiener index of the n-web graph.
  • A180577 (program): The Wiener index of the windmill graph D(6,n). The windmill graph D(m,n) is the graph obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs).
  • A180578 (program): The Wiener index of the Dutch windmill graph D(6,n) (n>=1).
  • A180579 (program): The Wiener index of the Dutch windmill graph D(5,n) (n>=1).
  • A180589 (program): a(n)=floor(n!*h(n)/n), where h(n)=sum(1/k,k=1..10)
  • A180592 (program): Digital root of 2n.
  • A180593 (program): Digital root of 3n.
  • A180594 (program): Digital root of 4n.
  • A180595 (program): Digital root of 5n.
  • A180596 (program): Digital root of 6n.
  • A180597 (program): Digital root of 7n.
  • A180598 (program): Digital root of 8n.
  • A180599 (program): Zero followed by infinitely many 9’s.
  • A180602 (program): (2^(n+1) - 1)^n.
  • A180606 (program): G.f.: A(x) = exp( Sum_{n>=1} (2^n-1)^(n-1)*x^n/n ).
  • A180608 (program): O.g.f.: exp( Sum_{n>=1} A067692(n)*x^n/n ), where A067692(n) = [sigma(n)^2 + sigma(n,2)]/2.
  • A180613 (program): The number of palindromic primes in the first n terms of A006530.
  • A180617 (program): Sum of divisors of the product of two consecutive primes.
  • A180633 (program): a(n) is the number of iterations of function f(x) = phi(x)-1 needed before zero is reached, when starting from the initial value x = n.
  • A180634 (program): Numbers n such that the discriminant of the n-th cyclotomic polynomial is a square.
  • A180637 (program): Digital root of A179899.
  • A180642 (program): Numbers k such that phi(k)/4 is a prime, where phi is the Euler totient function.
  • A180662 (program): The Golden Triangle: T(n,k) = A001654(k) for n>=0 and 0<=k<=n.
  • A180663 (program): Mirror image of the Golden Triangle: T(n,k) = A001654(n-k) for n>=0 and 0<=k<=n.
  • A180664 (program): Golden Triangle sums: a(n) = a(n-1) + A001654(n+1) with a(0)=0.
  • A180665 (program): Golden Triangle sums: a(n)=a(n-2)+A001654(n) with a(0)=0 and a(1)=1.
  • A180666 (program): Golden Triangle sums: a(n)=a(n-4)+A001654(n) with a(0)=0, a(1)=1, a(2)=2 and a(3)=6.
  • A180668 (program): a(n) = a(n-1)+a(n-2)+a(n-3)+4*n-8 with a(0)=0, a(1)=0 and a(2)=1.
  • A180669 (program): a(n) = a(n-1)+a(n-2)+a(n-3)+4*n^2-16*n+18 with a(0)=0, a(1)=0 and a(2)=1.
  • A180670 (program): a(n) = a(n-1)+a(n-2)+a(n-3)+(8*n^3-48*n^2+112*n-96)/3 with a(0)=0, a(1)=0 and a(2)=1.
  • A180671 (program): a(n) = Fibonacci(n+6) - Fibonacci(6).
  • A180672 (program): a(n) = Fibonacci(n+7) - Fibonacci(7).
  • A180673 (program): a(n) = Fibonacci(n+8) - Fibonacci(8).
  • A180674 (program): a(n) = Fibonacci(n+9) - Fibonacci(9).
  • A180675 (program): The Ca3 sums of the Pell-Jacobsthal triangle A013609.
  • A180676 (program): The Gi3 sums of the Pell-Jacobsthal triangle A013609.
  • A180677 (program): The Gi4 sums of the Pell-Jacobsthal triangle A013609.
  • A180678 (program): The Ze2 sums of the Pell-Jacobsthal triangle A013609.
  • A180680 (program): Expansion of e.g.f. (1 - sqrt(1 - 4*LambertW(x)))/2.
  • A180687 (program): G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x/(1-x))^n/n!.
  • A180707 (program): a(n) = sigma(2*a(n-1)) for n>1 with a(1)=1.
  • A180708 (program): a(n) = sigma(3*a(n-1)) for n>1 with a(1)=1.
  • A180709 (program): a(n) = sigma(n*a(n-1)) for n>1 with a(1)=1.
  • A180713 (program): If n is even then a(n) = 3n, if n == 1 mod 4 then a(n) = 3n+1, if n == 3 mod 4 then a(n) = 3n+2.
  • A180714 (program): Sum of the x- and y-coordinates of a point moving in a clockwise spiral.
  • A180724 (program): a(n) = n^2 + largest prime < n^2.
  • A180733 (program): Largest element of n-th row of Pascal’s triangle that is not a multiple of n.
  • A180735 (program): Expansion of (1+x)*(1-x)/(1 - x + x^2 + x^3).
  • A180736 (program): a(n) = [r]*[2r]*…[nr], where r=sqrt(2) and []=floor.
  • A180739 (program): Diagonal of array arising in computing the number of numerical semigroups using generating functions.
  • A180746 (program): Partial sums of A004144.
  • A180748 (program): Numbers k such that k^2 - k + 1 is semiprime.
  • A180752 (program): Half the number of nX3 binary arrays with each element equal to at least two neighbors
  • A180762 (program): Half the number of nX2 binary arrays with each element equal to at least one neighbor
  • A180772 (program): Number of distinct solutions to the congruence x(1)*x(2) == 0 (mod n), with x() only in 1..n-1.
  • A180844 (program): a(n) = (27^n - 2^n)/25.
  • A180845 (program): a(n) = (16^n-3^n)/13
  • A180846 (program): a(n) = (81^n - 2^n)/79.
  • A180847 (program): a(n) = (27^n-4^n)/23.
  • A180851 (program): Sum of divisors as increasing powers.
  • A180853 (program): Trajectory of 4 under map n->A006368(n).
  • A180854 (program): Square array read by antidiagonals: T(m,n) is the Wiener index of the lollipop graph L(m,n) (m>=1, n>=1). L(m,n) is the graph obtained by joining the complete graph K_m to the path graph P_n by an edge. The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
  • A180857 (program): Wiener index of the Moebius ladder M(n).
  • A180858 (program): Square array read by antidiagonals: T(p,n) is the Wiener index of the fan graph F(p,n) (p>=1, n>=1). F(p,n) is the graph obtained by placing an edge between each node of the empty graph on p nodes and each node of the path graph on n nodes.
  • A180859 (program): Square array read by antidiagonals: T(m,n) is the Wiener index of the windmill graph D(m,n) obtained by taking n copies of the complete graph K_m with a vertex in common (i.e., a bouquet of n pieces of K_m graphs; m>=2, n>=1).
  • A180861 (program): Wiener index of the n-pan graph.
  • A180862 (program): Square array read by antidiagonals: T(m,n) is the Wiener index of the flower graph F(m,n) (m>=2, n>=1). F(m,n) is the graph obtained by joining with an edge a node in the star graph on m nodes to an end-node of the path graph P_n. The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
  • A180863 (program): Wiener index of the n-sun graph.
  • A180864 (program): Trajectory of 13 under map n->A006368(n).
  • A180870 (program): D(n,x) is the Dirichlet kernel = sin((n+1/2)x)/sin(x/2). This triangle gives in row n, n >= 0, the coefficients of descending powers of x of the polynomial D(n, arccos(x)).
  • A180875 (program): Sum_{j>=1} j^n*2^j/binomial(2*j,j) = r_n*Pi/2 + s_n with integer r_n and s_n; sequence gives s_n.
  • A180879 (program): Number of permutations p() of 1..n+2 with centered difference p(i+1)-p(i-1) < 0 exactly once
  • A180918 (program): ‘DPE(n,k)’ triangle read by rows. DPE(n,k) is the number of k-double-palindromes of n up to cyclic equivalence.
  • A180919 (program): a(n) = n^2 + 731*n + 1.
  • A180920 (program): Numbers k such that the sum of the cubes of the k consecutive integers starting from k is a square.
  • A180923 (program): Numbers n such that 111*n + 1 is prime.
  • A180926 (program): Numbers k such that 6*k and 10*k are triangular numbers.
  • A180938 (program): Smallest k such that k*n has an even number of 1’s in its base-2 expansion.
  • A180955 (program): Numerator in triangle T(n,k)=A180955/A180956 read by rows. A001790(A004736).
  • A180956 (program): Denominator in triangle T(n,k)=A180955/A180956 read by rows. A046161(A004736).
  • A180958 (program): Diagonal sums of generalized Narayana triangle A180957.
  • A180963 (program): Numbers divisible by 3 with an odd number of 1s in their base 2 representation.
  • A180964 (program): a(0)=1; for n>0, a(n) = 1 + 3*A117571(n-1).
  • A180965 (program): Number of tatami tilings of a 2 X n grid (with monomers allowed).
  • A180966 (program): Hankel transform of A123164.
  • A180967 (program): Number of n-game win/loss series that contain at least one dead game.
  • A180968 (program): The only integers that cannot be partitioned into a sum of six positive squares.
  • A180969 (program): Array read by antidiagonals: a(k,n) = natural numbers each repeated 2^k times.
  • A180972 (program): Numbers n such that 8^9 + n^2 is a square.
  • A180973 (program): Numbers n such that 9^10 + n^2 is a square.
  • A180975 (program): Array of the “egg-drop” numbers, read by downwards antidiagonals.
  • A180986 (program): T(n,k) = number of n X k binary matrices with rows in lexicographically nondecreasing order and columns in lexicographically nonincreasing order.
  • A180987 (program): T(n,k)=number of nXk binary matrices with rows in lexicographically nonincreasing order and columns in lexicographically strictly increasing order
  • A181020 (program): Maximum number of 1s in an nX(n+1) binary matrix with no three 1s adjacent in a line along a row, column or diagonally.
  • A181021 (program): Maximum number of 1s in an nX(n+2) binary matrix with no three 1s adjacent in a line along a row, column or diagonally.
  • A181048 (program): Decimal expansion of (log(1+sqrt(2))+Pi/2)/(2*sqrt(2)) = Sum_{k>=0} (-1)^k/(4*k+1).
  • A181049 (program): Decimal expansion of (Pi/2 - log(1+sqrt(2)))/(2*sqrt(2)) = Sum_{k>=0} (-1)^k/(4k+3).
  • A181050 (program): Decimal expansion of the constant 1+3/(5+7/(9+11/(13+…))), using all odd integers in this generalized continued fraction.
  • A181062 (program): Prime powers minus 1.
  • A181065 (program): a(n)=(F(n)-sumofdigits(F(n)))/9, where F(n) = A000045(n).
  • A181066 (program): Expansion of g.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^3 *x^k ] *x^n/n ).
  • A181067 (program): a(n) = Sum_{k=0..n-1} binomial(n-1,k)^2 * binomial(n,k).
  • A181068 (program): Expansion of g.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^4 *x^k ] *x^n/n ).
  • A181069 (program): Expansion of l.g.f.: Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^4 *x^k ] *x^n/n.
  • A181070 (program): Expansion of G.f.: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^(k+1)*x^k)*x^n/n ).
  • A181071 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^(k+1) * n/(n-k).
  • A181074 (program): Expansion of g.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^(k+1) *x^k ] *x^n/n ).
  • A181075 (program): a(n) = Sum_{k=0..n-1} C(n-1,k)^(k+1) * n/(n-k).
  • A181076 (program): G.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^n *x^k ] *x^n/n ).
  • A181077 (program): a(n) = Sum_{k=0..n-1} C(n-1,k)^(n-k) * n/(n-k).
  • A181078 (program): Expansion of g.f.: exp( Sum_{n>=1} [ Sum_{k>=0} C(n+k-1,k)^(n+k-1) *x^k ] *x^n/n ).
  • A181079 (program): a(n) = Sum_{k=0..n-1} binomial(n-1,k)^(n-1) * n/(n-k).
  • A181082 (program): Expansion of g.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^(n+k) * x^k] * x^n/n ).
  • A181083 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^n * n/(n-k).
  • A181084 (program): Expansion of g.f.: exp( Sum_{n>=1} [Sum_{k=0..n} binomial(n,k)^(n+k+1) * x^k] * x^n/n ).
  • A181085 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^(n+1) * n/(n-k).
  • A181090 (program): Sum_{d|F(n)} d^3, where F(n) are the Fibonacci numbers
  • A181092 (program): a(n) is the sum of n addends nested as follows: floor(sqrt(floor(sqrt(…(n)…)))).
  • A181093 (program): p*(p+2)/3 where p and p+4 are primes.
  • A181099 (program): Exchange rightmost two ternary digits of n > 1; a(0)=0, a(1)=3.
  • A181100 (program): Numbers k such that A028260(k) + 1 is prime.
  • A181106 (program): Largest odd number strictly less than a square.
  • A181116 (program): Triangle T(n,k) read by rows. T(n,k) = A046643(A126988).
  • A181117 (program): Triangle T(n,k) read by rows. T(n,k) = A046644(A126988).
  • A181118 (program): Sequencing of all rational numbers p/q > 0 as ordered pairs (p,q). The rational (p,q) occurs as the n-th ordered pair where n=(p+q-1)*(p+q-2)/2+q.
  • A181120 (program): Partial sums of round(n^2/12) (A069905).
  • A181132 (program): a(0)=0; thereafter a(n) = total number of 0’s in binary expansions of 1, …, n.
  • A181133 (program): a(n) = n + A003056(n).
  • A181134 (program): Sum of 13th powers: a(n) = Sum_{j=0..n} j^13.
  • A181137 (program): The number of ways to color n balls in a row with 3 colors with no color runs having lengths greater than 3.
  • A181138 (program): Least positive integer k such that n^2 + k is a cube.
  • A181140 (program): The number of ways to color n balls in a row with 3 colors with no color runs having lengths greater than 4. This sequence is a special case of the general problem for coloring n balls in a row with p colors where each color has a given maximum run-length. In this example, the bounds are uniformly 4. It can be phrased in terms of tossing a p-faced dice n times, requiring each face having no runs longer than b.
  • A181142 (program): Number of permutations of {1,2,…,2n} , say x(1),x(2), … , x(2n) , such that x(i) + x(i+1) is not equal to 2n-1 for all i, 1<=i<=2n-1.
  • A181149 (program): a(n) = prime(n)^3 + prime(n)^2 + prime(n).
  • A181150 (program): a(n) = prime(n)^3 + prime(n) + 1.
  • A181151 (program): a(n) = prime(n)^3 + prime(n)^2 + 1.
  • A181155 (program): Odious numbers (A000069) plus one; complement of A026147.
  • A181156 (program): Odd Fibonacci numbers F which have a proper Fibonacci divisor G such that F/G is a Lucas number or a product of Lucas numbers.
  • A181161 (program): Numerator in abs(binomial(-1/8,n)).
  • A181167 (program): G.f.: 1 = Sum_{n>=0} a(n)*x^n* Sum_{k>=0} C(2n+k,k)^2*(-x)^k.
  • A181170 (program): Number of connected 9-regular simple graphs on 2n vertices with girth at least 4.
  • A181172 (program): Primes whose base 4 representation does not contain a 0.
  • A181173 (program): Primes whose base 5 representation does not contain a 0.
  • A181174 (program): The “Row2” sums of the powers-of-2 triangle A000079
  • A181175 (program): The “Fi1” sums of the powers-of-2 triangle A000079
  • A181176 (program): The minimum absolute value obtainable by partitioning the first n consecutive integers into two sets and subtracting the two sums of the sets.
  • A181183 (program): a(n) = sigma(tau(n)) (mod 2).
  • A181184 (program): | (n-th digit of Pi) - (n-th digit of phi (golden ratio)) |.
  • A181189 (program): Maximal number of elements needed to identify an abelian group of order n by testing the order of random elements.
  • A181192 (program): Number of n X 5 matrices containing a permutation of 1..n*5 in increasing order rowwise, columnwise, diagonally and (downwards) antidiagonally.
  • A181201 (program): a(n) = 0!*1!*2!*(3*n)!*3*n*(n-1) / ((n)!*(n+1)!*(n+2)!).
  • A181202 (program): a(n)=0!*1!*2!*3!*(4*n)!*6*n*(n-1) / ((n)!*(n+1)!*(n+2)!*(n+3)!)
  • A181208 (program): Number of n X 4 binary matrices with no two 1’s adjacent diagonally or antidiagonally.
  • A181214 (program): Number of n X 3 binary matrices with no three 1’s adjacent in a line diagonally or antidiagonally.
  • A181237 (program): Number of (3n) X 3 binary matrices with all row sums equal and all column sums equal.
  • A181246 (program): Number of n X 3 binary matrices with no 2 X 2 block having four 1’s.
  • A181270 (program): Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly increasing order.
  • A181278 (program): Number of 2 X n binary matrices M with rows in strictly increasing order and rows of M*Mtranspose (mod 2) in strictly decreasing order.
  • A181281 (program): A version of Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,…,n in a circle, increasing clockwise. Starting with i=1, delete the integer 4 places clockwise from i. Repeat, counting 4 places from the next undeleted integer, until only one integer remains.
  • A181282 (program): a(n) is the number of associate Rota-Baxter words in one idempotent generator x and one idempotent operator P of degree n. Such words are Rota-Baxter words that begin and/or ends with x, and P is applied n times in the word.
  • A181286 (program): Partial sums of floor(n^2/3) (A000212).
  • A181287 (program): Numbers of the form i*5^j-1 (i=1..4, j >= 0).
  • A181288 (program): Numbers of the form i*6^j-1 (i=1..5, j >= 0).
  • A181289 (program): Triangle read by rows: T(n,k) is the number of 2-compositions of n having length k (0 <= k <= n).
  • A181290 (program): The sum of the lengths of the 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n. The length of the 2-composition is the number of columns.
  • A181292 (program): The sum of the entries in the top rows of all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181294 (program): Number of 0’s in all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181296 (program): The number of odd entries in all the 2-compositions of n.
  • A181298 (program): The number of even entries in all the 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181300 (program): Number of columns with top entry equal to bottom entry in all the 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181301 (program): Number of 2-compositions of n having no column with equal entries. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181303 (program): Numbers of the form i*7^j-1 (i=1..6, j >= 0).
  • A181305 (program): Number of increasing columns in all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181306 (program): Number of 2-compositions of n having no increasing columns. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181318 (program): a(n) = A060819(n)^2.
  • A181319 (program): Numbers n with property that there is a different number m such that the lunar squares n*n and m*m are the same.
  • A181324 (program): G.f. 1/(1-sum(n=1,N,x^(n*(3*n-1)/2)))
  • A181326 (program): Number of columns with an odd sum in all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181329 (program): Number of 2-compositions of n having no column with an even sum. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181330 (program): Triangle read by rows: T(n,k) is the number of 2-compositions of n having k 0’s in the top row A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181331 (program): Number of 0’s in the top rows of all 2-compositions of n.
  • A181332 (program): Triangle read by rows: T(n,k) is the number of 2-compositions of n having k nonzero entries in the top row. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181335 (program): Partial products of A036691.
  • A181337 (program): Number of even entries in the top rows of all 2-compositions of n. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181342 (program): a(n) = (35*n^4 - 105*n^3 + 160*n^2 - 120*n + 36)/6.
  • A181343 (program): a(n) = (35*n^4 - 35*n^3 + 55*n^2 - 25*n + 6)/6.
  • A181346 (program): Absolute difference between (sum of previous terms) and prime(n) with a(0) = 1 and a(1) = 2.
  • A181351 (program): Exchange 2 and 5 in the prime factorization of n.
  • A181353 (program): a(n) = 9*a(n-1) + 3*a(n-2); a(0)=0, a(1)=1.
  • A181354 (program): Number of n-digit perfect cubes.
  • A181357 (program): Sum of squares of digits of Fibonacci(n).
  • A181358 (program): Number of twiddle factors in the first stage of a Pease Radix 4 Fast Fourier Transform.
  • A181361 (program): Sum of cubes of digits of Fibonacci(n).
  • A181363 (program): 1 followed by the primes, interleaved recursively.
  • A181364 (program): Fibonacci numbers whose digits, when squared, sum to a prime.
  • A181367 (program): Number of 2-compositions of n containing at least one 0 entry. A 2-composition of n is a nonnegative matrix with two rows, such that each column has at least one nonzero entry and whose entries sum up to n.
  • A181371 (program): Triangle read by rows: T(n,k) is the number of ternary words (i.e., finite sequences of 0’s, 1’s and 2’s) of length n having k occurrences of 01’s (0 <= k <= floor(n/2)).
  • A181372 (program): Square array read by antidiagonals: a(p,n) is the number of inversions in all p-ary words of length n on {0,1,2,…,p-1} (p>=2, n>=2).
  • A181374 (program): Let f(n) = Sum_{j>=1} j^n*3^j/binomial(2*j,j) = r_n*Pi/sqrt(3) + s_n; sequence gives s_n.
  • A181385 (program): Maximal number that can be obtained by reversing n in an integer base.
  • A181388 (program): a(n) = Sum_{k=1..n} 2^T(k-1), where T = A000217 are the triangular numbers 0, 1, 3, 6, 10, … . For n=0 we have the empty sum equal to 0.
  • A181389 (program): Absolute difference between (sum of previous terms) and (n-th-even square) with a(1) = 2.
  • A181390 (program): Absolute difference between (sum of previous terms) and (n-th-odd square) with a(1) = 1.
  • A181402 (program): Total number of positive integers below 10^n requiring 7 positive cubes in their representation as sum of cubes.
  • A181404 (program): Total number of positive integers below 10^n requiring 8 positive cubes in their representation as sum of cubes.
  • A181405 (program): Total number of n-digit numbers requiring 8 positive cubes in their representation as sum of cubes.
  • A181406 (program): Symbolic sequence at the accumulation point of the 3*2^{k} supercycles of unimodal maps.
  • A181407 (program): a(n) = (n-4)*(n-3)*2^(n-2).
  • A181410 (program): G.f.: exp( Sum_{n>=1} A181411(n)*x^n/n ) where A181411(n) = Sum_{k=0..n} C(n,k)*sigma(n+k).
  • A181411 (program): a(n) = Sum_{k=0..n} C(n,k)*sigma(n+k) for n>=1.
  • A181418 (program): a(n) = A000984(n)*A000172(n), which is the term-wise product of the Central binomial coefficients and Franel numbers, respectively.
  • A181426 (program): Numerator of Sum_{k=1..n} k^4 / Product_{k=1..n} k^4.
  • A181427 (program): a(n) = n + [n^2 if n is odd or n^3 if n is even].
  • A181428 (program): a(n) = prime(n+2) + prime(n+1) - prime(n).
  • A181432 (program): Symmetric square array T(n,k) read by antidiagonals. T(n,k)=A008836(n)*A008836(k).
  • A181433 (program): Numbers k such that 11*k is 5 less than a square.
  • A181434 (program): First column in matrix inverse of a mixed convolution of A052542.
  • A181435 (program): First column in matrix inverse of a mixed convolution of A052906.
  • A181440 (program): a(1) = 2; for n > 1, a(n) = A000217(n)-(sum of previous terms).
  • A181442 (program): Expansion of (1 + x - 8*x^2 + x^3 + x^4) / ( (1 - x)*(1 - 10*x^2 + x^4) ).
  • A181443 (program): Solutions a(n) to (r(n)-5)*(r(n)-6) = 21 *a(n)*(a(n)-1).
  • A181449 (program): Numbers n such that 7 is the largest prime factor of n^2 - 1.
  • A181472 (program): Riordan array ((1+x)/(1+2x+2x^2),x(1+x)/(1+2x+2x^2)).
  • A181474 (program): Sequence related to the Hankel transform of A105523(n+5).
  • A181475 (program): a(n) = 3*n^4 + 6*n^3 - 3*n + 1.
  • A181477 (program): a(n) has generating function 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)) for k=5.
  • A181478 (program): a(n) has generating function 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)) for k=6.
  • A181479 (program): a(n) has generating function 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)) for k=7.
  • A181480 (program): a(n) has generating function 1/((1-x)^k*(1-x^2)^(k*(k-1)/2)) for k=8.
  • A181482 (program): The sum of the first n integers, with every third integer taken negative.
  • A181486 (program): Record values in A171919 = number of solutions to n=x*y*z, x+y=z+1.
  • A181497 (program): a(n) is the smallest m such that A056753(m) = 2*n + 1.
  • A181509 (program): a(1) = 2, a(n) = (n-th-even n^3) - (sum of previous terms)
  • A181510 (program): Number of permutations of the multiset {1,1,2,2,3,3,…,n+1,n+1} avoiding the permutation patterns {132, 231, 2134}
  • A181511 (program): Triangle T(n,k) = n!/(n-k)! read by rows, 0 <= k < n.
  • A181516 (program): Primes in A011371.
  • A181518 (program): a(n) is the number for which 2^A181516(n)||(2*a(n))!
  • A181520 (program): 2*A181518(n)-A181516(n).
  • A181527 (program): Binomial transform of A113127; (1, 1, 3, 7, 15, 31, …) convolved with (1, 3, 7, 15, 31, 63, …).
  • A181531 (program): Number of partitions of n with no part equal to 1 or 3.
  • A181532 (program): a(0) = 0, a(1) = 1, a(2) = 1; a(n) = a(n-1) + a(n-2) + a(n-4)
  • A181534 (program): Minimum number of rounds to be played to decide a two-player game of up to n rounds in which the winner of round j receives j points.
  • A181538 (program): T(n, k) = sum_(1 <= j <= k) [j | k] j mu(k / j) gcd(n, k), triangle read by rows.
  • A181540 (program): a(n) = Sum_{k=0..n} gcd(n,k)*phi(k).
  • A181543 (program): Triangle of cubed binomial coefficients, T(n,k) = C(n,k)^3, read by rows.
  • A181545 (program): G.f.: A(x) = Sum_{n>=0} (3n)!/(n!)^3 * x^(3n)/(1-x-x^2)^(3n+1).
  • A181546 (program): a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)^4.
  • A181547 (program): a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)^5.
  • A181549 (program): a(n) = Sum_{k|n} k*mu_2(n/k).
  • A181553 (program): Coefficient of x^n in (x^2 + 98*x + 1)^n.
  • A181560 (program): a(n+1) = a(n-1) + 2 a(n-2) - a(n-4) ; a(0)=1, a(n)=0 for 0 < n < 5;
  • A181563 (program): Almost-Liouville function.
  • A181565 (program): a(n) = 3*2^n + 1.
  • A181566 (program): Expected number of elements needed to identify an abelian group of order n by testing the order of random elements.
  • A181569 (program): Greatest common divisor of n! and n+1.
  • A181570 (program): Primes in A050798.
  • A181571 (program): Third column of triangle in A179898.
  • A181577 (program): Prime number of trailing end 0’s associated with p! where p = A181576.
  • A181578 (program): The number k such that each of the five factorials (5k+j)!, j=0..4, has exactly n trailing zeros in its base-10 representation; 0 if no such k exists.
  • A181579 (program): Smallest number m such that m! ends in exactly n trailing 0’s (or 0 if no such m exists).
  • A181586 (program): a(0)=0; a(n+1) = 2*a(n) + period 4:repeat 0,1,-2,1.
  • A181587 (program): If n is even, a(n) = 0, if n is odd, a(n) = A002321(n), where A002321 is Mertens’s function.
  • A181589 (program): Least value of n such that P(n) - 1/e < 10^(-i), i=1,2,3… . P(n) = (n/(n+1))^(n-1) the probability of a random forest on n be a tree.
  • A181590 (program): Least value of n such that |P(n) - 1/e| < 10^(-i), i=1,2,3… . P(n)=floor(n!/e + 1/2)/n! is the probability of a random permutation on n objects be a derangement.
  • A181591 (program): a(n) = binomial(bigOmega(n),omega(n)), where omega = A001221 and bigOmega = A001222.
  • A181600 (program): Expansion of 1/(1 - x - x^2 + x^8 - x^10).
  • A181603 (program): Twin primes ending in 1.
  • A181604 (program): Twin primes ending in 3.
  • A181605 (program): Twin primes ending in 7.
  • A181606 (program): Twin primes ending in 9.
  • A181611 (program): Position of rightmost zero in 2^n (including leading zero).
  • A181617 (program): Molecular topological indices of the complete graph K_n.
  • A181618 (program): Number of n-game win/loss/draw series that contain at least one dead game.
  • A181624 (program): Decimal expansion of 486^(1/3).
  • A181625 (program): Problem 17 in Knuth’s Art of Computer Programming, vol. 1, section 1.3.3 asks which is the average length L(k) of the cycles among the permutations on k elements. The n-th term of this sequence is the least k such that L(k) >= n.
  • A181626 (program): Number of closed walks of length n in a kite graph (K4 with one edge deleted).
  • A181631 (program): Triangle by rows, number of leading 1’s in Fibonacci Maximal notation.
  • A181635 (program): Expansion of 36*x^2*(1+36*x^2-6*x) / ((36*x^2+6*x+1)*(1-6*x)^2).
  • A181639 (program): Numbers n such that omega(n) = digit-reverse(n).
  • A181640 (program): Partial sums of floor(n^2/5) (A118015).
  • A181641 (program): Expansion of sqrt(1-4*x)/(1+x).
  • A181645 (program): Triangle Id-(xc(x),xc(x)), c(x) the g.f. of the Catalan numbers A000108.
  • A181648 (program): Expansion of x^(-2/3) * psi(x) * c(x^2) / 3 in powers of x where psi() is a Ramanujan theta function and c() is a cubic AGM theta function.
  • A181649 (program): An INVERT sequence for A010054.
  • A181650 (program): Inverse of number triangle A070909.
  • A181651 (program): Eigentriangle of number triangle A070909.
  • A181652 (program): Inverse of number triangle A181651.
  • A181653 (program): Generalized (conditional) Riordan array with k-th column generated by x^k*(1+x) if k mod 2 = 0, x^k*(1+x+x^2) otherwise.
  • A181654 (program): An eigentriangle of the number triangle A181653.
  • A181655 (program): Expansion of (1+2x-x^3+x^4)/(1-4x^2+3x^4).
  • A181656 (program): Generalized (conditional) Riordan array with k-th column generated by x^k*(1+x^2) if k mod 2 = 0, x^k*(1+x) otherwise.
  • A181658 (program): Row sums of A181657.
  • A181663 (program): a(n) = A105801(n) mod 2.
  • A181666 (program): Odd part of a(n) is of form (4^k-1)/3.
  • A181668 (program): Period 12: repeat [5,5,5,2,2,2,8,8,8,2,2,2].
  • A181670 (program): Triangle read by rows: 2^(n-1) mod prime(k), 1<=k<=n.
  • A181675 (program): V(n,n^2), where V is the number of integer points in an n-dimensional sphere of Lee-radius n^2 centered at the origin.
  • A181679 (program): a(n) = 121*n^2 + 2*n.
  • A181685 (program): Expansion of 36*x^2*(1+6*x-36*x^2) / ( (1-6*x)^2 *(1+6*x+36*x^2) ).
  • A181687 (program): Numbers n such that the number of odd divisors of (2n)^2 is an odd divisor of (2n)^2, and the number of even divisors of (2n)^2 is an even divisor of (2n)^2.
  • A181688 (program): Number of maximal self-avoiding walks from NW to SW corners of a 4-by-n grid
  • A181690 (program): Riordan array T((1-x)^(-2) | 2x-1) read by rows.
  • A181691 (program): Numbers n with property that Fibonacci(n) has exactly two 1’s.
  • A181697 (program): Length of the complete Cunningham chain of the first kind starting with prime(n).
  • A181709 (program): Indices of primes in A007310.
  • A181712 (program): Floor(3*n*tau)-Floor(2*n*tau)-Floor(n*tau), where tau=(1+sqrt(5))/2, the golden ratio.
  • A181713 (program): Solutions of A181712(n)=0.
  • A181714 (program): Solutions of A181712(n)=1.
  • A181715 (program): Length of the complete Cunningham chain of the second kind starting with prime(n).
  • A181716 (program): a(n) = a(n-1) + a(n-2) + (-1)^n, with a(0)=0 and a(1)=1.
  • A181717 (program): Fibonacci-Collatz sequence: a(1)=0, a(2)=1; for n>2, let fib=a(n-1)+a(n-2); if fib is odd then a(n)=3*fib+1 else a(n)=fib/2.
  • A181718 (program): a(n) = (1/9)*(10^(2*n) + 10^n - 2).
  • A181719 (program): a(n) = A133473(n+1)^2.
  • A181732 (program): Numbers n such that 90n + 1 is prime.
  • A181733 (program): a(n) = A139708(n) - A092323(n).
  • A181734 (program): G.f. A(x) satisfies: A(x) = (1 + x*A(x)) * (1 + x^2*A(x)^3).
  • A181736 (program): The number of integers in base 2n such that all digits are used exactly once (so length is 2n) and for each m<=2n the base 2n integer consisting of the first m digits is divisible by m.
  • A181738 (program): T(n, k) is the coefficient of x^k of the polynomial p(n) which is defined as the scalar part of P(n) = Q(x+1, 1, 1, 1) * P(n-1) for n > 0 and P(0) = Q(1, 0, 0, 0) where Q(a, b, c, d) is a quaternion, triangle read by rows.
  • A181741 (program): Primes of the form 2^t-2^k-1, k>=1.
  • A181742 (program): Let A181741(n)=2^(t(n))-2^(k(n))-1, where k(n)>=1, t(n)>=k(n)+1. Then a(n)=t(n).
  • A181743 (program): The exponent k which defines A181741(n) = 2^t-2^k-1.
  • A181744 (program): Numbers n such that x(x+n)=y*y has one and only one positive integer solution (x,y).
  • A181747 (program): Odd noncomposite numbers that are the difference of 2 primes.
  • A181754 (program): a(1) = 1, a(2) = 2. For n >= 3, a(n) is found by concatenating the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).
  • A181755 (program): a(1) = 1, a(2) = 5. For n >= 3, a(n) is found by concatenating the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).
  • A181759 (program): Denominators of an extended Rydberg-Ritz spectrum of hydrogen atom: 1/9 -1/n^2.
  • A181760 (program): a(n) = (n!)(n!-1)(n!-2)…(n!-n+1).
  • A181762 (program): a(n) = n/2 if n is even, otherwise 3n+5.
  • A181763 (program): a(n) = A061037(n)^2.
  • A181766 (program): Numbers k such that 3*k + 7 is not prime.
  • A181768 (program): G.f.: (1/2)*(3 - sqrt((1-5*x)/(1-x))).
  • A181773 (program): Molecular topological indices of the cocktail party graphs.
  • A181780 (program): Numbers n which are Fermat pseudoprimes to some base b, 2 <= b <= n-2.
  • A181787 (program): Number of solutions to n^2 = a^2 + b^2 + c^2 with positive a, b, c.
  • A181788 (program): Number of solutions to n^2 = a^2 + b^2 + c^2 with nonnegative a, b, c.
  • A181795 (program): Numbers k such that the number of odd divisors of k is an odd divisor of k, and the number of even divisors of k is an even divisor of k.
  • A181796 (program): a(n) = number of divisors of n whose canonical prime factorizations contain no repeated positive exponents (cf. A130091).
  • A181797 (program): a(n) = n multiplied by the sum of its squarefree divisors (A048250(n)).
  • A181801 (program): Number of divisors of n that are highly composite (A002182).
  • A181811 (program): a(n) = smallest integer that, upon multiplying any divisor of n, produces a member of A025487.
  • A181812 (program): Range of values of A181811, in order of first appearance: a(n) = A181811(2n-1).
  • A181813 (program): a(n)=smallest integer that, upon multiplying any integer from 1 to n, produces a member of A025487.
  • A181814 (program): a(n)=smallest integer that, when divided by any integer from 1 to n, yields a member of A025487.
  • A181819 (program): Prime shadow of n: a(1) = 1; for n>1, if n = Product prime(i)^e(i), then a(n) = Product prime(e(i)).
  • A181821 (program): a(n) = smallest integer with factorization as Product p(i)^e(i) such that Product p(e(i)) = n.
  • A181829 (program): a(n) = 4*A060819(n-2)*A060819(n+2).
  • A181830 (program): The number of positive integers <= n that are strongly prime to n.
  • A181831 (program): The sum of positive integers <= n that are strongly prime to n.
  • A181832 (program): The product of the positive integers <= n that are strongly prime to n.
  • A181833 (program): The number of positive integers <= n that are not strongly prime to n.
  • A181836 (program): The product of primes <= n that are strongly prime to n.
  • A181839 (program): Minimum of { k<n | k>0 is strong prime to n}, or zero if this set is empty.
  • A181840 (program): Maximum of { k>0 | k<n and k is strongly prime to n }, or zero if this set is empty.
  • A181857 (program): a(n) = lcm(n^2, n!).
  • A181861 (program): a(n) = gcd(n^2, n!/floor(n/2)!^2).
  • A181867 (program): a(1) = 2, a(2) = 1. For n >= 3, a(n) is found by concatenating the first n-1 terms of the sequence in reverse order and then dividing the resulting number by a(n-1).
  • A181868 (program): a(1) = 10, a(2) = 1. For n >= 3, a(n) = concatenate a(n-1), a(n-2), …, a(1) and then divide the resulting number by a(n-1).
  • A181874 (program): Minute hand closest to hour hand on analog quartz clock. Best approximation for seconds.
  • A181878 (program): Coefficient array for square of Chebyshev S-polynomials.
  • A181879 (program): Expansion of x*(1+x)/(1-3*x-4*x^2-x^3).
  • A181880 (program): Expansion of 1/(1-4*x-3*x^2-x^3).
  • A181885 (program): Integer nearest (1/n)*(r^n), where r = golden ratio = (1 + sqrt(5))/2.
  • A181888 (program): Second column of triangle in A182971.
  • A181889 (program): Bisection of A181888.
  • A181890 (program): a(n) = 8*n^2 + 14*n + 5.
  • A181892 (program): (n!/4-1)^2.
  • A181894 (program): Sum of factors from A050376 in Fermi-Dirac representation of n.
  • A181900 (program): a(n) = n * A022998(n).
  • A181904 (program): a(n) = 2*(4^n - 1) / A027760(n)
  • A181905 (program): Expansion of (b(q^3)^3 - b(q)^3) / 9 in powers of q where b() is a cubic AGM theta function.
  • A181923 (program): Nonprimes (A018252) mod 2.
  • A181932 (program): A003136(n) mod 2.
  • A181933 (program): a(n) = Sum_{k=0..n} binomial(n+k,k)*sin(Pi*(n+k)/2).
  • A181940 (program): a(0)=0, and there are a(n) terms between a(n) and the nearest a(n)+1.
  • A181952 (program): n!, digits ordered, zeros omitted.
  • A181956 (program): Smallest prime greater than n*(n+1)^2/2.
  • A181962 (program): Numbers not expressed in form pi(n)+pi(sqrt(n)) with prime n.
  • A181963 (program): Prime-generating polynomial: 25*n^2 - 1185*n + 14083.
  • A181965 (program): a(n) = 10^(2n+1) - 10^n - 1.
  • A181966 (program): Sum of the sizes of normalizers of all prime order cyclic subgroups of the symmetric group S_n.
  • A181968 (program): 54n^3 - 1.
  • A181969 (program): Prime-generating polynomial: 16*n^2 - 292*n + 1373.
  • A181971 (program): Triangle read by rows: T(n,0) = 1, T(n,n) = floor((n+3)/2) and T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.
  • A181972 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=floor(n/2).
  • A181973 (program): Prime-generating polynomial: 16*n^2 - 300*n + 1447.
  • A181975 (program): The sequence {1, 2, 3, 4, 5, 4, 3, 2} repeated.
  • A181977 (program): Expansion of b(q) * c(q^3)^2 / 9 in powers of q where b(), c() are cubic AGM theta functions.
  • A181982 (program): Expansion of (1 - x^2)^2 * (1 + x)^2 / (1 - x^6) in powers of x.
  • A181983 (program): a(n) = (-1)^(n+1) * n.
  • A181984 (program): INVERT transform of A028310.
  • A181988 (program): If n is odd, a(n) = (n+1)/2; if n is even, a(n) = a(n/2) + A003602(n).
  • A181989 (program): Number of independent sets of nodes in graph C_5 x P_n (n >= 0).
  • A181993 (program): Denominator of (4^n*(4^n-1)/2)*B_{2n}/(2n)!, B_{n} Bernoulli number.
  • A181995 (program): a(n) = if n mod 2 = 1 then n*(n - 1) else (n - 1)^2 + (n - 2)/2.
  • A182000 (program): G.f.: exp( Sum_{n>=1} 2^A090740(n) * x^n/n ) where A090740(n) = highest exponent of 2 in 3^n-1.
  • A182001 (program): Riordan array ((2*x+1)/(1-x-x^2), x/(1-x-x^2)).
  • A182004 (program): Expansion of q^(-1/4) * (eta(q^4) * eta(q^25) + eta(q) * eta(q^100))^2 / (eta(q^2) * eta(q^50)) in powers of q.
  • A182007 (program): Decimal expansion of 2*sin(Pi/5); the ‘associate’ of the golden ratio.
  • A182013 (program): Triangle of partial sums of Motzkin numbers.
  • A182016 (program): Central coefficients of triangle A182013.
  • A182017 (program): Row square-sums of triangle A182013.
  • A182018 (program): Row square-sums of triangle A210658.
  • A182025 (program): a(n) = 31*binomial(2*n,n-4) + Sum_{i=1..n-4} binomial(2*n,n-4-i)*(4+i).
  • A182026 (program): a(n) = 288*binomial(2*n,n-5) + 8*Sum_{i=1..n-5} binomial(2*n,n-5-i)*(5+i).
  • A182027 (program): a(n) = number of n-lettered words in the alphabet {1, 2} with as many occurrences of the substring (consecutive subword) [1, 1] as of [2, 2].
  • A182028 (program): Take first n bits of the infinite Fibonacci word A003849, regard them as a binary number, then convert it to base 10.
  • A182031 (program): Expansion of q^(-5/24) * (eta(q^3) * eta(q^6))^3 / (eta(q) * eta(q^2))^4 in powers of q.
  • A182037 (program): Expansion of 1 - (1 - 2x - x^2)^(1/2).
  • A182042 (program): Triangle T(n,k), read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (3, 0, -3/2, 3/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A182047 (program): Smallest prime > n*(n+1).
  • A182056 (program): Expansion of psi(x) * chi(-x^3) * f(-x^16) * chi(-x^24) / phi(-x^12)^2 in powers of x where phi(), psi(), chi(), f() are Ramanujan theta functions.
  • A182057 (program): Expansion of psi(x) * f(x^4) / (psi(x^3) * f(x^6) * chi(-x^24)) in powers of x where psi(), chi(), f() are Ramanujan theta functions.
  • A182058 (program): Number of moves needed to solve the Towers of Hanoi puzzle with 6 pegs and n disks.
  • A182059 (program): Triangle, read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (2, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A182062 (program): T(n,k) = C(n+1-k,k)*k!*(n-k)!, the number of ways for k men and n-k women to form a queue in which no man is next to another man.
  • A182067 (program): a(n) = floor(n) - floor(n/2) - floor(n/3) - floor(n/5) + floor(n/30).
  • A182069 (program): Triangle of numbers 2^i*C(n,i) mod 3 converted to decimal.
  • A182079 (program): a(n) = floor(n*floor((n-1)/2)/3).
  • A182081 (program): Next semiprime after the partial sum of the first n semiprimes.
  • A182082 (program): Number of pairs, (x,y), with x >= y, whose LCM does not exceed n.
  • A182084 (program): 3*n - n/p, where p is the smallest prime dividing n.
  • A182091 (program): Numbers n such that (n-1)*n^2/2-1 is prime.
  • A182093 (program): Partial sums of A005590.
  • A182097 (program): Expansion of 1/(1-x^2-x^3).
  • A182105 (program): Number of elements merged by bottom-up merge sort.
  • A182112 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and (w+n)^2=x+y+w.
  • A182122 (program): Expansion of exp( arcsinh( 2*x ) ).
  • A182126 (program): a(n) = prime(n)*prime(n+1) mod prime(n+2).
  • A182139 (program): Inverse Moebius transform of A061142.
  • A182143 (program): Number of independent vertex sets in the Moebius ladder graph with 2n nodes (n >= 0).
  • A182148 (program): a(n) = Fibonacci(n-1)^n.
  • A182166 (program): The total number of components of size 2 over all simple labeled graphs on n nodes.
  • A182167 (program): Min( f(n), n-f(n) ), where f(n) = A002708(n) = Fibonacci(n) mod n.
  • A182168 (program): Decimal expansion of imaginary part of i^(1/4).
  • A182174 (program): a(n) = prime(n)^2 - n.
  • A182176 (program): Number of affine subspaces of GF(2)^n.
  • A182185 (program): G.f.: exp( Sum_{n>=1} 3^b(n) * x^n/n ) where b(n) = highest exponent of 3 in 2^n+1.
  • A182186 (program): Number b(n) of basic ideals in the Borel subalgebra of the untwisted affine Lie algebra of type B.
  • A182188 (program): A sequence of row differences for table A182119.
  • A182189 (program): a(n) = 6*a(n-1) - a(n-2) - 4 with n > 1, a(0)=1, a(1)=3.
  • A182190 (program): a(n) = 6*a(n-1) - a(n-2) + 4 with n > 1, a(0)=0, a(1)=4.
  • A182191 (program): a(n) = 6*a(n-1) - a(n-2) + 12 with n>1, a(0)=-1, a(1)=5.
  • A182193 (program): Sequence of row differences related to table A182355.
  • A182194 (program): a(1)=2, a(n)=a(n-1)^2 if the minimal natural number > 1 not yet in the sequence is greater than a(n-1), else a(n)=a(n-1)-1.
  • A182195 (program): Numbers n for which no numbers w,x,y, all in {1,…,n} satisfy x^2+x^2+y^2=2n.
  • A182200 (program): a(n) = prime(n)^2-3.
  • A182201 (program): Fibonacci-type sequence based on bitwise exclusive-or: a(0) = 0, a(1) = 1 and a(n) = a(n-1) + (a(n-1) xor a(n-2)).
  • A182202 (program): Fibonacci-type sequence based on bitwise inclusive-or: a(0) = 0, a(1) = 1 and a(n) = a(n-1) + (a(n-1) or a(n-2)).
  • A182205 (program): Iterate the map in A006368 starting at 40.
  • A182210 (program): Triangle T(n,k) = floor(k*(n+1)/(k+1)), 1 <= k <= n.
  • A182212 (program): Floor(n! / Fibonacci(n)).
  • A182213 (program): a(n) = n! mod Fibonacci(n).
  • A182214 (program): Bondage number of the Cartesian product graph G = C_n X K_2.
  • A182215 (program): Bondage number of the Cartesian product graph G = C_n X C_3.
  • A182220 (program): Largest number k such that there exists an extensional acyclic digraph on n labeled nodes with k sources.
  • A182228 (program): a(n) = 3*a(n-2) - a(n-1) for n > 1, a(0) = 0, a(1) = 1.
  • A182229 (program): a(n) = a(n-1) + floor(a(n-2)/3) with a(0)=2, a(1)=3.
  • A182230 (program): a(n) = a(n-1)+floor(a(n-2)/4) with a(0)=3, a(1)=4.
  • A182241 (program): a(n) = A161151(2*n)/2
  • A182242 (program): a(0)=0, a(n) = (a(n-1) + n) AND n.
  • A182243 (program): a(0)=0, a(n) = (a(n-1) AND n) + n.
  • A182247 (program): a(0)=0, a(n) = (a(n-1) + n) OR n.
  • A182248 (program): a(0)=0, a(n) = (a(n-1) OR n) + n.
  • A182253 (program): Nonprime numbers n such that n^2 + n + 1 is prime.
  • A182254 (program): Primorial(n) mod n!
  • A182255 (program): 81n^2 - 2247n + 15383.
  • A182256 (program): a(n) = 2^n - 2*n*A000048(n).
  • A182260 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w<x+y.
  • A182268 (program): Denominator of Euler(n, 3/14).
  • A182280 (program): a(n) = floor(a(n-1)/4)+a(n-2) with a(0)=3, a(1)=4.
  • A182281 (program): a(n) = floor(a(n-1)/3)+a(n-2) with a(0)=2, a(1)=3.
  • A182305 (program): a(n+1) = a(n) + floor(a(n)/4) with a(0)=4.
  • A182306 (program): a(n+1) = a(n) + floor(a(n)/5) with a(0)=5.
  • A182307 (program): a(n+1) = a(n) + floor(a(n)/6) with a(0)=6.
  • A182308 (program): a(n+1) = a(n) + floor(a(n)/7) with a(0)=7
  • A182310 (program): a(0)=0, a(n+1) = (a(n) XOR floor(a(n)/2)) + 1, where XOR is the bitwise exclusive-or operator
  • A182316 (program): a(n) = binomial(n^2 + 3*n, n) / (n+1)^2.
  • A182318 (program): List of positive integers whose prime tower factorization, as defined in comments, does not contain the prime 2.
  • A182321 (program): Number of iterations of A025581(n) required to reach 0.
  • A182323 (program): a(n) = (194*n + 3*(-1)^n + 1)/4 + 24.
  • A182324 (program): n + (initial digit of n) in decimal representation.
  • A182332 (program): Primes of the form n^3 + n - 1.
  • A182334 (program): Triangular numbers that differ from a square by 1.
  • A182339 (program): List of positive integers whose prime tower factorization, as defined in comments, contains the prime 2.
  • A182346 (program): Primes of the form n^4 + 6.
  • A182347 (program): Primes of the form n^4 - 2.
  • A182348 (program): Primes of the form n^4 - 3.
  • A182349 (program): G.f.: exp( Sum_{n>=1} 6 * A084214(n) * x^n/n ) where g.f. of A084214 is (1+x^2)/((1+x)*(1-2*x)).
  • A182350 (program): Primes of the form n^4 - 5.
  • A182358 (program): Numbers n for which the number of divisors of n is congruent to 2 mod 4.
  • A182361 (program): a(n+1) = a(n) + floor(a(n)/8) with a(0)=8.
  • A182362 (program): a(n+1) = a(n) + floor(a(n)/9) with a(0)=9.
  • A182363 (program): a(n+1) = a(n) + floor(a(n)/10) with a(0)=10.
  • A182384 (program): Primes of the form n^5 + n^4 + n^3 + n^2 + n - 1.
  • A182385 (program): Primes of the form n^4 + n^3 + n^2 + n - 1.
  • A182386 (program): a(0) = 1, a(n) = 1 - n * a(n-1).
  • A182388 (program): a(0)=1, a(n) = (a(n-1) XOR n) + n.
  • A182394 (program): Signs of differences of number of divisors function: a(n) = sign(d(n)-d(n-1)), cf. A000005.
  • A182398 (program): a(n) = (Sum_{k=1..2n} k^2n) mod 2n.
  • A182400 (program): Integral factorial ratio sequence: a(n) = (2*n)!*(8*n)!/(n!*(4*n)!*(5*n)!).
  • A182401 (program): Number of paths from (0,0) to (n,0), never going below the x-axis, using steps U=(1,1), H=(1,0) and D=(1,-1), where the H steps come in five colors.
  • A182402 (program): Total number of digits in n-th row of a triangle formed by the positive integers.
  • A182409 (program): Prime-generating polynomial: 4n^2 + 12n - 1583.
  • A182411 (program): Triangle T(n,k) = (2*k)!*(2*n)!/(k!*n!*(k+n)!) with k=0..n, read by rows.
  • A182415 (program): a(0) = 1, a(1) = 2; for n>1, a(n) = a(n-1) + a(n-2) + 4.
  • A182417 (program): a(0)=0, a(n+1) = (a(n) XOR floor(a(n)/4)) + 1, where XOR is the bitwise exclusive-or operator.
  • A182421 (program): a(n) = Sum_{k = 0..n} C(n,k)^7.
  • A182422 (program): a(n) = Sum_{k = 0..n} C(n,k)^8.
  • A182427 (program): Triangular numbers that can be represented as a sum of a nonzero square number and a nonzero triangular number.
  • A182428 (program): a(n) = 2n(19-n).
  • A182430 (program): n! - A003149(n-1)
  • A182432 (program): Recurrence a(n)*a(n-2) = a(n-1)*(a(n-1)+3) with a(0) = 1, a(1) = 4.
  • A182434 (program): Number of primes p < n such that 4*p+1 is also prime.
  • A182435 (program): a(n) = 6*a(n-1) - a(n-2) - 2 with n>1, a(0)=0, a(1)=1.
  • A182442 (program): a(0)=0, a(1)=1, for n>1, a(n) = a(n-1)*2 + floor(a(n-2)/n).
  • A182443 (program): a(0)=0, a(1)=1, for n>1, a(n) = floor(a(n-1)/n) + a(n-2)*2.
  • A182444 (program): a(0)=0, a(1)=1, for n>1, a(n) = a(n-1) + (a(n-2) mod n).
  • A182445 (program): a(0)=0, a(1)=1, for n>1, a(n) = a(n-2) + (a(n-1) mod n).
  • A182446 (program): a(n) = Sum_{k = 0..n} C(n,k)^9.
  • A182447 (program): a(n) = Sum_{k = 0..n} C(n,k)^10.
  • A182448 (program): Decimal expansion of Pi^2/15.
  • A182453 (program): a(n) = 3^n - n*(n-1)/2.
  • A182454 (program): G.f. satisfies: A(x) = 1 + x*A(x) + x^2*A(x)^5.
  • A182455 (program): a(0)=1, a(n) = (a(n-1) mod (n+2))*(n+2).
  • A182456 (program): a(0)=1; for n>0, a(n) = ( a(n-1) mod (n+3) )*(n+3).
  • A182457 (program): a(0)=0, a(1)=1, a(n) = (a(n-2)*a(n-1)+1) mod n.
  • A182458 (program): a(0)=1, a(1)=2, a(n) = (a(n-2)*a(n-1)+1) mod n.
  • A182459 (program): Numbers n of initial person such that the n-th person survives in the duck-duck-goose game.
  • A182460 (program): a(n) = (3/5)*2^(4n+1) - (1/5).
  • A182461 (program): a(n) = 3*a(n-1) - 2*a(n-2) with a(0)=16 and a(1)=40.
  • A182462 (program): a(n) = 3a(n-1) - 2a(n-2) with a(0)=20 and a(1)=50.
  • A182464 (program): a(n) = 3a(n-1) - 2a(n-2) with a(0)=24 and a(1)=60.
  • A182465 (program): a(n) = 3a(n-1) - 2a(n-2) with a(0)=28 and a(1)=70.
  • A182466 (program): a(n) = 3a(n-1) - 2a(n-2) with a(0)=32 and a(1)=80.
  • A182467 (program): a(n) = 3a(n-1) - 2a(n-2) with a(0)=36 and a(1)=90.
  • A182469 (program): Triangle read by rows in which row n lists the odd divisors of n.
  • A182475 (program): Primes of the form p^2+10, where p is prime.
  • A182476 (program): Primes of the form p^2+100, where p is prime.
  • A182480 (program): Decimal expansion of 16000000/63.
  • A182481 (program): a(n) is the least k such that 6*k*n-1 and 6*k*n+1 are twin primes, and a(n)=0, if such k does not exist.
  • A182482 (program): 6*n*A182481(n)-1.
  • A182486 (program): Expansion of 2 * (2 + x) / (4 - x - x * sqrt(1 - 4*x)) in powers of x.
  • A182491 (program): T(n,k), a triangular array read by rows, is the Wiener index for the complete bipartite graph K(n,k).
  • A182492 (program): Expansion of 1 - x - (1 - sqrt(1 + 4*x^4)) / (2*x) in powers of x.
  • A182494 (program): Decimal expansion of 9091/9901.
  • A182505 (program): a(0)=0, a(1)=1, a(n) = ( (a(n-1)+a(n-2)) AND n) + n.
  • A182508 (program): a(0)=0, a(1)=1, a(n) = (a(n-2)+a(n-1)+n) AND n.
  • A182511 (program): a(0)=1, a(1)=2, a(n) = (a(n-2)*a(n-1) mod n) + 1.
  • A182512 (program): a(n) = (16^n - 1)/5.
  • A182520 (program): G.f.: x = Sum_{n>=1} a(n)*x^n * Sum_{k=0..n} (k+1)*binomial(n,k)*(-x)^k.
  • A182522 (program): a(0) = 1; thereafter a(2*n + 1) = 3^n, a(2*n + 2) = 2 * 3^n.
  • A182525 (program): a(n) = n! * Sum_{k=0..n} binomial(2*n, 2*k) / binomial(n,k).
  • A182531 (program): Extremal graph numbers for a triangle with an edge off it.
  • A182535 (program): Number of terms in Zeckendorf representation of prime(n).
  • A182536 (program): a(0)=0, a(1)=1, a(n)=(a(n-1) XOR a(n-2)) + n.
  • A182538 (program): a(n) = (a(n-1) AND a(n-2)) + n.
  • A182539 (program): a(n) = a(n-1) + (a(n-2) AND n).
  • A182541 (program): Coefficients in g.f. for certain marked mesh patterns.
  • A182542 (program): Second diagonal of triangle in A145879.
  • A182543 (program): Penultimate diagonal of triangle in A145879.
  • A182555 (program): G.f.: (3-4*x-sqrt(1-4*x^2))/(2*(1-2*x)^2).
  • A182556 (program): a(0)=1, a(n+1) = (a(n)*6) XOR a(n).
  • A182565 (program): Decimal expansion of Madelung constant (negated) for cuprous oxide Cu_2O.
  • A182566 (program): Decimal expansion of Madelung constant (negated) for zinc sulfide ZnS.
  • A182567 (program): Decimal expansion of Madelung constant (negated) for calcium fluoride CaF_2.
  • A182568 (program): a(n) = 2*floor(n/4)*(n - 2*(1 + floor(n/4))).
  • A182569 (program): Primes that have two terms in their Zeckendorf representation.
  • A182571 (program): Primes that have four terms in their Zeckendorf representation.
  • A182572 (program): Primes that have five terms in their Zeckendorf representation.
  • A182573 (program): Primes that have six terms in their Zeckendorf representation.
  • A182575 (program): Primes with equal number of 1’s and 0’s in their representation in base of Fibonacci numbers (A014417).
  • A182576 (program): Number of 1’s in the Zeckendorf representation of n^2.
  • A182577 (program): Number of ones in Zeckendorf representation of n!
  • A182578 (program): Number of ones in Zeckendorf representation of n^n.
  • A182579 (program): Triangle read by rows: T(0,0) = 1, for n>0: T(n,n) = 2 and for k<=floor(n/2): T(n,2*k) = n/(n-k) * binomial(n-k,k), T(n,2*k+1) = (n-1)/(n-1-k) * binomial(n-1-k,k).
  • A182581 (program): (3-adic valuation of n), read mod 2.
  • A182582 (program): a(n) = (A096268(n) + A182581(n)) mod 2.
  • A182583 (program): Primes p such that (5p^2-1)/4 is also prime.
  • A182584 (program): Central terms of the triangle A182579.
  • A182589 (program): Number of p-gons in cubic curve, where p = n-th prime.
  • A182614 (program): Least k such that floor(k/r^n)=n, where r = golden ratio = (1+sqrt(5))/2.
  • A182616 (program): Number of partitions of 2n that contain odd parts.
  • A182617 (program): Number of toothpicks in a toothpick spiral around n cells on hexagonal net.
  • A182618 (program): Number of new grid points that are covered by the toothpicks added at n-th-stage to the toothpick spiral of A182617.
  • A182619 (program): Number of vertices that are connected to two edges in a spiral without holes constructed with n hexagons.
  • A182620 (program): Triangle T(n,k) read by rows in which row n lists the divisors of n, written in base 2.
  • A182626 (program): a(n) = Hypergeometric([-n, n], [1], 2).
  • A182627 (program): Total number of digits in binary expansion of all divisors of n.
  • A182628 (program): Triangle T(n,k) read by rows in which row n lists the number of digits of the binary expansion of the divisors of n.
  • A182630 (program): T(n,k) = A002024(k+1)*n + A002262(k), n >= 0, k >= 0, read by antidiagonals.
  • A182636 (program): Numbers whose Wythoff representation has odd length.
  • A182637 (program): Numbers whose Wythoff representation has even length.
  • A182640 (program): a(n)=n+floor(r*a(n-1)), where r = golden ratio = (1+sqrt(5))/2, a(0)=0, a(1)=1.
  • A182647 (program): a(n) = the largest n-digit number with exactly 5 divisors, a(n) = 0 if no such number exists.
  • A182654 (program): Floor-sum sequence of r, with r=sqrt(2) and a(1)=1, a(2)=2.
  • A182660 (program): a(2^(k+1)) = k; 0 everywhere else.
  • A182661 (program): Expansion of x^3*exp(-x)/(3*(1-x)).
  • A182664 (program): a(n) = A088828(n) + A157502(n).
  • A182665 (program): Greatest x < n such that n divides x*(x-1).
  • A182687 (program): a(n) = the smallest 1-digit number with exactly n divisors, a(n) = 0 if no such number exists.
  • A182688 (program): a(n) = the largest 1-digit number with exactly n divisors, a(n) = 0 if no such number exists.
  • A182691 (program): Composite Beatty sequence of sqrt(2).
  • A182700 (program): Triangle T(n,k) = n*A000041(n-k), 0<=k<=n, read by rows.
  • A182701 (program): Triangle T(n,k) = n*A000041(n-k) read by rows, 1 <= k <= n. Sum of the parts of all partitions of n that contain k as a part.
  • A182702 (program): Triangle T(n,k) = n*(A000041(n-k)) read by rows, k>=0.
  • A182704 (program): Row sums of triangle A182700.
  • A182705 (program): Row sums of triangle A182701.
  • A182706 (program): Row sums of triangle A182702.
  • A182712 (program): Number of 2’s in the last section of the set of partitions of n.
  • A182713 (program): Number of 3’s in the last section of the set of partitions of n.
  • A182714 (program): Number of 4’s in the last section of the set of partitions of n.
  • A182716 (program): Number of 2’s in all partitions of 2n that do not contain 1 as a part.
  • A182720 (program): Triangle read by rows: T(n,k) = A000041(k) if k divides n, T(n,k)=0 otherwise.
  • A182723 (program): Sum of (all parts of) all partitions of prime(n).
  • A182724 (program): Sum of all parts of all partitions of n minus the number of partitions of n.
  • A182727 (program): Sum of largest parts of the shell model of partitions with n regions.
  • A182728 (program): Array T(n,k) = n*k*A000041(n) read by antidiagonals, n,k >= 1.
  • A182736 (program): Sum of parts in all partitions of 2n that do not contain 1 as a part.
  • A182737 (program): Sum of parts in all partitions of 2n+1 that do not contain 1 as a part.
  • A182738 (program): Partial sums of A066186.
  • A182740 (program): A shell model of partitions as a table of partitions.
  • A182741 (program): A shell model of partitions as a binary code.
  • A182746 (program): Bisection (even part) of number of partitions that do not contain 1 as a part A002865.
  • A182747 (program): Bisection (odd part) of number of partitions that do not contain 1 as a part A002865.
  • A182748 (program): Triangle T(n,k) read by rows in which row n lists the first n terms of A002865, except the first term, in reverse order together with 0.
  • A182751 (program): a(1)=1, a(2)=3, a(3)=6; a(n) = 3*a(n-2) for n > 3.
  • A182752 (program): a(1) = 1, a(2) = 6, for n >= 3; a(n) = the smallest number greater than a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + a(n)] * [a(n-1) + a(n)]] / [a(n-2) * a(n-1) * a(n)] is an integer.
  • A182753 (program): Expansion of (1 + 14*x)/(1 - 35*x^2).
  • A182754 (program): a(1) = 1, a(2) = 21, a(n) = 77*a(n-2) for n>=3.
  • A182755 (program): Expansion of (1+35*x)/(1-90*x^2).
  • A182757 (program): Numbers k > 1 such that is no sequence B of type: {b(1) = 1, b(2) = k, for n >= 3; b(n) = the smallest number h > b(n-1) such that [[b(n-2) + b(n-1)] * [b(n-2) + h] * [b(n-1) + h]] / [b(n-2) * b(n-1) * h] is integer}.
  • A182760 (program): Beatty sequence for (3 + 5^(-1/2))/2.
  • A182761 (program): Beatty sequence for (7 - sqrt(5))/2.
  • A182765 (program): Beatty sequence for (6 + sqrt(2))/4.
  • A182766 (program): Beatty sequence for 5 - 2*sqrt(2).
  • A182767 (program): Beatty sequence for 1+e^2.
  • A182768 (program): Beatty sequence for 1+e^(-2).
  • A182769 (program): Beatty sequence for (4 + sqrt(2))/2.
  • A182770 (program): Beatty sequence for 3-sqrt(2).
  • A182771 (program): Beatty sequence for (6+sqrt(3))/3.
  • A182772 (program): Beatty sequence for (5-sqrt(3))/2.
  • A182773 (program): Beatty sequence for 1+2^(2/3).
  • A182774 (program): Beatty sequence for 1+2^(-2/3).
  • A182777 (program): Beatty sequence for 3-sqrt(3).
  • A182778 (program): Beatty sequence for 3 + sqrt(3).
  • A182780 (program): Twice A024537.
  • A182788 (program): Number of n-colorings of the Triangle Graph of order 3.
  • A182789 (program): Number of n-colorings of the Triangle Graph of order 4.
  • A182799 (program): Positions of primes in A167171.
  • A182800 (program): Positions of composites in A167171.
  • A182806 (program): Number of partitions of 3n into parts >= 3.
  • A182807 (program): Number of partitions of 3n+1 into parts >= 3.
  • A182808 (program): Number of partitions of 3n+2 into parts >= 3.
  • A182810 (program): Array read by antidiagonals which lists the partition number of the numbers of the table A182630.
  • A182814 (program): Main diagonal of table A182630.
  • A182815 (program): The third row of table A182630.
  • A182816 (program): Number of values b in Z/nZ such that b^n = b.
  • A182817 (program): Number of elements k in Z/mZ such that k^m=k, for nonprime m = A018252(n).
  • A182818 (program): G.f.: exp( Sum_{n>=1} sigma(2n)*x^n/n ).
  • A182819 (program): G.f.: exp( Sum_{n>=1} sigma(3n)*x^n/n ).
  • A182820 (program): G.f.: exp( Sum_{n>=1} sigma(4n)*x^n/n ).
  • A182821 (program): Expansion of g.f.: exp( Sum_{n>=1} sigma(5*n)*x^n/n ).
  • A182827 (program): E.g.f. 1/sqrt(1+2x+4x^2).
  • A182828 (program): Array of the numbers (3*i+1)*3^j, i>=0, j>=0, read by antidiagonals.
  • A182830 (program): Array of the numbers (3*i+2)*3^j, i>=0, j>=0, read by antidiagonals.
  • A182834 (program): Complement of A007590, except for initial zeros.
  • A182835 (program): n+floor(sqrt(2n+3)), complement of A179207.
  • A182836 (program): Toothpick sequence starting at the vertex of the outside corner of an infinite 120-degree wedge on hexagonal net.
  • A182843 (program): Number of composite integers greater than or equal to n whose proper divisors are all less than n.
  • A182844 (program): a(0)=0: a(n)=A002865(2*n)+A002865(2*n+1), n>=1.
  • A182845 (program): a(n) = A002865(2*n-1)+A002865(2*n).
  • A182850 (program): a(n) = number of iterations that n requires to reach a fixed point under the x -> A181819(x) map.
  • A182851 (program): Numbers k such that A182850(k) is odd.
  • A182852 (program): Numbers k such that A182850(k) is even.
  • A182853 (program): Squarefree composite integers and powers of squarefree composite integers.
  • A182854 (program): Integers whose prime signature a) contains at least two distinct numbers, and b) contains no number that occurs less often than any other number.
  • A182855 (program): Numbers that require exactly five iterations to reach a fixed point under the x -> A181819(x) map.
  • A182859 (program): Numbers n such that A036459(n) is even.
  • A182860 (program): Number of distinct prime signatures represented among the unitary divisors of n.
  • A182866 (program): Number of edges in the n^2 X n^2 Sudoku graph.
  • A182868 (program): a(n) = -1 + n + 4*n^2.
  • A182878 (program): Triangle read by rows: T(n,k) is the number of lattice paths L_n of weight n having length k (0 <= k <= n). These are paths that start at (0,0) and end on the horizontal axis and whose steps are of the following four kinds: a (1,0)-step with weight 1, a (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1.
  • A182879 (program): The sum of the lengths of all weighted lattice paths in L_n.
  • A182881 (program): Number of (1,1)-steps in all weighted lattice paths in L_n.
  • A182883 (program): Number of weighted lattice paths of weight n having no (1,0)-steps of weight 1.
  • A182884 (program): Number of (1,0)-steps of weight 1 in all weighted lattice paths in L_n.
  • A182887 (program): Number of (1,0)-steps in all weighted lattice paths in L_n.
  • A182889 (program): Number of weighted lattice paths in L_n having no (1,0)-steps at level 0. The members of L_n are paths of weight n that start at (0,0), end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.
  • A182890 (program): Number of (1,0)-steps of weight 1 at level 0 in all weighted lattice paths in L_n.
  • A182892 (program): Number of weighted lattice paths in L_n having no (1,0)-steps of weight 2 at level 0.
  • A182894 (program): Number of weighted lattice paths in L_n having no (1,0)-steps at level 0. The members of L_n are paths of weight n that start at (0,0) , end on the horizontal axis and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.
  • A182895 (program): Number of (1,0)-steps at level 0 in all weighted lattice paths in L_n.
  • A182902 (program): Number of valleys in all weighted lattice paths in B(n).
  • A182905 (program): Number of weighted lattice paths in F[n]. The members of F[n] are paths of weight n that start at (0,0), do not go below the horizontal axis, and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps.
  • A182921 (program): Sum of exponents in prime-power factorization of the swinging factorial (A056040) n$ = n!/floor(n/2)!^2; also bigomega(n$).
  • A182922 (program): a(n) = n! / A055773(n).
  • A182930 (program): Triangle read by rows: Number of set partitions of {1,2,..,n} such that |k| is a block and no block |m| with m < k exists, (1 <= n, 1 <= k <= n).
  • A182932 (program): Generalized Bell numbers, row 3 of A182933.
  • A182936 (program): Greatest common divisor of the proper divisors of n, 0 if there are none.
  • A182938 (program): If n = Product (p_j^e_j) then a(n) = Product (binomial(p_j, e_j)).
  • A182942 (program): Ranks of primes when all odd prime powers p^j, for j>=1, are jointly ranked.
  • A182944 (program): Square array A(i,j), i >= 1, j >= 1, of prime powers prime(i)^j, by descending antidiagonals.
  • A182945 (program): Array of prime powers p^j, as transpose of A182944.
  • A182946 (program): Array of odd prime powers p^j, where j>=1, by antidiagonals.
  • A182959 (program): G.f. 2*(1+x)^2/(1-2*x+sqrt(1-8*x)).
  • A182960 (program): G.f.: exp( Sum_{n>=1} C(6n-1,2n-1)*x^n/n ).
  • A182986 (program): Zero together with the prime numbers (A000040).
  • A182991 (program): Numbers with property that their divisors are odd, even, odd, even, and so on.
  • A182994 (program): Sum of all parts of the n-th subshell of the head of the last section of the set of partitions of any even integer >= 2n.
  • A182995 (program): Sum of parts of the n-th subsection of the head of the last section of the set of partitions of any odd integer >= 2n+1.
  • A182996 (program): Numbers congruent to 2 (mod 4) that are not in A182991.
  • A183002 (program): a(n) is the total number of noncentral divisors in all positive integers <= n.
  • A183003 (program): a(n) = A183002(n)/2.
  • A183006 (program): a(n) = 24*A138879(n).
  • A183008 (program): a(n) = 24*p(n) = 24*A000041(n).
  • A183009 (program): a(n) = 24*n*p(n) = 24*n*A000041(n).
  • A183010 (program): a(n) = 24*n - 1.
  • A183011 (program): (24n - 1)p(n): traces of partition class polynomials, with a(0) = -1.
  • A183012 (program): a(n) = 24*A138879(n) - A187219(n).
  • A183030 (program): Decimal expansion of sum_{j>=1} tau(j)/j^3 = zeta(3)^2.
  • A183031 (program): Decimal expansion of Sum_{j>=1} tau(j)/j^4 = Pi^8/8100.
  • A183032 (program): Seconds (rounded down) at which the minute hand overlaps with hour hand on the analog clock.
  • A183033 (program): Minute with hour hand overlap problem on analog clock. Fractions of seconds.
  • A183036 (program): G.f.: exp( Sum_{n>=1} A001511(n)*2^A001511(n)*x^n/n ) where A001511(n) equals the 2-adic valuation of 2n.
  • A183037 (program): a(n) = A001511(n)*2^A001511(n) where A001511(n) equals the 2-adic valuation of 2n.
  • A183038 (program): G.f.: exp( Sum_{n>=1} A051064(n)*3^A051064(n)*x^n/n ) where A051064(n) equals the 3-adic valuation of 3n.
  • A183039 (program): a(n) = A051064(n)*3^A051064(n) where A051064(n) equals the 3-adic valuation of 3n.
  • A183041 (program): Least number of knight’s moves from (0,0) to (n,1) on infinite chessboard.
  • A183060 (program): Number of “ON” cells at n-th stage in a simple 2-dimensional cellular automaton (see Comments for precise definition).
  • A183061 (program): First differences of A183060.
  • A183063 (program): Number of even divisors of n.
  • A183066 (program): G.f.: A(x) = (1 + 21*x + 3*x^2 - x^3)/(1-x)^5.
  • A183069 (program): L.g.f.: Sum_{n>=1,k>=0} CATALAN(n,k)^2 * x^(n+k)/n = Sum_{n>=1} a(n)*x^n/n, where CATALAN(n,k) = n*C(n+2*k-1,k)/(n+k) is the coefficient of x^k in C(x)^n and C(x) is the g.f. of the Catalan numbers.
  • A183070 (program): G.f.: A(x) = exp( Sum_{n>=1,k>=0} CATALAN(n,k)^2*x^(n+k)/n ), where CATALAN(n,k) = n*C(n+2*k-1,k)/(n+k) is the coefficient of x^k in C(x)^n and C(x) is the g.f. of the Catalan numbers.
  • A183091 (program): a(n) is the product of the divisors p^k of n where p is prime and k >= 1.
  • A183092 (program): a(n) is the product of divisors d of n such that d is not equal to m^k where m = noncomposite number, k >= 1.
  • A183093 (program): a(1) = 0; thereafter, a(n) = number of divisors d of n such that if d = Product_(i) (p_i^e_i) then all e_i <= 1.
  • A183094 (program): a(n) = number of powerful divisors d (excluding 1) of n.
  • A183095 (program): a(n) = number of divisors d of n which are either 1 or of the form Product_(i) (p_i^e_i) where the e_i are <= 1.
  • A183096 (program): a(n) = number of divisors of n that are not perfect powers.
  • A183097 (program): a(n) = sum of powerful divisors d (including 1) of n.
  • A183098 (program): a(1) = 0, a(n) = sum of divisors d of n such that if d = Product_(i) (p_i^e_i) then all e_i are <= 1.
  • A183099 (program): a(n) = sum of powerful divisors d (excluding 1) of n.
  • A183100 (program): a(n) = sum of divisors d of n which are either 1 or of the form Product_(i) (p_i^e_i) where the e_i are <= 1.
  • A183101 (program): a(n) = sum of divisors of n that are not perfect powers.
  • A183102 (program): a(n) = product of powerful divisors d of n.
  • A183103 (program): a(n) = product of non-powerful divisors d of n.
  • A183104 (program): a(n) = product of divisors of n that are perfect powers.
  • A183105 (program): a(n) = product of divisors of n that are not perfect powers.
  • A183110 (program): Period-length of the ultimate periodic behavior of the orbit of a list [1,1,1,…,1] of n 1’s under the mapping defined in the comments.
  • A183111 (program): Magnetic Tower of Hanoi, number of moves of disk number k, optimally solving the [RED ; BLUE ; NEUTRAL] or [NEUTRAL ; RED ; BLUE] pre-colored puzzle.
  • A183112 (program): Magnetic Tower of Hanoi, total number of moves, optimally solving the [RED ; BLUE ; NEUTRAL] or [NEUTRAL ; RED ; BLUE] pre-colored puzzle.
  • A183113 (program): Magnetic Tower of Hanoi, number of moves of disk number k, optimally solving the [RED ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183114 (program): Magnetic Tower of Hanoi, total number of moves, optimally solving the [RED ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183115 (program): Magnetic Tower of Hanoi, number of moves of disk number k, optimally solving the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183116 (program): Magnetic Tower of Hanoi, total number of moves, optimally solving the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183117 (program): Magnetic Tower of Hanoi, number of moves of disk number k, optimally solving the [NEUTRAL ; NEUTRAL ; NEUTRAL] pre-colored puzzle.
  • A183118 (program): Magnetic Tower of Hanoi, total number of moves, optimally solving the [NEUTRAL ; NEUTRAL ; NEUTRAL] pre-colored puzzle.
  • A183119 (program): Magnetic Tower of Hanoi, total number of moves generated by a certain algorithm, yielding a “forward moving” non-optimal solution of the [RED ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183120 (program): Magnetic Tower of Hanoi, number of moves of disk number k, generated by a certain algorithm, yielding a “forward moving” non-optimal solution of the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183121 (program): Magnetic Tower of Hanoi, total number of moves, generated by a certain algorithm, yielding a “forward moving” non-optimal solution of the [RED ; NEUTRAL ; NEUTRAL] or [NEUTRAL ; NEUTRAL ; BLUE] pre-colored puzzle.
  • A183122 (program): Magnetic Tower of Hanoi, number of moves of disk number k, generated by a certain algorithm, yielding a “forward moving” non-optimal solution of the [NEUTRAL ; NEUTRAL ; NEUTRAL] pre-colored puzzle.
  • A183123 (program): Magnetic Tower of Hanoi, total number of moves, generated by a certain algorithm, yielding a “forward moving” non-optimal solution of the [NEUTRAL ; NEUTRAL ; NEUTRAL] pre-colored puzzle.
  • A183126 (program): Toothpick sequence with toothpicks connected by their endpoints.
  • A183127 (program): Number of toothpicks added at n-th stage to the toothpick structure of A183126.
  • A183136 (program): a(n) = [1/r]+[2/r]+…+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.
  • A183137 (program): [1/s]+[2/s]+…+[n/s], where s=(golden ratio)^2 and []=floor.
  • A183138 (program): a(n) = floor(n/(2+sqrt(2))).
  • A183139 (program): a(n) = [1/r]+[2/r]+…+[n/r], where r=sqrt(2) and []=floor.
  • A183140 (program): a(n) = [1/s]+[2/s]+…+[n/s], where s=2+sqrt(2) and []=floor.
  • A183142 (program): Beatty sequence for 2/(3+sqrt(3)).
  • A183143 (program): [1/r]+[2/r]+…+[n/r], where r=sqrt(3) and []=floor.
  • A183144 (program): [1/s]+[2/s]+…+[n/s], where s=(3+sqrt(3))/2, []=floor.
  • A183147 (program): 1 together with the numbers with property that at least two successive of their divisors are odd or even.
  • A183148 (program): Toothpick sequence on the semi-infinite square grid with toothpicks connected by their endpoints.
  • A183149 (program): Number of toothpicks added at n-th stage to the toothpick structure of A183148.
  • A183151 (program): Number of partitions of n minus the number of primes <= n.
  • A183153 (program): T(n,k) is the number of order-preserving partial isometries of an n-chain of height k (height of alpha = |Im(alpha)|).
  • A183154 (program): T(n,k) is the number of order-preserving partial isometries (of an n-chain) of fixed k (fix of alpha is the number of fixed points of alpha)
  • A183155 (program): The number of order-preserving partial isometries (of an n-chain) of fix zero (fix of alpha = 0). Equivalently, the number of order-preserving partial derangement isometries (of an n-chain).
  • A183156 (program): The number T(n) of isometries of all subspaces of the finite metric space {1,2,…,n} (as a subspace of the reals with the Euclidean metric).
  • A183157 (program): Triangle read by rows: T(n,k) is the number of partial isometries of an n-chain of height k (height of alpha = |Im(alpha)|).
  • A183159 (program): The number of partial isometries (of an n-chain) of fix zero (fix of alpha = 0)). Equivalently, the number of partial derangement isometries (of an n-chain).
  • A183160 (program): a(n) = Sum_{k=0..n} C(n+k,n-k)*C(2*n-k,k).
  • A183188 (program): a(n) = 3*a(n-1) + a(n-3) with a(0)=1, a(1)=2, a(2)=6.
  • A183189 (program): Triangle T(n,k), read by rows, given by (2, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A183190 (program): Triangle T(n,k), read by rows, given by (1, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A183199 (program): Least integer k such that Floor(k*f(n+1)>k*f(n), where f(n)=(n^2)/(1+n^2).
  • A183204 (program): Central terms of triangle A181544.
  • A183205 (program): a(n) = [x^n] (1-x)^(3n+1)/(n+1) * Sum_{k>=0} C(n+k-1,k)^3*x^k.
  • A183207 (program): Termwise products of the natural numbers and odd integers repeated
  • A183208 (program): Iterates of f(x)=floor((3x-1)/2) from x=6.
  • A183213 (program): Ordering of the numbers in the set S generated by these rules: 1 is in S, and if n is in S, then floor[(3n-1)/2] and 3n are in S.
  • A183217 (program): Complement of the pentagonal numbers.
  • A183218 (program): Complement of the hexagonal numbers.
  • A183219 (program): Complement of the heptagonal (7-gonal) numbers.
  • A183220 (program): Complement of the octagonal numbers.
  • A183221 (program): Complement of the 9-gonal numbers.
  • A183222 (program): Complement of the 10-gonal numbers.
  • A183223 (program): Complement of the 11-gonal numbers.
  • A183224 (program): Complement of the 12-gonal numbers.
  • A183225 (program): Array: row r is the complement of the (r+1)-gonal numbers; by antidiagonals.
  • A183226 (program): Sum of digits of (2^n) in base 5, also sum of digits of (10^n) in base 5.
  • A183227 (program): a(n) is the base-5 digit sum of 10^n-1.
  • A183228 (program): a(n) is the base-5 digit sum of 10^n+1.
  • A183233 (program): Ordering of the numbers in the tree A183231; complement of A183234.
  • A183234 (program): Ordering of the numbers in tree A183232; complement of A183233.
  • A183245 (program): Number of permutations of 1..2*n+2 with each element displaced by at least n.
  • A183264 (program): Number of singly defective permutations of 1..n with exactly 1 maximum.
  • A183292 (program): Complement of A055999.
  • A183293 (program): Complement of A056000.
  • A183294 (program): Complement of A005449.
  • A183295 (program): Complement of A115067.
  • A183296 (program): Complement of A005476.
  • A183297 (program): Complement of A005475.
  • A183298 (program): Complement of A147875.
  • A183299 (program): Complement of A005563.
  • A183300 (program): Positive integers not of the form 2n^2.
  • A183301 (program): Complement of A014105.
  • A183302 (program): Complement of A014106.
  • A183304 (program): Half the number of nX3 binary arrays with no element equal to a strict majority of its horizontal and vertical neighbors
  • A183314 (program): Number of n X 2 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.
  • A183324 (program): Number of nX3 binary arrays with each 1 adjacent to exactly two other 1s
  • A183330 (program): Number of n X 2 binary arrays with each 1 adjacent to exactly two 0’s.
  • A183336 (program): Number of n X 4 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.
  • A183344 (program): Number of n X 2 binary arrays with each 1 adjacent to exactly one 0 vertically and one 0 horizontally.
  • A183345 (program): Number of n X 3 binary arrays with each 1 adjacent to exactly one 0 vertically and one 0 horizontally.
  • A183354 (program): One quarter the number of nX2 1..4 arrays with no two neighbors of any element equal to each other
  • A183355 (program): One quarter the number of nX3 1..4 arrays with no two neighbors of any element equal to each other
  • A183356 (program): One quarter the number of n X 4 1..4 arrays with no two neighbors of any element equal to each other.
  • A183393 (program): Half the number of n X 2 binary arrays with no element equal to a strict majority of its knight-move neighbors.
  • A183409 (program): Number of n X 2 binary arrays with each sum of a(1..i,1..j) no greater than i*j/2 and rows and columns in nondecreasing order.
  • A183422 (program): Ordering of the numbers in the tree A183420; complement of A183423.
  • A183423 (program): Ordering of the numbers in tree A183421; complement of A183422.
  • A183425 (program): Half the number of n X 2 0..2 arrays with no element equal its row sum plus its column sum mod 3.
  • A183430 (program): One third the number of n X 2 0..3 arrays with no element equal to its row sum plus its column sum mod 4.
  • A183435 (program): Number of n X 2 binary arrays with every 1 having exactly one king-move neighbor equal to 1.
  • A183436 (program): Number of n X 3 binary arrays with every 1 having exactly one king-move neighbor equal to 1.
  • A183467 (program): Number of n X 2 binary arrays with every element equal to either the sum mod 2 of its vertical neighbors or the sum mod 2 of its horizontal neighbors.
  • A183494 (program): Half the number of nX1 0..2 arrays with no element equal to the sum mod 3 of its horizontal and vertical neighbors
  • A183503 (program): Number of n X 1 0..3 arrays with no element equal to the sum mod 4 of its horizontal and vertical neighbors.
  • A183543 (program): Second of two complementary trees generated by the Wythoff sequences.
  • A183544 (program): Ordering of the numbers in the tree A183542; complement of A183545.
  • A183545 (program): Ordering of the numbers in the tree A183543; complement of A183544.
  • A183555 (program): Positions of the records of the positive integers in A179319; a(n) is the first position in A179319 equal to +n.
  • A183556 (program): Positions of the records of the negative integers in A179319; a(n) is the first position in A179319 equal to -n.
  • A183569 (program): n+floor(sqrt(4n-3)), complement of A024206.
  • A183570 (program): a(n) = n + floor(sqrt(n + 1)).
  • A183571 (program): n+floor(sqrt(n+2)).
  • A183572 (program): a(n) = n + floor(sqrt(2*n-1)).
  • A183573 (program): a(n) = n + floor(sqrt(2n+1)).
  • A183574 (program): n+Floor[sqrt(2n+2)].
  • A183575 (program): a(n) = n - 1 + ceiling((n^2-2)/2); complement of A183574.
  • A183586 (program): 1/24 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock containing exactly three distinct values.
  • A183604 (program): E.g.f.: Sum_{n>=0} (1+x)^(n^2)*x^n/n!.
  • A183611 (program): E.g.f. satisfies: A’(x) = A(x)^2 + x*A(x)^3, with A(0) = 1.
  • A183612 (program): Logarithmic derivative of Sum_{n>=0} (n+1)!^2*x^n.
  • A183615 (program): 1/120 the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock containing four distinct values.
  • A183623 (program): Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock summing to 4
  • A183624 (program): Number of (n+1) X 2 0..2 arrays with every 2 x 2 subblock summing to 4.
  • A183625 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock summing to 4.
  • A183626 (program): Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock summing to 4.
  • A183627 (program): Number of (n+1) X 5 0..2 arrays with every 2 x 2 subblock summing to 4.
  • A183628 (program): Number of (n+1)X6 0..2 arrays with every 2x2 subblock summing to 4
  • A183629 (program): Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock summing to 4.
  • A183630 (program): Number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock summing to 4.
  • A183631 (program): Number of (n+1) X 9 0..2 arrays with every 2 X 2 subblock summing to 4.
  • A183634 (program): Number of (n+1) X 2 0..3 arrays with every 2 x 2 subblock summing to 6.
  • A183635 (program): Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock summing to 6.
  • A183636 (program): Number of (n+1) X 4 0..3 arrays with every 2 X 2 subblock summing to 6.
  • A183637 (program): Number of (n+1) X 5 0..3 arrays with every 2 X 2 subblock summing to 6.
  • A183644 (program): Number of (n+1) X 2 0..4 arrays with every 2 X 2 subblock summing to 8.
  • A183645 (program): Number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock summing to 8.
  • A183654 (program): Number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock summing to 10.
  • A183655 (program): Number of (n+1) X 3 0..5 arrays with every 2 X 2 subblock summing to 10.
  • A183664 (program): Number of (n+1) X 2 0..6 arrays with every 2 X 2 subblock summing to 12.
  • A183665 (program): Number of (n+1) X 3 0..6 arrays with every 2 X 2 subblock summing to 12.
  • A183674 (program): Number of (n+1) X 2 0..7 arrays with every 2 X 2 subblock summing to 14.
  • A183675 (program): Number of (n+1) X 3 0..7 arrays with every 2 X 2 subblock summing to 14.
  • A183682 (program): Number of (n+1) X 3 binary arrays with every 2 X 2 subblock nonsingular.
  • A183690 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock nonsingular.
  • A183702 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock nonsingular.
  • A183712 (program): 1/20 of the number of (n+1) X 3 0..4 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease.
  • A183761 (program): Number of 2 X 2 nonsingular 0..n matrices with rows in increasing order.
  • A183766 (program): 1/32 the number of (2n+1) X 4 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.
  • A183767 (program): 1/32 the number of (n+1) X 5 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.
  • A183769 (program): 1/32 the number of (n+1) X 7 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.
  • A183771 (program): 1/32 the number of (n+1) X 9 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.
  • A183774 (program): Half the number of (n+1)X2 binary arrays with no 2X2 subblock having exactly 2 ones
  • A183775 (program): Half the number of (n+1) X 3 binary arrays with no 2 X 2 subblock having exactly 2 ones.
  • A183784 (program): Half the number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock having sum 4.
  • A183804 (program): 1/16 the number of (n+1) X 3 binary arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.
  • A183855 (program): n+floor(sqrt(3n-3)); complement of A128422.
  • A183856 (program): n+floor(sqrt(3n-2)); complement of A143975.
  • A183857 (program): a(n) = n - 1 + ceiling((2/3)*n^2); complement of A183874.
  • A183858 (program): a(n) = n + floor(sqrt(3n)).
  • A183859 (program): a(n) = n - 1 + ceiling((n^2)/3); complement of A183858.
  • A183860 (program): a(n) = n+floor(sqrt(3n+1)); complement of A183861.
  • A183861 (program): a(1) = 1; for n > 1, a(n) = n - 1 + ceiling((n^2 - 1)/3); complement of A183860.
  • A183862 (program): a(n) = n + floor(sqrt(5*n/2)); complement of A183863.
  • A183863 (program): n-1+ceiling((2/5)(-1/2+n^2)); complement of A183862.
  • A183864 (program): n+floor(sqrt(5*n/3)); complement of A183865.
  • A183865 (program): n-1+ceiling(3(n+2)/5); complement of A183864.
  • A183866 (program): n+floor(2*sqrt(n-1)); complement of A035106.
  • A183867 (program): a(n) = n + floor(2*sqrt(n)); complement of A184676.
  • A183868 (program): a(n) = n + floor(2*sqrt(n+1)); complement of A079524.
  • A183869 (program): n+floor(sqrt(4n+5)); complement of A004116.
  • A183870 (program): n+floor(sqrt(5n-5)); complement of A183871.
  • A183871 (program): a(n) = n + ceiling( (1/5)*n^2 ). Complement of A183870.
  • A183872 (program): n+floor(sqrt(5n)); complement of A183873.
  • A183873 (program): n-1+ceiling((1/5)n^2); complement of A183872.
  • A183874 (program): a(n) = n + floor(sqrt(3*n/2)). Complement of A183857.
  • A183875 (program): Triangle T(n,k) for A(x)^k=sum(n>=k T(n,k)*x^n), where o.g.f. A(x) satisfies A(x)=(a+b*x*A(x))/(c-d*x*A(x)), a=1,b=2,c=1,d=2.
  • A183876 (program): G.f. satisfies: A(x) = Sum_{n>=0} x^n*[Sum_{k=0..n} C(n,k)^2 *x^k* A(x)^(2k)].
  • A183877 (program): Number of arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.
  • A183893 (program): Real part of a Gaussian integer sequence with a Gaussian integer Somos-4 Hankel transform.
  • A183895 (program): Real part of a (-4,-4) Gaussian integer Somos-4 sequence.
  • A183896 (program): Imaginary part of a (-4,-4) Gaussian integer Somos-4 sequence.
  • A183897 (program): Number of nondecreasing arrangements of n+3 numbers in 0..2 with each number being the sum mod 3 of three others.
  • A183898 (program): Number of nondecreasing arrangements of n+3 numbers in 0..3 with each number being the sum mod 4 of three others.
  • A183905 (program): Number of nondecreasing arrangements of n+2 numbers in 0..2 with each number being the sum mod 3 of two others.
  • A183906 (program): Number of nondecreasing arrangements of n+2 numbers in 0..3 with each number being the sum mod 4 of two others.
  • A183907 (program): Number of nondecreasing arrangements of n+2 numbers in 0..4 with each number being the sum mod 5 of two others.
  • A183918 (program): Characteristic sequence for cos(2*Pi/n) being rational.
  • A183919 (program): Characteristic sequence for sin(2Pi/n) being rational.
  • A183954 (program): Number of strings of numbers x(i=1..3) in 0..n with sum i^2*x(i) equal to n*9.
  • A183977 (program): 1/4 the number of (n+1)X(n+1) binary arrays with all 2X2 subblock sums the same
  • A183978 (program): 1/4 the number of (n+1) X 2 binary arrays with all 2 X 2 subblock sums the same.
  • A183979 (program): 1/4 the number of (n+1) X 3 binary arrays with all 2 X 2 subblock sums the same.
  • A183980 (program): 1/4 the number of (n+1) X 4 binary arrays with all 2 X 2 subblock sums the same.
  • A183981 (program): 1/4 the number of (n+1) X 5 binary arrays with all 2 X 2 subblock sums the same.
  • A183982 (program): 1/4 the number of (n+1) X 6 binary arrays with all 2 X 2 subblock sums the same.
  • A183983 (program): 1/4 the number of (n+1) X 7 binary arrays with all 2 X 2 subblock sums the same.
  • A183984 (program): 1/4 the number of (n+1) X 8 binary arrays with all 2 X 2 subblock sums the same.
  • A183985 (program): 1/4 the number of (n+1) X 9 binary arrays with all 2 X 2 subblock sums the same.
  • A183987 (program): Ranks of (odd i)+j*r, when all i+j*r are ranked; r=golden ratio (1+sqrt(5))/2), i>=0, j>=0. Complement of A183988.
  • A183988 (program): Ranks of (even i)+j*r, when all i+j*r are ranked, r=golden ratio, i>=0, j>=0.
  • A183995 (program): Number of (n+1) X 2 0..2 arrays with all 2 X 2 subblock sums the same.
  • A184004 (program): a(n) = n + floor(sqrt(4n/3)); complement of A184005.
  • A184005 (program): a(n) = n - 1 + ceiling(3*n^2/4); complement of A184004.
  • A184006 (program): floor(nr+h), where r=sqrt(3), h=-1/3; complement of A184007.
  • A184007 (program): floor(n*s+h-h*s), where s=(3+sqrt(3))/2, h=-1/3. Complement of A184006.
  • A184008 (program): n+floor(sqrt(7n/3)); complement of A184009.
  • A184009 (program): n-1+ceiling((3/4)n^2); complement of A184008.
  • A184010 (program): n + floor(sqrt(-1+4n/3)); complement of A001859 (except for initial zero).
  • A184012 (program): n + floor(sqrt(5n-4)); complement of A184013.
  • A184013 (program): n - 1 + ceiling((4+n^2)/5); complement of A184012.
  • A184014 (program): n + floor(sqrt(e*n)); complement of A184015.
  • A184015 (program): n-1+ceiling(n^2/e); complement of A184014.
  • A184016 (program): n+floor(3*sqrt(n)); complement of A184017.
  • A184017 (program): n-1+ceiling((n/3)^2); complement of A184016.
  • A184018 (program): Expansion of c(x/(1-x-x^2)) / (1-x-x^2), c(x) the g.f. of A000108.
  • A184019 (program): A (9,-5) Somos-4 sequence
  • A184030 (program): 1/16 the number of (n+1)X(n+1) 0..3 arrays with all 2X2 subblocks having the same four values
  • A184031 (program): 1/16 the number of (n+1) X 2 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184032 (program): 1/16 the number of (n+1) X 3 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184033 (program): 1/16 the number of (n+1) X 4 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184034 (program): 1/16 the number of (n+1) X 5 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184035 (program): 1/16 the number of (n+1) X 6 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184036 (program): 1/16 the number of (n+1) X 7 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184037 (program): 1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184038 (program): 1/16 the number of (n+1) X 9 0..3 arrays with all 2 X 2 subblocks having the same four values.
  • A184040 (program): 1/9 the number of (n+1)X(n+1) 0..2 arrays with all 2X2 subblocks having the same four values
  • A184041 (program): 1/9 the number of (n+1) X 3 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184042 (program): 1/9 the number of (n+1) X 4 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184043 (program): 1/9 the number of (n+1) X 5 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184044 (program): 1/9 the number of (n+1) X 6 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184045 (program): 1/9 the number of (n+1) X 7 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184046 (program): 1/9 the number of (n+1) X 8 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184047 (program): 1/9 the number of (n+1) X 9 0..2 arrays with all 2 X 2 subblocks having the same four values.
  • A184049 (program): T(n,k) is the number of order-preserving and order-decreasing partial isometries (of an n-chain) of height k (height of alpha = |Im(alpha)|).
  • A184050 (program): T(n,k) is the number of order-preserving and order-decreasing partial isometries (of an n-chain) with exactly k fixed points.
  • A184052 (program): The number of order-decreasing partial isometries (of an n-chain)
  • A184063 (program): Number of (n+1) X 2 binary arrays with rows and columns in nondecreasing order and with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.
  • A184096 (program): Half the number of n X n toroidal binary arrays with each element having the sum of its vertical neighbors equal to the sum of its horizontal neighbors
  • A184102 (program): n+floor(4*sqrt(n)); complement of A184103.
  • A184103 (program): a(n) = n-1+ceiling(n^2/16); complement of A184102.
  • A184104 (program): n+floor(5*sqrt(n)); complement of A184105.
  • A184105 (program): n-1+ceiling((n/5)^2); complement of A184104.
  • A184106 (program): n+floor(6*sqrt(n)); complement of A184107.
  • A184107 (program): n-1+ceiling((n/6)^2); complement of A184106.
  • A184108 (program): n + floor(3*sqrt(n-1)); complement of A184109.
  • A184109 (program): n + ceiling(n^2/9); complement of A184108.
  • A184110 (program): n + floor(3*sqrt(n+1)).
  • A184111 (program): n+floor(4*sqrt(n-1)); complement of A184112.
  • A184112 (program): n+ceiling(n^2/16); complement of A184111.
  • A184113 (program): n + floor(4*sqrt(n+1)).
  • A184114 (program): n + floor(5*sqrt(n-1)); complement of A184115.
  • A184115 (program): n + ceiling(n^2/25); complement of A184114.
  • A184116 (program): a(n) = n + floor(5*sqrt(n + 1)).
  • A184117 (program): Lower s-Wythoff sequence, where s(n) = 2n + 1.
  • A184118 (program): Upper s(n)-Wythoff sequence, where s(n) = 2n + 1.
  • A184119 (program): Upper s(n)-Wythoff sequence, where s(n) = 2n - 1; complement of A136119.
  • A184120 (program): Expansion of (1/(1+4x+2x^2))*c(x/(1+4x+2x^2)), c(x) the g.f. of A000108.
  • A184121 (program): A (4,-3) Somos-4 sequence.
  • A184138 (program): Number of n X 3 binary arrays with rows and columns in nondecreasing order.
  • A184145 (program): 1/4 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.
  • A184171 (program): Number of partitions of n into an even number of distinct primes.
  • A184172 (program): Number of partitions of n into an odd number of distinct primes.
  • A184181 (program): Number of permutations of {1,2,…,n} whose shortest block is of length 1. A block of a permutation is a maximal sequence of consecutive integers which appear in consecutive positions. For example, the permutation 5412367 has 4 blocks: 5, 4, 123, and 67. Its shortest block has length 1.
  • A184185 (program): Number of permutations of {1,2,…,n} having no cycles of the form (i, i+1, i+2, …, i+j-1) (j >= 1).
  • A184189 (program): Half the number of (n+1) X 2 binary arrays with no 2 X 2 subblock containing exactly one 1.
  • A184218 (program): a(n) = largest k such that A000217(n+1) = A000217(n) + (A000217(n) mod k), or 0 if no such k exists.
  • A184220 (program): a(n) = largest k such that A000290(n+1) = A000290(n) + (A000290(n) mod k), or 0 if no such k exists.
  • A184223 (program): Half the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 3.
  • A184327 (program): a(1)=1, a(2)=17; thereafter a(n) = 6*a(n-1)-a(n-2)+c, where c=-4 if n is odd, c=12 if n is even.
  • A184334 (program): Period 6 sequence [0, 2, 2, 0, -2, -2, …] except a(0) = 1.
  • A184336 (program): a(n) = n + floor((3*n)^(1/3) - 2/3).
  • A184337 (program): a(n) is the integer whose decimal representation consists of n 8’s followed by n 1’s.
  • A184357 (program): a(n) = Sum_{k=0..n} C(n^2-k^2, n-k)*C(k^2, k).
  • A184358 (program): a(n) = (n+1)!^2/2^n.
  • A184362 (program): G.f.: eta(x) + x*eta’(x).
  • A184363 (program): G.f.: eta(x)^3*(1 + x*eta’(x)/eta(x)), where eta(x) is Dedekind’s eta(q) function without the q^(1/24) factor.
  • A184365 (program): G.f.: eta(x) - x*eta’(x), where eta(x) is Dedekind’s eta(q) function without the q^(1/24) factor.
  • A184366 (program): G.f.: eta(x)^3*(1 - x*eta’(x)/eta(x)), where eta(x) is Dedekind’s eta(q) function without the q^(1/24) factor.
  • A184368 (program): 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.
  • A184387 (program): a(n) = sum of numbers from 1 to sigma(n), where sigma(n) = A000203(n).
  • A184388 (program): a(n) = product of numbers from 1 to sigma(n), where sigma(n) = A000203(n).
  • A184389 (program): a(n) = Sum_{k=1..tau(n)} k, where tau is the number of divisors of n (A000005).
  • A184390 (program): a(n) = sum of numbers from 1 to pi(n), where pi(n) = A007955(n).
  • A184392 (program): a(n) is the product of palindromic divisors of n.
  • A184413 (program): Lower s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2]; complement of A184414.
  • A184414 (program): Upper s(n)-Wythoff sequence, where s(n)=floor[(n+1)/2].
  • A184417 (program): p^2 + (p+2)^2 - 1 where (p,p+2) is the n-th twin prime pair.
  • A184418 (program): Convolution square of A040001.
  • A184423 (program): a(n) = (2*n)!*(3*n)!/n!^5.
  • A184424 (program): a(n) = (3^n/n!^2) * Product_{k=1..n} (6k-4)*(6k-5).
  • A184427 (program): Lower s-Wythoff sequence of A000290 (the squares). Complement of A184428.
  • A184428 (program): Upper s-Wythoff sequence of A000290 (the squares). Complement of A184427.
  • A184478 (program): Lower s-Wythoff sequence, where s(n) = 3n + 1. Complement of A184479.
  • A184479 (program): Upper s-Wythoff sequence, where s(n)=3n+1. Complement of A184478.
  • A184480 (program): Lower s-Wythoff sequence, where s(n)=3n. Complement of A001956.
  • A184481 (program): Semiprime centered triangular numbers.
  • A184482 (program): Lower s-Wythoff sequence, where s(n)=3n-1. Complement of A184483.
  • A184483 (program): Upper s-Wythoff sequence, where s(n)=3n-1. Complement of A184482.
  • A184484 (program): Lower s-Wythoff sequence, where s(n)=3n-2. Complement of A184485.
  • A184485 (program): Upper s-Wythoff sequence, where s(n)=3n-2. Complement of A184484.
  • A184486 (program): Lower s-Wythoff sequence, where s(n)=4n+1. Complement of A184487.
  • A184487 (program): Upper s-Wythoff sequence, where s(n)=4n+1. Complement of A184486.
  • A184514 (program): Lower s-Wythoff sequence, where s(n)=4n-1. Complement of A184515.
  • A184515 (program): Upper s-Wythoff sequence, where s=4n-1. Complement of A184514.
  • A184516 (program): Lower s-Wythoff sequence, where s=4n-2. Complement of A184517.
  • A184517 (program): Upper s-Wythoff sequence, where s=4n-2. Complement of A184516.
  • A184518 (program): Lower s-Wythoff sequence, where s=4n-3. Complement of A184519.
  • A184519 (program): Upper s-Wythoff sequence, where s=4n-3. Complement of A184518.
  • A184520 (program): Lower s-Wythoff sequence, where s=5n+1. Complement of A184521.
  • A184521 (program): Upper s-Wythoff sequence, where s=5n+1. Complement of A184520.
  • A184522 (program): Upper s-Wythoff sequence, where s=5n. Complement of A184523.
  • A184523 (program): Upper s-Wythoff sequence, where s=5n. Complement of A184522.
  • A184524 (program): Lower s-Wythoff sequence, where s=5n-1. Complement of A184525.
  • A184525 (program): Upper s-Wythoff sequence, where s=5n-1. Complement of A184524.
  • A184526 (program): Lower s-Wythoff sequence, where s=5n-2. Complement of A184527.
  • A184527 (program): Upper s-Wythoff sequence, where s=5n-2. Complement of A184526.
  • A184528 (program): Lower s-Wythoff sequence, where s=5n-3. Complement of A184529.
  • A184529 (program): Upper s-Wythoff sequence, where s=5n-3. Complement of A184528.
  • A184530 (program): Lower s-Wythoff sequence, where s=5n-4. Complement of A184531.
  • A184531 (program): Upper s-Wythoff sequence, where s=5n-4. Complement of A184530.
  • A184533 (program): a(n) = floor(1/{(2+n^3)^(1/3)}), where {}=fractional part.
  • A184534 (program): a(n) = floor(1/{(4+n^3)^(1/3)}), where {}=fractional part.
  • A184535 (program): a(n) = floor(3/5 * n^2), with a(1)=1.
  • A184536 (program): a(n) = floor(1/{(1+n^4)^(1/4)}), where {} = fractional part.
  • A184537 (program): a(n) = floor(1/{(2+n^4)^(1/4)}), where {} = fractional part.
  • A184538 (program): Floor[1/{(3+n^4)^(1/4)}], where {}=fractional part.
  • A184540 (program): Number of (n+2) X 3 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
  • A184541 (program): Number of (n+2) X 4 binary arrays with each 3 X 3 subblock having rows and columns in lexicographically nondecreasing order.
  • A184549 (program): Super-birthdays (falling on the same weekday), version 1 (birth within the year following a February 29).
  • A184550 (program): Super-birthdays (falling on the same weekday), version 2 (birth within 1 and 2 years after a February 29).
  • A184551 (program): Super-birthdays (falling on the same weekday), version 3 (birth within 2 and 3 years after a February 29).
  • A184552 (program): Super-birthdays (falling on the same weekday), version 4 (birth in the year preceding a February 29).
  • A184553 (program): a(n) = Sum_{k=0..n} C(3n+k,n-k)*C(4n-k,k).
  • A184578 (program): a(n) = floor((n+1/3)*sqrt(2)), complement of A184579.
  • A184579 (program): a(n) = floor((n-1/3)*(2+sqrt(2))), complement of A184578.
  • A184580 (program): a(n) = floor((n-1/4)*sqrt(2)), complement of A184581.
  • A184581 (program): a(n) = floor((n + 1/4)*(2 + sqrt(2))).
  • A184582 (program): floor[(n+1/5)r] where r=(1+sqrt(5))/2; complement of A184583.
  • A184583 (program): floor[(n-1/5)(1+r)], where r=(1+sqrt(5))/2; complement of A184582.
  • A184584 (program): floor[(n-1/3)r], where r=sqrt(5); complement of A184585.
  • A184585 (program): a(n) = floor(n*s + c*s), where r = sqrt(5), c = 1/3, s = r/(r-1); complement of A184584.
  • A184586 (program): a(n) = floor((n-1/2)*r), where r=sqrt(5); complement of A184587.
  • A184587 (program): a(n) = floor((n+1/2)*s), where s=(5+sqrt(5))/4; complement of A184586.
  • A184588 (program): floor[(n+1/2)*e/(e-1)].
  • A184589 (program): floor(n*e-1); complement of A184590.
  • A184590 (program): floor[(n*e+1)/(e-1)]; complement of A184589.
  • A184591 (program): a(n) = floor(n*(Pi-1)-1); complement of A184592.
  • A184592 (program): a(n) = floor((n*(Pi-1) + 1)/(Pi-2)); complement of A184591.
  • A184593 (program): 5n - A101306: sum_{i=1..n} the last digit of prime(i).
  • A184606 (program): Half the number of (n+1) X 2 binary arrays with no 2 X 2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one.
  • A184615 (program): Positive parts of the nonadjacent forms for n
  • A184616 (program): Negated negative parts of the nonadjacent forms
  • A184617 (program): With nonadjacent forms: A184615(n) + A184616(n).
  • A184618 (program): a(n) = floor(n*r + h), where r=sqrt(2) and h=1/3; complement of A184619.
  • A184619 (program): a(n) = floor((n-h)*s+h), where s=2+sqrt(2) and h=1/3; complement of A184618.
  • A184620 (program): a(n) = floor(nr+h), where r=sqrt(2), h=1/4; complement of A184621.
  • A184621 (program): a(n) = floor((n-h)*s+h), where s=2+sqrt(2) and h=1/4; complement of A184620.
  • A184622 (program): a(n) = floor(n*r+h), where r=sqrt(2), h=-1/3; complement of A184623.
  • A184623 (program): a(n) = floor((n-h)*s+h), where s=2+sqrt(2) and h=-1/3; complement of A184622.
  • A184624 (program): a(n) = floor(n*r +h), where r=sqrt(2), h=-1/4; complement of A184619.
  • A184625 (program): a(n) = floor((n-h)*s +h), where s=2+sqrt(2) and h=-1/4; complement of A184624.
  • A184626 (program): floor(nr+h), where r=sqrt(3), h=1/4; complement of A184627.
  • A184627 (program): floor((n-h)*s+h), where s=(3+sqrt(3))/2 and h=1/4; complement of A184626.
  • A184628 (program): Floor(1/frac((4+n^4)^(1/4))), where frac(x) is the fractional part of x.
  • A184629 (program): Floor(1/{(5+n^4)^(1/4)}), where {}=fractional part.
  • A184630 (program): Floor(1/{(6+n^4)^(1/4)}), where {}=fractional part.
  • A184631 (program): Floor(1/{(7+n^4)^(1/4)}), where {}=fractional part.
  • A184632 (program): Floor(1/{(8+n^4)^(1/4)}), where {}=fractional part.
  • A184633 (program): Floor(1/{(9+n^4)^(1/4)}), where {} = fractional part.
  • A184634 (program): a(n) = floor(1/{(10+n^4)^(1/4)}), where {}=fractional part.
  • A184635 (program): a(n) = floor(1/{(n+n^4)^(1/4)}), where {} = fractional part.
  • A184636 (program): floor(1/{(n^4+2*n)^(1/4)}), where {}=fractional part.
  • A184637 (program): a(n) = floor(1/{(n^4+3*n)^(1/4)}), where {}=fractional part.
  • A184638 (program): floor(nr+h), where r=sqrt(3), h=-1/2; complement of A184653.
  • A184653 (program): floor(n*s+h-h*s), where s=(3+sqrt(3))/2, h=-1/2; complement of A184638.
  • A184654 (program): floor(n*sqrt(3)-2/3); complement of A184655.
  • A184655 (program): floor(n*s+h-h*s), where s=(3+sqrt(3))/2, h=-2/3; complement of A184654.
  • A184656 (program): floor(nr+h), where r=(1+sqrt(5))/2, h=-1/2; complement of A184657.
  • A184657 (program): floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/2; complement of A184656.
  • A184658 (program): floor(nr+h), where r=(1+sqrt(5))/2, h=-1/3; complement of A184659.
  • A184659 (program): floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/3; complement of A184658.
  • A184674 (program): a(n) = n+floor((n/2-1/(2*n))^2); complement of A184675.
  • A184675 (program): n + floor(sqrt(n) + sqrt(n+1)); complement of A184674.
  • A184676 (program): a(n) = n + floor((n/2-1/(4*n))^2); complement of A183867.
  • A184679 (program): Number of (n+1) X 3 binary arrays with every 2 X 2 subblock singular.
  • A184688 (program): 1/3 the number of n X 3 0..2 arrays with no element equal both to the element above and to the element to its left.
  • A184726 (program): a(n) = A005408(n-1)/A090368(n-1) for n > 2 and a(n) = 0 for n <= 2.
  • A184727 (program): a(n) = A005843(n-1)/A090369(n-1) for n > 2 and a(n) = 0 for n <= 2.
  • A184730 (program): G.f.: exp( Sum_{n>=1} A184731(n)*x^n/n ) where A184731(n) = Sum_{k=0..n} C(n,k)^(k+1).
  • A184731 (program): a(n) = Sum_{k=0..n} C(n,k)^(k+1).
  • A184732 (program): floor(nr+h), where r=(1+sqrt(5))/2, h=-1/4; complement of A184733.
  • A184733 (program): floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=-1/4; complement of A184732.
  • A184734 (program): a(n)=floor(nr+h), where r=(1+sqrt(5))/2, h=1/3; complement of A184735.
  • A184735 (program): a(n)=floor(n*s+h-h*s), where s=(3+sqrt(5))/2, h=1/3; complement of A184734.
  • A184736 (program): floor(nr+h), where r=-1+2^(3/2), h=-1/2; complement of A184735.
  • A184737 (program): floor(n*s+h-h*s), where s=-1+2^(3/2), h=-1/2; complement of A184736.
  • A184738 (program): floor(nr+h), where r=-1+sqrt(5), h=1/2; complement of A184735.
  • A184739 (program): floor(n*s+h-h*s), where s=3+sqrt(5), h=1/2; complement of A184738.
  • A184740 (program): floor(n*(e-1)-1/2); complement of A184741.
  • A184741 (program): floor(n*s+h-h*s), where s=(e-1)/(e-2) and h=-1/2; complement of A184740.
  • A184742 (program): a(n) = floor(n*r + h), where r = sqrt(Pi), h = -1/2.
  • A184743 (program): a(n) = floor(n*s + h - h*s), where s = sqrt(Pi)/(sqrt(Pi)-1), h = -1/2; complement of A184742.
  • A184744 (program): floor(nr+h), where r=1+1/e, h=1/2; complement of A184745.
  • A184745 (program): floor(n*(e-1/2)+1/2); complement of A184744.
  • A184746 (program): floor(nr+h), where r=1+1/sqrt(5), h=1/2; complement of A184747.
  • A184747 (program): floor(n*s+h-h*s), where s=1+sqrt(5), h=1/2; complement of A184746.
  • A184748 (program): a(n) = floor(n*r + h), where r = 4 - sqrt(5), h = -1/2. Also, complement of A184749.
  • A184749 (program): a(n) = floor(n*s+h-h*s), where s = (7 + sqrt(5))/4, h = -1/2; complement of A184748.
  • A184750 (program): a(n) = largest k such that A000326(n+1) = A000326(n) + (A000326(n) mod k), or 0 if no such k exists.
  • A184755 (program): Half the number of n X 3 binary arrays with no 1 having an adjacent 1 both above and to its left.
  • A184765 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock singular.
  • A184774 (program): Primes of the form floor(k*sqrt(2)).
  • A184775 (program): Numbers k such that floor(k*sqrt(2)) is prime.
  • A184776 (program): Numbers m such that prime(m) is of the form floor(k*sqrt(2)); complement of A184779.
  • A184777 (program): Primes of the form 2k + floor(k*sqrt(2)).
  • A184778 (program): Numbers k such that 2k + floor(k*sqrt(2)) is prime.
  • A184779 (program): Numbers m such that prime(m) is of the form 2k + floor(k*sqrt(2)); complement of A184776.
  • A184792 (program): Numbers k such that floor(k*r) is prime, where r = golden ratio=(1+sqrt(5))/2.
  • A184793 (program): Numbers m such that prime(m) is of the form floor(k*r), where r=(1+sqrt(5))/2; complement of A180736.
  • A184794 (program): Numbers k such that floor(k*s) is prime, where s = (3 + sqrt(5))/2.
  • A184795 (program): Numbers m such that prime(m) is of the form floor(k*s), where s=(3+sqrt(5))/2; complement of A184793.
  • A184796 (program): Primes of the form floor(k*sqrt(3)).
  • A184797 (program): Numbers k such that floor(k*sqrt(3)) is prime.
  • A184798 (program): Numbers m such that prime(m) is of the form floor(k*sqrt(3)); complement of A184801.
  • A184799 (program): Primes of the form floor(k*s), where s=(3+sqrt(3))/2.
  • A184800 (program): Numbers k such that floor(k*s) is prime, where s = (3 + sqrt(3))/2.
  • A184801 (program): Numbers m such that prime(m) is of the form floor(ks), where s=(3+sqrt(3))/2; complement of A184778.
  • A184802 (program): Primes of the form floor(k*sqrt(5)).
  • A184803 (program): Numbers k such that floor(k*sqrt(5)) is prime.
  • A184804 (program): Numbers m such that prime(m) is of the form floor(k*sqrt(5)); complement of A184807.
  • A184805 (program): Primes of the form floor(k*s), where s=(5+sqrt(5))/4.
  • A184807 (program): Numbers m such that prime(m) is of the form floor(k*s), where s=(5+sqrt(5))/4; complement of A184804.
  • A184808 (program): n + floor(r*n), where r = sqrt(2/3); complement of A184809.
  • A184809 (program): a(n) = n + floor(sqrt(3/2)*n).
  • A184812 (program): n+floor(ns/r)+floor(nt/r), where r=sqrt(2), s=sqrt(3), t=sqrt(5).
  • A184830 (program): a(n) = largest k such that A000961(n+1) = A000961(n) + (A000961(n) mod k), or 0 if no such k exists.
  • A184855 (program): Numbers m such that prime(m) is of the form (k*e); complement of A184858.
  • A184856 (program): Primes of the form floor(k*e/(e-1)).
  • A184857 (program): Numbers k such that floor(k*e/(e-1)) is prime.
  • A184858 (program): Numbers m such that prime(m) is of the form floor(k*e/(e-1)); complement of A184855.
  • A184859 (program): Primes of the form floor(kr+h), where r=(1+sqrt(5))/2 and h=1/2.
  • A184860 (program): Numbers k such that floor(nr+h) is prime, where r=(1+sqrt(5))/2 and h=1/2.
  • A184861 (program): Numbers m such that prime(m) is of the form floor(nr+h), where r=(1+sqrt(5))/2 and h=1/2; complement of A184864.
  • A184862 (program): Primes of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2.
  • A184863 (program): Numbers k such that floor(n+nr-r/2) are prime, where r=(1+sqrt(5))/2.
  • A184864 (program): Numbers m such that prime(m) is of the form floor(n+nr-r/2), where r=(1+sqrt(5))/2; complement of A184861.
  • A184865 (program): Primes of the form floor(nr+h), where r=sqrt(2), h=1/2.
  • A184866 (program): Numbers k such that floor(1/2+k*sqrt(2)) is prime.
  • A184867 (program): Numbers m such that prime(m) is of the form floor(1/2+k*sqrt(2)). Complement of A184870.
  • A184868 (program): Primes of the form floor((k-1/2)*(2+sqrt(2))+1/2); i.e., primes in A063957.
  • A184869 (program): Numbers k such that floor[(k-1/2)*(2+2^(1/2))+1/2] is prime.
  • A184870 (program): Numbers m such that prime(m) is of the form floor[(k-1/2)*(2+2^(1/2))+1/2]; complement of A184867.
  • A184877 (program): a(n) = n^2*(n-2)^2*(n-4)^2*…*(1 or 2)^2.
  • A184879 (program): Triangular array T read by rows: T(n, k) = Sum_{i=0..2*n-2*k} binomial(2*n-2*k, i)*binomial(2*k, i)*(-1)^i, 0 <= k <= n.
  • A184881 (program): a(n) = A184879(2*n, n) - A184879(2*n, n+1) where A184879(n, k) = Hypergeometric2F1(-2*k, 2*k-2*n, 1, -1) if 0<=k<=n.
  • A184882 (program): a(n)=1-4*n-4*n^2.
  • A184883 (program): Number triangle T(n,k) = [k<=n]*Hypergeometric2F1([-k, 2k-2n], [1], 2).
  • A184884 (program): Diagonal sums of number triangle A184883.
  • A184887 (program): a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+3)*(16k+5).
  • A184888 (program): a(n) = C(2n,n) * (8^n/n!^2) * Product_{k=0..n-1} (8k+3)*(8k+5).
  • A184889 (program): a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+2)*(10k+3).
  • A184890 (program): a(n) = C(2n,n) * (5^n/n!^2) * Product_{k=0..n-1} (5k+2)*(5k+3).
  • A184891 (program): a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4).
  • A184892 (program): a(n) = C(2n,n) * (5^n/n!^2) * Product_{k=0..n-1} (5k+1)*(5k+4).
  • A184895 (program): a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+1)*(14k+6).
  • A184896 (program): a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+1)*(7k+6).
  • A184897 (program): a(n) = (8^n/n!^2) * Product_{k=0..n-1} (16k+1)*(16k+7).
  • A184898 (program): a(n) = C(2n,n) * (8^n/n!^2) * Product_{k=0..n-1} (8k+1)*(8k+7).
  • A184899 (program): n such that the n-th centered 12-gonal number is prime. Indices of prime star numbers.
  • A184901 (program): n+floor(ns/r)+floor(nt/r), where r=(1+sqrt(5))/2, s=r+1, t=r+2.
  • A184903 (program): n+floor(nr/t)+floor(ns/t), where r=(1+sqrt(5))/2, s=r+1, t=r+2.
  • A184921 (program): n+[rn/s]+[tn/s]+[un/s], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3.
  • A184922 (program): n+[rn/t]+[sn/t]+[un/t], where []=floor and r=2^(1/2), s=r+1, t=r+2, u=r+3.
  • A184937 (program): a(n) = binomial(2n, n) + binomial(2n-1, n-1) + binomial(2n+1, n).
  • A184939 (program): From the base sequence of the positive integers, keep the first two, remove the next three, keep the next five, remove the next seven, …, block lengths determined by the prime numbers.
  • A184947 (program): Expansion of e.g.f. exp(x)*(1-x)^(-x).
  • A184955 (program): Number of connected 5-regular simple graphs on 2n vertices with girth exactly 5.
  • A184958 (program): Number of nonincreasing even cycles in all permutations of {1,2,…,n}. A cycle (b(1), b(2), …) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<… . A cycle is said to be even if it has an even number of entries.
  • A184959 (program): Fibonacci sequence beginning 10, 9.
  • A184969 (program): a(n) = [Pi]+[2*Pi]+…+[n*Pi], where []=floor.
  • A184976 (program): a(n) = [e]+[2*e]+…+[n*e], where []=floor.
  • A184977 (program): a(n) = Sum_{k=1..n} floor(k*gamma) where gamma is Euler’s constant (A001620).
  • A184985 (program): Nonnegative integers excluding 2.
  • A184997 (program): Number of distinct remainders that are possible when a safe prime p is divided by n (for p > 2*n+1).
  • A185003 (program): a(n) = Sum_{k=1..n} binomial(n,k)*sigma(k).
  • A185008 (program): Next semiprime after 10*n.
  • A185009 (program): Row sums of A051949 (differences of factorial numbers), seen as a triangle.
  • A185010 (program): a(n) = A000108(n)*A015518(n+1), where A000108 are the Catalan numbers and A015518(n) = 2*A015518(n-1) + 3*A015518(n-2).
  • A185012 (program): Characteristic function of two.
  • A185013 (program): Characteristic function of {3}.
  • A185014 (program): Characteristic function of four.
  • A185015 (program): Characteristic function of 5.
  • A185016 (program): Characteristic function of 6.
  • A185017 (program): Characteristic function of 7.
  • A185018 (program): Inverse to sequence matrix for natural numbers.
  • A185019 (program): a(n) = n*(14*n-3).
  • A185020 (program): a(n) = A000108(n)*A002605(n+1), where A000108 are the Catalan numbers.
  • A185021 (program): a(n) = h(1)*h(2)*…*h(n), where h(i) = i/[g(i/2)*g(i/4)*g(i/8)*…] and g(x) = x if x is an integer and g(x) = 1 otherwise.
  • A185026 (program): The first bisection of the sequence A002616 of reduced totients.
  • A185027 (program): Sum of the triangular divisors of n.
  • A185039 (program): Numbers of the form 9*m^2 + 4*m, m an integer.
  • A185045 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208659; see the Formula section.
  • A185047 (program): Expansion of 2F1( (1, 4/3); (3); 9 x).
  • A185048 (program): Length of the continued fraction for floor(Fibonacci(n)*(1+sqrt(5))/2) / Fibonacci(n).
  • A185049 (program): Last term in the continued fraction for floor(Fibonacci(n)*(1+sqrt(5))/2) / Fibonacci(n).
  • A185050 (program): Least k such that G(k) > 3 - 1/2^n, where G(k) is the sum of the first k terms of the geometric series 1 + 2/3 + (2/3)^2 + ….
  • A185055 (program): Number of representations of 5^(2n) as a sum a^2 + b^2 + c^2 with 0 < a <= b <= c.
  • A185057 (program): a(n) = n^n! (mod 5).
  • A185058 (program): a(n) = n^n! mod 7.
  • A185059 (program): a(n) = A010815(7*n).
  • A185061 (program): Position of the first occurrence of n in A193358 when it is considered to have the starting offset 1 instead of 0.
  • A185064 (program): Numbers k such that a Golay sequence of length k exists.
  • A185065 (program): a(n) = n*(n^3 + 2).
  • A185080 (program): 6 * binomial(2*n,n-1) + binomial(2*n-1,n).
  • A185083 (program): Partitions of 2*n into parts not congruent to 0, +-2, +-12, +-14, 16 (mod 32).
  • A185087 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*A000108(k+1).
  • A185089 (program): A transform of the little Schroeder numbers.
  • A185090 (program): Triangle read by rows: T(n,k) (n >= 2, 2 <= k <= n) = number of edge-disjoint spanners of delay 2 for complete bipartite graph K_{n,k}.
  • A185093 (program): Decimal expansion of the volume of small rhombicosidodecahedron with edge = 1.
  • A185096 (program): Let T(n) = n(n+1)/2 be the n-th triangular number (A000217); a(n) = T(8T(n)).
  • A185102 (program): a(n) is the recursion depth of repeatedly factoring n and then the exponents in its prime product factorization, until 1 is reached.
  • A185106 (program): Column 4 of A181783.
  • A185107 (program): a(n) is the first digit of prime(n) minus the sum of the other digits.
  • A185108 (program): a(0)=0; for n>0, a(n) = (n+2)*a(n-1) + 1.
  • A185109 (program): a(0)=2; for n > 0, a(n) = (n+2)*a(n-1) + 1.
  • A185113 (program): Number of dissections of a convex (3n+3)-sided polygon into n pentagons and one triangle (up to equivalence)
  • A185114 (program): Number of connected 2-regular simple graphs on n vertices with girth at least 4.
  • A185115 (program): Number of connected 2-regular simple graphs on n vertices with girth at least 5.
  • A185116 (program): Number of connected 2-regular simple graphs on n vertices with girth at least 6.
  • A185117 (program): Number of connected 2-regular simple graphs on n vertices with girth at least 7.
  • A185118 (program): Number of connected 2-regular simple graphs on n vertices with girth at least 8.
  • A185119 (program): Number of connected 2-regular simple graphs on n vertices with girth at least 9.
  • A185123 (program): a(n) = n 9’s sandwiched between two 1’s.
  • A185127 (program): a(n) = n 3’s sandwiched between two 1’s.
  • A185132 (program): Number of 4-Motzkin paths of length n with no level steps at height 0.
  • A185138 (program): a(4*n) = n*(4*n-1); a(2*n+1) = n*(n+1)/2; a(4*n+2) = (2*n+1)*(4*n+1).
  • A185139 (program): Triangle T(n,k) = Sum_{i=1..n} 2^(i-1)*C(n+2*k-i-1, k-1), 1 <= k <= n.
  • A185147 (program): Number of times each value of the sigma function occurs.
  • A185148 (program): Number of rectangular arrangements of [1,3n] in 3 increasing sequences of size n and n monotonic sequences of size 3.
  • A185149 (program): a(n) = 3^n*A003046(n+1)/A002457(n).
  • A185152 (program): Expansion of (q/2) * phi(q)^3 (d/dq) phi(q) in powers of q.
  • A185157 (program): G.f. A(x) = sum(n>0, a(n)*x^n/(2*n-1)!) is the inverse function to x*Bernoulli(x).
  • A185159 (program): a(n) = 2^n*A122827(n).
  • A185160 (program): Somos-4 variation with periodic coefficients.
  • A185170 (program): a(n) = floor( (2*n^2 - 6*n + 9) / 5).
  • A185171 (program): Dimensions of primitive Lie algebras connected with the Mantaci-Reutenauer algebra MR^(2).
  • A185172 (program): Dimensions of primitive Lie algebras connected with the Mantaci-Reutenauer algebra MR^(3).
  • A185175 (program): a(n) = A010815(7*n + 5).
  • A185180 (program): Enumeration table T(n,k) by antidiagonals. The order of the list is symmetrical movement from center to edges diagonal.
  • A185189 (program): Powers of 2 >= 16 and powers of odd primes.
  • A185197 (program): Decimal expansion of 2/Pi^2.
  • A185199 (program): Decimal expansion of 4/Pi^2.
  • A185208 (program): Numbers having no divisors d > 1 such that d + 1 are prime powers.
  • A185212 (program): a(n) = 12*n^2 - 8*n + 1.
  • A185220 (program): Expansion of phi(x^3) * psi(x)^2 / chi(-x) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A185248 (program): Expansion of 3F2( (1/2, 3/2, 5/2); (3, 5))(64 x)
  • A185251 (program): a(n) = Sum_{k=0..floor(n/2)} k*binomial(n,k).
  • A185252 (program): a(n) = Sum_{k=0..ceiling(n/2)} k*binomial(n,k).
  • A185255 (program): Number of disconnected 5-regular simple graphs on 2n vertices with girth at least 5.
  • A185256 (program): Stanley Sequence S(0,3).
  • A185260 (program): Decimal expansion of sqrt(4*sqrt(3) - 3) - 1, the solution to the problem of dissecting an equilateral triangle into a square, with 3 cuts (Haberdasher’s problem).
  • A185265 (program): a(0)=1, a(1)=2; thereafter a(n) = f(n-1) + f(n-2) where f() = A164387().
  • A185269 (program): The subsequence of primes, in order of occurrence, in A005351.
  • A185270 (program): a(n) = 648 * n^6.
  • A185273 (program): Period 6: repeat [1, 6, 5, 6, 1, 0].
  • A185275 (program): Products of the first terms of the arithmetic sequence f(n) defined by f(2^k l) = l^{1 - k} (for k a nonnegative integer and l a positive odd integer).
  • A185276 (program): Kronecker symbol (-100 / n).
  • A185277 (program): a(n) = n^9 + 9^n.
  • A185283 (program): Least k such that sigma(1) + sigma(2) + sigma(3) +…+ sigma(k) >= n.
  • A185292 (program): Expansion of (x*(1+x)/(1-x^3))^4
  • A185294 (program): Number of disconnected 9-regular simple graphs on 2n vertices with girth at least 4.
  • A185295 (program): a(n) = - A010815(7*n + 1).
  • A185296 (program): Triangle of connection constants between the falling factorials (x)_(n) and (2*x)_(n).
  • A185297 (program): Consider all pairs of primes (p,q) with p+q = 2n, p <= q; a(n) is the sum of all the p’s.
  • A185298 (program): Expansion of e.g.f. x*exp(x)*exp(x*exp(x)).
  • A185300 (program): Numbers k such that (sum of the decimal digits of k) + (product of the decimal digits of k) is prime.
  • A185306 (program): Number of maximally nonhamiltonian graphs on n vertices.
  • A185308 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + n*a(n-2) + 1.
  • A185309 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n+1)*a(n-2) + 1.
  • A185322 (program): a(n) = ceiling(prime(n)/10).
  • A185331 (program): Riordan array ((1-x+x^2)/(1+x^2), x/(1+x^2)).
  • A185333 (program): Number of binary necklaces of n beads for which a cut exists producing a palindrome.
  • A185338 (program): McKay-Thompson series of class 16B for the Monster group with a(0) = -2.
  • A185342 (program): Triangle of successive recurrences in columns of A117317(n).
  • A185346 (program): a(n) = 2^n - 9.
  • A185353 (program): a(n) = (1^1 + 2^2 . . . + n^n) mod 10.
  • A185355 (program): Number of n X n symmetric (0,1)-matrices containing four ones.
  • A185359 (program): Numbers k such that {m^m mod k: m >= 1} is not purely periodic.
  • A185369 (program): Number of simple labeled graphs on n nodes of degree 1 or 2 without cycles.
  • A185371 (program): Product of two consecutive primes divided by the next prime and rounded down.
  • A185375 (program): a(n) = n*(n-1)*(2*n+1)*(2*n-1)*(2*n-3)*(10*n-17)/90.
  • A185376 (program): Number of binary necklaces of 2n beads for which a cut exists producing a palindrome.
  • A185378 (program): Number of binary necklaces of 2n beads that are identical when turned over yet cannot be cut to produce a palindrome.
  • A185381 (program): a(n) = Fibonacci(k) where k = floor( n*(1+sqrt(5))/2 ).
  • A185382 (program): Sum_{j=1..n-1} P(n)-P(j), where P(j) = A065091(j) is the j-th odd prime.
  • A185383 (program): a(n) is the denominator of the fraction |n^2/A049417(n)-A064380(n)|.
  • A185384 (program): A binomial transform of Fibonacci numbers.
  • A185387 (program): E.g.f. exp(x)+log(1/(1-x)).
  • A185391 (program): a(n) = Sum_{k=0..n} A185390(n,k) * k.
  • A185392 (program): Position of g(n) when the numbers f(j) and g(k) are jointly ranked, where f(j) = j + |cos j| and g(k) = k + |sin k|.
  • A185393 (program): Decimal expansion of e/(e-1) = 1 + 1/e + 1/e^2 + …
  • A185395 (program): a(3n) = n^2, a(3n+1) = a(3n+2) = 3*n*(n+1)/2.
  • A185400 (program): Numbers with property that the digital sum plus the product of the digits is a power of 2.
  • A185401 (program): a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+2)*(14k+5).
  • A185402 (program): a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+2)*(7k+5).
  • A185403 (program): a(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+3)*(14k+4).
  • A185404 (program): a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+3)*(7k+4).
  • A185437 (program): The least number of colors required to color an n-bead necklace so that each bead can be identified.
  • A185438 (program): a(n) = 8*n^2 - 2*n + 1.
  • A185452 (program): Image of n under the map n -> n/2 if n even, (5*n+1)/2 if n odd.
  • A185453 (program): Trajectory of 1 under repeated application of the map in A185452.
  • A185454 (program): Trajectory of 5 under repeated application of the map in A185452.
  • A185455 (program): Trajectory of 7 under repeated application of the map in A185452.
  • A185456 (program): Payphone packing sequence.
  • A185505 (program): a(n) = (7*n^4 + 5*n^2)/12.
  • A185513 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock singular.
  • A185526 (program): Number of (n+2) X 3 binary arrays with each 3 X 3 subblock nonsingular.
  • A185541 (program): a(n) = m*(m+1)/2, where m = floor(n^(3/2)).
  • A185542 (program): a(n) = m*(m+1)/2, where m = floor(n^(5/2)).
  • A185543 (program): Numbers not of the form floor(k^(3/2)); complement of A000093.
  • A185546 (program): a(n) = floor((1/2)*(n+1)^(3/2)); complement of A185547.
  • A185547 (program): Numbers not of the form floor((1/2)(n+1)^(3/2)); complement of A185546.
  • A185549 (program): a(n) = ceiling(n^(3/2)); complement of A185550.
  • A185550 (program): Numbers not of the form ceiling(n^(3/2)); complement of A185549.
  • A185561 (program): 1/4 the number of n X 3 0..3 arrays with no element equal both to the element above and to the element to its left.
  • A185590 (program): Iterate the map in A006369 starting at 44.
  • A185592 (program): a(n) = floor(n^(3/2))*floor(1 + n^(3/2))*floor(2 + n^(3/2))/6.
  • A185593 (program): a(n) = floor(n^(3/2))*floor(3+n^(3/2))/2.
  • A185594 (program): a(n) = floor((n^2+n)^(3/2)-n^3).
  • A185595 (program): a(n) = floor(n^(3/2)) - floor(n^(1/2)); complement of A185596.
  • A185596 (program): Complement of A185595.
  • A185597 (program): a(n) = floor(n^(3/2) - n^(1/2)); complement of A185598.
  • A185598 (program): Numbers not of the form floor(n^(3/2)-n^(1/2)); complement of A185597.
  • A185599 (program): a(n) = floor(n^(3/2) - n^(1/2)) - n; complement of A185600.
  • A185600 (program): Numbers not of the form floor(n^(3/2) - n^(1/2)); complement of A185599.
  • A185601 (program): a(n) = floor(n^(3/2))-floor(n^(1/2))-n; complement of A185602.
  • A185602 (program): Numbers not of the form floor(n^(3/2))-floor(n^(1/2))-n; complement of A185601.
  • A185603 (program): a(n) = floor(floor(n^(5/2))^(1/2)); complement of A185604.
  • A185604 (program): Complement of A185603.
  • A185632 (program): Primes of the form n^2 + n + 1 where n is nonprime.
  • A185633 (program): For odd n, a(n) = 2; for even n, a(n) = denominator of Bernoulli(n)/n; The number 2 alternating with the elements of A006953.
  • A185634 (program): Number of n-length cycles from any point in a complete graph on n nodes.
  • A185647 (program): Expansion of (1+2x)*(1+2*x^2)/((1-x)*(1+x)*(1-2*x^2)).
  • A185653 (program): Expansion of exp( Sum_{n>=1} -3*sigma(2n)*x^n/n ) in powers of x.
  • A185654 (program): G.f.: exp( Sum_{n>=1} -sigma(3n)*x^n/n ).
  • A185655 (program): a(n) = Sum_{k=0..n} binomial(n+k, k)*binomial(n+k+1, k+1)/(n+1).
  • A185669 (program): a(n) = 4*n^2 + 3*n + 2.
  • A185670 (program): Number of pairs (x,y) with 1 <= x < y <= n with at least one common factor.
  • A185672 (program): Let f(n) = Sum_{j>=1} j^n*3^j/binomial(2*j,j) = r_n*Pi/sqrt(3) + s_n; sequence gives r_n.
  • A185679 (program): Number of digits in decimal expansion of n^2.
  • A185688 (program): First differences of A060819(n-4)*A060819(n).
  • A185691 (program): Fibonacci sequence with initial terms 10 and 21.
  • A185694 (program): Eigensequence for the Moebius mu triangle A152904.
  • A185696 (program): Eigensequence for the Gould sequence triangle (with general term A001316(n-k) if k<=n, 0 otherwise).
  • A185699 (program): Expansion of (11 * E_2(x^11) - E_2(x)) / 2 in powers of x where E_2() is an Eisenstein series.
  • A185705 (program): Characteristic function of positive numbers that are primes ending in 1.
  • A185706 (program): Characteristic function of positive numbers that are primes ending in 3.
  • A185708 (program): Characteristic function of positive numbers that are primes ending in 7.
  • A185709 (program): Characteristic function of positive numbers that are primes ending in 9.
  • A185712 (program): a(n) = number of primes <= n that end in 3.
  • A185714 (program): a(n) = number of primes <= n that end in 7.
  • A185717 (program): Expansion of q^(-1) * c(q^2) * (c(q) - c(q^4)) / 9 in powers of q^2 where c() is a cubic AGM theta function.
  • A185721 (program): Arises in the maximum number of C5’s in a triangle-free graph.
  • A185727 (program): Integers of the form A145911(k)/(k+1) sorted along increasing k.
  • A185732 (program): Accumulation array of the polygonal number array (A086270), by antidiagonals.
  • A185738 (program): Rectangular array T(n,k) = 2^n + k - 2, by antidiagonals.
  • A185740 (program): Weight array of A185738, by antidiagonals.
  • A185761 (program): Number of (n+1) X 2 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.
  • A185762 (program): Number of (n+1) X 3 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.
  • A185771 (program): Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock sum equal to any horizontal or vertical neighbor 2 X 2 subblock sum.
  • A185779 (program): Third accumulation array of Pascal’s triangle (as a rectangle), by antidiagonals.
  • A185780 (program): Array T(n,k) = k*(n*k-n+1), by antidiagonals.
  • A185781 (program): Accumulation array of A185780, by antidiagonals.
  • A185782 (program): Weight array of A185780, by antidiagonals.
  • A185784 (program): Accumulation array of A107985, by antidiagonals.
  • A185785 (program): Second accumulation array of A107985, by antidiagonals.
  • A185786 (program): Third accumulation array of A107985, by antidiagonals.
  • A185787 (program): Sum of first k numbers in column k of the natural number array A000027; by antidiagonals.
  • A185788 (program): Sum of the first k-1 numbers in the k-th column of the natural number array A000027, by antidiagonals.
  • A185790 (program): Number of (n+1) X 2 binary arrays with no 2 X 2 subblock sum equal to any horizontal or vertical neighbor 2 X 2 subblock sum.
  • A185826 (program): Sum of the next n natural numbers raised to the n-th power.
  • A185828 (program): Half the number of n X 2 binary arrays with every element equal to exactly one or two of its horizontal and vertical neighbors.
  • A185858 (program): 1/128 the number of (n+2) X 3 binary arrays with no 3 X 3 subblock trace equal to any horizontal or vertical neighbor 3 X 3 subblock trace.
  • A185868 (program): (Odd,odd)-polka dot array in the natural number array A000027, by antidiagonals.
  • A185869 (program): (Odd,even)-polka dot array in the natural number array A000027; read by antidiagonals.
  • A185870 (program): (Even,odd)-polka dot array in the natural number array A000027, by antidiagonals.
  • A185871 (program): (Even,even)-polka dot array in the natural number array A000027, by antidiagonals.
  • A185874 (program): Second accumulation array of A051340, by antidiagonals.
  • A185876 (program): Fourth accumulation array of A051340, by antidiagonals.
  • A185877 (program): Array T given by T(n,k) = k^2 +(2*n-3)*k -2*n +3, by antidiagonals.
  • A185878 (program): Accumulation array of A185877, by antidiagonals.
  • A185879 (program): Weight array of A185877, by antidiagonals.
  • A185904 (program): Multiplication table for the tetrahedral numbers (A000292), by antidiagonals.
  • A185905 (program): Rectangular array binomial(k+3,4)*binomial(n+3,4), by antidiagonals.
  • A185906 (program): Weight array of A000007 (which has only one nonzero term and whose second accumulation array is the multiplication table for the positive integers), by antidiagonals.
  • A185907 (program): Weight array of A185908, by antidiagonals.
  • A185908 (program): Array: T(n,k) = n-1 + min{n,k}, by antidiagonals.
  • A185909 (program): Accumulation array of A185908, by antidiagonals.
  • A185910 (program): Array: T(n,k) = n^2 + k - 1, by antidiagonals.
  • A185911 (program): Weight array of A185910, by antidiagonals.
  • A185914 (program): Array: T(n,k)=k-n+1 for k>=n; T(n,k)=0 for k<n; by antidiagonals.
  • A185915 (program): Accumulation array of A185914, by antidiagonals.
  • A185916 (program): Weight array of A185914, by antidiagonals.
  • A185917 (program): Weight array of max{n,k}, by antidiagonals.
  • A185918 (program): a(n) = 12*n^2 - 2*n - 1.
  • A185934 (program): Lesser of two consecutive primes which both equal 1 (mod 3).
  • A185935 (program): Lesser of two consecutive primes which both equal 2 (mod 3).
  • A185939 (program): a(n) = 9*n^2 - 6*n + 2.
  • A185940 (program): a(n) = 1 - 2^(n+1) + 3^(n+2).
  • A185943 (program): Riordan array ((1/(1-x))^m, x*A000108(x)), m = 2.
  • A185944 (program): Riordan array ( (1/(1-x))^m , x*A000108(x) ), m = 3.
  • A185945 (program): Riordan array ( (1/(1-x))^m , x*A000108(x) ), m =4.
  • A185946 (program): Exponential Riordan array (e^(x), x*A000108(x)).
  • A185947 (program): Exponential Riordan array (e^(mx),x*A000108(x)), m=2.
  • A185948 (program): Exponential Riordan array (e^(mx),x*A000108(x)), m=3.
  • A185950 (program): a(n) = 4*n^2 - n - 1.
  • A185952 (program): Partial products of A002313, the primes that are 1 or 2 (mod 4).
  • A185954 (program): G.f.: A(x) = exp( Sum_{n>=1} A163659(2n)*x^n/n ), where x*exp(Sum_{n>=1} A163659(n)*x^n/n) = S(x) is the g.f. of Stern’s diatomic series (A002487).
  • A185957 (program): Second accumulation array of the array min{n,k}, by antidiagonals.
  • A185958 (program): Accumulation array of the array max{n,k}, by antidiagonals.
  • A185962 (program): Riordan array ((1-x)^2/(1-x+x^2), x(1-x)^2/(1-x+x^2)).
  • A185963 (program): Row sums of number triangle A185962.
  • A185964 (program): Diagonal sums of number triangle A185962.
  • A185965 (program): Central coefficients of number triangle A185962.
  • A185966 (program): Series reversion of A028310.
  • A185967 (program): Inverse of Riordan array ((1-x)(1-x^2)(1-x^3)/(1-x^6), x(1-x)(1-x^2)(1-x^3)/(1-x^6)).
  • A185968 (program): a(n) = n^2*2^(n^2-1).
  • A185970 (program): a(n) = 2^((n^2-n-2)/2)*(n+2)!
  • A185971 (program): Convolution inverse of A001147.
  • A185976 (program): Number of multiset repetition class defining partitions of N with 1<=N<=n.
  • A185979 (program): Numbers which are the sum of two positive triangular numbers in more than one way.
  • A186002 (program): Hankel transform of A186001.
  • A186021 (program): a(n) = Bell(n)*(2 - 0^n).
  • A186024 (program): Inverse of eigentriangle of triangle A085478.
  • A186025 (program): a(n) = 0^n + 1 - F(n-1)^2 - F(n)^2, where F = A000045.
  • A186029 (program): a(n) = n*(7*n+3)/2.
  • A186030 (program): a(n) = n*(13*n-3)/2.
  • A186031 (program): Number of Dyck paths of semilength n with a valley (DU) spanning the midpoint.
  • A186032 (program): a(n) = (-1)^A048881(n).
  • A186034 (program): 2-adic valuation of the n-th Motzkin number.
  • A186035 (program): a(n) = (-1)^A186034(n).
  • A186037 (program): a(n) = log_2((1+A002426(n))/numerator((1+A002426(n))/2^n)).
  • A186038 (program): a(n) = log_3(A002426(n)/numerator(A002426(n)/3^n)).
  • A186039 (program): a(n) = (-1)^A186038(n).
  • A186041 (program): Numbers of the form 3*k + 2, 5*k + 3, or 7*k + 4.
  • A186042 (program): Numbers of the form 2*k + 1, 3*k + 2, or 5*k + 3.
  • A186080 (program): Fourth powers that are palindromic in base 10.
  • A186099 (program): Sum of divisors of n congruent to 1 or 5 mod 6.
  • A186100 (program): Expansion of 2 * a(q^2)^2 - a(q)^2 in powers of q where a() is a cubic AGM theta function.
  • A186101 (program): a(n) = 2*n / 3 if n divisible by 3, a(n) = n otherwise.
  • A186102 (program): Smallest prime p such that p == n (mod prime(n)).
  • A186111 (program): a(n) = -n if n odd, a(2n) = 3n if n odd, a(4n) = 2n.
  • A186113 (program): a(n) = 13*n + 6.
  • A186129 (program): Numbers that can be partitioned into four parts s, t, u, v such that s+k = t-k = u*k = v/k for some k > 1.
  • A186133 (program): Number of (n+1) X 2 0..2 arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.
  • A186144 (program): Number of elements in the symmetric group S_n whose distance from a fixed element is the group diameter under compositions of (1,2) and (1,2,…,n).
  • A186145 (program): Rank of n^2 when {i^2: i>=1} and {j^3: j>=1} are jointly ranked with i^2 before j^3 when i^2=j^3. Complement of A186146.
  • A186146 (program): Rank of n^3 when {i^2: i>=1} and {j^3: j>=1} are jointly ranked with i^2 before j^3 when i^2=j^3. Complement of A186145.
  • A186147 (program): Rank of n^3 when {i^2: i>=1} and {j^3: j>=1} are jointly ranked with i^2 after j^3 when i^2=j^3. Complement of A135674.
  • A186148 (program): Rank of (1/4)n^3 when {(1/4)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/4)i^3 before j^2 when (1/4)i^3=j^2. Complement of A186149.
  • A186149 (program): Rank of n^2 when {(1/4)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/4)i^3 before j^2 when (1/4)i^3=j^2. Complement of A186148.
  • A186150 (program): Rank of (1/4)n^3 when {(1/4)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/4)i^3 after j^2 when (1/4)i^3=j^2. Complement of A186151.
  • A186151 (program): Rank of n^2 when {(1/4)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/4)i^3 after j^2 when (1/4)i^3=j^2. Complement of A186150.
  • A186152 (program): Rank of (1/8)n^3 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 before j^2 when (1/8)i^3=j^2. Complement of A186153.
  • A186153 (program): Rank of n^2 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 before j^2 when (1/8)i^3=j^2. Complement of A186152.
  • A186154 (program): Rank of (1/8)n^3 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 after j^2 when (1/8)i^3=j^2. Complement of A186155.
  • A186155 (program): Rank of n^2 when {(1/8)i^3: i>=1} and {j^2>: j>=1} are jointly ranked with (1/8)i^3 after j^2 when (1/8)i^3=j^2. Complement of A186154.
  • A186156 (program): Rank of n^3 when {i^3: i>=1} and {2j^2: j>=1} are jointly ranked with i^3 before 2j^2 when i^3=2j^2. Complement of A186157.
  • A186157 (program): Rank of 2n^2 when {i^3: i>=1} and {2j^2: j>=1} are jointly ranked with i^3 before 2j^2 when i^3=2j^2. Complement of A186156.
  • A186159 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and octagonal numbers. Complement of A186274.
  • A186170 (program): Number of prime factors times n minus sum of divisors.
  • A186181 (program): Period 4 sequence [ 2, 2, 3, 2, …] except a(0) = 1.
  • A186182 (program): Expansion of 1/(1-x*A002294(x)).
  • A186183 (program): Expansion of 1/(1-x*A002295(x)).
  • A186184 (program): Expansion of 1/(1 - x*A002296(x)).
  • A186185 (program): Expansion of 1/(1 - x*A001764(x/(1-x))/(1-x)).
  • A186186 (program): Expansion of 1/(1-x/(1-x)*A(x/(1-x))) where A(x) is the g.f. of A002293.
  • A186187 (program): Period 8 sequence [ 2, 2, 1, 2, 4, 2, 1, 2, …] except a(0) = 1.
  • A186188 (program): Least k such that A156077^(k)(n)=1 where a^(k)=a(a^(k-1)).
  • A186189 (program): least k such that A074286^(k)(n)=1 where a^(k)=a(a^(k-1)).
  • A186190 (program): First digit of tribonacci sequence A000213.
  • A186191 (program): First digit of tetranacci numbers A000288.
  • A186192 (program): First digit of pentanacci numbers A000322.
  • A186193 (program): Numbers n such that n!! is divisible by (n+1).
  • A186194 (program): A002275(n) * (A002275(n)+1).
  • A186195 (program): Expansion of (1+5x+sqrt(1+2x+9x^2))/(2(1+2x)).
  • A186196 (program): a(n)=(-1)^n*(-2)^C(n,2)*A001045(n+1).
  • A186209 (program): Coefficients of modular function denoted g_5(tau) by Atkin.
  • A186210 (program): Coefficients of modular function denoted G_5(tau) by Atkin.
  • A186219 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186220.
  • A186220 (program): Adjusted joint rank sequence of (g(i)) and (f(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186219.
  • A186221 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186222.
  • A186222 (program): Adjusted joint rank sequence of (g(i)) and (f(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186221.
  • A186223 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and pentagonal numbers. Complement of A186224.
  • A186224 (program): Adjusted joint rank sequence of (g(i)) and (f(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and pentagonal numbers. Complement of A186223.
  • A186225 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and pentagonal numbers. Complement of A186226.
  • A186226 (program): Adjusted joint rank sequence of (g(j)) and (f(i)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and pentagonal numbers. Complement of A186225.
  • A186227 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and heptagonal numbers. Complement of A186228.
  • A186228 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and heptagonal numbers. Complement of A186227.
  • A186229 (program): Expansion of (2F1( (-(1/2), 1/6); (-2/3))( 16 x) -1)/(2*x).
  • A186231 (program): Expansion of ( 2F1([-1/4, 1/4]; [-1/2], 16*x) - 1 ) / (2*x).
  • A186235 (program): Total Wiener index of double-star trees with n nodes.
  • A186237 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers (A000217) and heptagonal numbers (A000566). Complement of A186238.
  • A186238 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and heptagonal numbers. Complement of A186237.
  • A186241 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2 + x^2*A(x)^4 + x^3*A(x)^6.
  • A186243 (program): Numbers n such that 6n-5 and 6n-1 are both primes.
  • A186244 (program): Number of ternary strings of length n containing 00.
  • A186245 (program): a(n) = binomial(n^2, 2*n).
  • A186246 (program): (2n+1)-th derivative of arccot(x) at x=0.
  • A186252 (program): a(n)=Product{k=0..n-1, (3k+1)*A000108(k)}.
  • A186262 (program): Expansion of 3F2( 2, 1/2, 3/2; 3, 4;16 x).
  • A186264 (program): Expansion of 3F2( 1, 3/2, 3/2; 3, 4;16 x).
  • A186266 (program): Expansion of 2F1( 1/2, 3/2; 4; 16*x ).
  • A186269 (program): a(n)=Product{k=0..n-1, A084057(k+1)}.
  • A186270 (program): a(n)=Product{k=0..n, A003665(k)}.
  • A186271 (program): a(n)=Product{k=0..n, A001333(k)}.
  • A186272 (program): The sum of the Fibonacci and shifted tribonacci sequences.
  • A186274 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and octagonal numbers. Complement of A186159.
  • A186275 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and octagonal numbers. Complement of A186276.
  • A186276 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the triangular numbers and octagonal numbers. Complement of A186275.
  • A186285 (program): Numbers of the form p^(3^k) where p is prime and k >= 0.
  • A186288 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and pentagonal numbers. Complement of A186289.
  • A186289 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and pentagonal numbers. Complement of A186289.
  • A186290 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and pentagonal numbers. Complement of A186291.
  • A186291 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and pentagonal numbers. Complement of A186290.
  • A186293 (program): (A007519(n)-1)/2.
  • A186294 (program): (A007519(n)+1)/2.
  • A186295 (program): A007519(n)-2.
  • A186296 (program): ( A007520(n)+1 )/2.
  • A186297 (program): ( A007520(n)-1)/2.
  • A186298 (program): A007520(n)-2.
  • A186299 (program): (A007521(n)-1)/2.
  • A186300 (program): (A007521(n)+1)/2.
  • A186301 (program): a(n) = A007521(n) - 2.
  • A186302 (program): a(n) = ( A007522(n)-1 )/2.
  • A186303 (program): a(n) = ( A007522(n)+1 )/2.
  • A186304 (program): A007522(n)-2.
  • A186305 (program): n^((p-1)/2) (mod p) for p = 29.
  • A186313 (program): Baron Munchhausen’s Omni-Sequence.
  • A186314 (program): Number of ternary strings of length n which contain 01.
  • A186315 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and hexagonal numbers. Complement of A186316.
  • A186316 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and hexagonal numbers. Complement of A186315.
  • A186317 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and hexagonal numbers. Complement of A186318.
  • A186318 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and hexagonal numbers. Complement of A186317.
  • A186320 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and heptagonal numbers. Complement of A186321.
  • A186321 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and heptagonal numbers. Complement of A186320.
  • A186322 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and heptagonal numbers. Complement of A186323.
  • A186323 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and heptagonal numbers. Complement of A186322.
  • A186324 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186325.
  • A186325 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186324.
  • A186326 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186327.
  • A186327 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186326.
  • A186328 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the hexagonal numbers. Complement of A186329.
  • A186329 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the hexagonal numbers. Complement of A186328.
  • A186330 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the hexagonal numbers. Complement of A186331.
  • A186331 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the hexagonal numbers. Complement of A186330.
  • A186332 (program): Riordan array (1, x + x^2 + x^3 + x^4) without 0-column.
  • A186334 (program): A transform of the Catalan numbers.
  • A186335 (program): A transform of the central binomial coefficients.
  • A186339 (program): a(n)=A006125(n+1)*2^A001840(n).
  • A186340 (program): a(n) = 2^A001840(n).
  • A186342 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the octagonal numbers. Complement of A186343.
  • A186343 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the octagonal numbers. Complement of A186342.
  • A186344 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the octagonal numbers. Complement of A186345.
  • A186345 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the pentagonal numbers and the octagonal numbers. Complement of A186344.
  • A186346 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186347.
  • A186347 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186346.
  • A186348 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186349.
  • A186349 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186348.
  • A186350 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers. Complement of A186351.
  • A186351 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers. Complement of A186350.
  • A186352 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers. Complement of A186353.
  • A186353 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers. Complement of A186353.
  • A186354 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=3i and g(j)=j(j+1)/2 (triangular number). Complement of A186355.
  • A186355 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=3i and g(j)=j(j+1)/2 (triangular number). Complement of A186354.
  • A186356 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=3i and g(j)=j(j+1)/2 (triangular number). Complement of A186357.
  • A186357 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=3i and g(j)=j(j+1)/2 (triangular number). Complement of A186357.
  • A186359 (program): Number of permutations of {1,2,…,n} having no up-down cycles. A cycle (b(1), b(2), …) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1)<b(2)>b(3)<… .
  • A186360 (program): Number of up-down cycles in all permutations of {1,2,…,n}. A cycle (b(1), b(2), …) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1)<b(2)>b(3)<… .
  • A186363 (program): Triangle read by rows: T(n,k) is the number of cycle-up-down permutations of {1,2,…,n} having k fixed points (0 <= k <= n). A permutation is said to be cycle-up-down if it is a product of up-down cycles. A cycle (b(1), b(2), …) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1) < b(2) > b(3) < … .
  • A186364 (program): Number of cycle-up-down permutations of {1,2,…,n} having no fixed points. A permutation is said to be cycle-up-down if it is a product of up-down cycles. A cycle (b(1), b(2), …) is said to be up-down if, when written with its smallest element in the first position, it satisfies b(1)<b(2)>b(3)<… .
  • A186365 (program): Number of fixed points in all cycle-up-down permutations of {1,2,…,n}.
  • A186371 (program): Number of up-down runs in all permutations of {1,2,…,n}.
  • A186374 (program): Number of strong fixed blocks in all the permutations of [n] (see first comment for definition).
  • A186375 (program): a(n) equals the sum of the squares of the expansion coefficients for (x + y + 2*z)^n.
  • A186378 (program): a(n) equals the least sum of the squares of the coefficients in ((1 + x^k)^2 + x^p)^n found at sufficiently large p for some fixed k>0.
  • A186379 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=4i and g(j)=j(j+1)/2 (triangular number). Complement of A186380.
  • A186380 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=4i and g(j)=j(j+1)/2 (triangular number). Complement of A186379.
  • A186381 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=4i and g(j)=j(j+1)/2 (triangular number). Complement of A186382.
  • A186382 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=4i and g(j)=j(j+1)/2 (triangular number). Complement of A186381.
  • A186383 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186384.
  • A186384 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186383.
  • A186385 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186386.
  • A186386 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i and g(j)=j(j+1)/2 (triangular number). Complement of A186385.
  • A186387 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186388.
  • A186388 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186387.
  • A186389 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186390.
  • A186390 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=6i and g(j)=j(j+1)/2 (triangular number). Complement of A186389.
  • A186391 (program): a(n) equals the least sum of the squares of the coefficients in (1 + x^k + x^(2k) + x^p)^n found at sufficiently large p for some fixed k>0.
  • A186392 (program): a(n) equals the least sum of the squares of the coefficients in ((1 + x^k)^3 + x^p)^n found at sufficiently large p for some fixed k>0.
  • A186410 (program): Number of “ON” cells at n-th stage of three-dimensional version of the cellular automaton A183060 using cubes.
  • A186411 (program): First differences of A186410.
  • A186414 (program): a(n) = binomial(2n,n)^3/(n+1)^2.
  • A186415 (program): a(n) = binomial(2n,n)^3/(n+1).
  • A186416 (program): a(n) = binomial(2n,n)^4/(n+1)^3.
  • A186417 (program): The number of unlabeled graphs on n nodes with degree of 1 or 2
  • A186418 (program): Binomial(2n,n)^4/(n+1)^2.
  • A186419 (program): Binomial(2n,n)^4/(n+1)
  • A186420 (program): a(n) = binomial(2n,n)^4.
  • A186421 (program): Even numbers interleaved with repeated odd numbers.
  • A186422 (program): First differences of A186421.
  • A186423 (program): Partial sums of A186421.
  • A186424 (program): Odd terms in A186423.
  • A186428 (program): sigma(n^2) modulo sigma(n).
  • A186432 (program): Triangle associated with the set S of squares {0,1,4,9,16,…}.
  • A186436 (program): Smallest number that equals n times its last digit, or 0 if no such number exists.
  • A186438 (program): Positive numbers whose squares end in two identical digits.
  • A186444 (program): The count of numbers <= n for which 3 is an infinitary divisor.
  • A186446 (program): Expansion of 1/(1 - 7*x + 2*x^2).
  • A186493 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=5i and g(j)=j-th pentagonal number. Complement of A186494.
  • A186494 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=5i and g(j)=j-th pentagonal number. Complement of A186493.
  • A186495 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i (A008587) and g(j)=j-th pentagonal number (A000326). Complement of A186496.
  • A186496 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i and g(j)=j-th pentagonal number. Complement of A186495.
  • A186497 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=3i-2 and g(j)=j-th triangular number. Complement of A186498.
  • A186498 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=3i-2 and g(j)=j-th triangular number. Complement of A186497.
  • A186499 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-4+5j^2. Complement of A186500.
  • A186500 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-4+5j^2. Complement of A186499.
  • A186511 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-4+5j^2. Complement of A186512.
  • A186512 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-4+5j^2. Complement of A186511.
  • A186513 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=4+5j^2. Complement of A186514.
  • A186514 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=4+5j^2. Complement of A186513.
  • A186515 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=4+5j^2. Complement of A186516.
  • A186516 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=4+5j^2. Complement of A186515.
  • A186524 (program): Numbers n such that n == prime(n) (mod 7).
  • A186525 (program): Semiprimes of the form 7k+1.
  • A186539 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-2+3j^2. Complement of A186540.
  • A186540 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-2+3j^2. Complement of A186539.
  • A186541 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-2+3j^2. Complement of A186542.
  • A186542 (program): Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=i^2 and g(j)=-2+3j^2. Complement of A186541.
  • A186544 (program): a(n) = floor((Pi-2)*n/(Pi-3)); complement of A187320.
  • A186546 (program): Floor-Sqrt transform of Catalan numbers (A000108).
  • A186575 (program): Expansion of (1 + 2*x + 6*x^2)/(1 - x - x^2 - 2*x^3) in powers of x.
  • A186620 (program): Fibonacci sequence beginning 12, 25.
  • A186621 (program): Semiprimes - 1.
  • A186633 (program): G.f.: Product_{n>=1} (1 + n^n*x^n)^(1/n).
  • A186636 (program): a(n) = n*(n^3+n^2+2*n+1).
  • A186638 (program): a(0)=a(1)=a(2)=0; thereafter a(n) = n*a(n-1) + n*a(n-2)/(n-2) + (-1)^(n-1)*4/(n-2).
  • A186639 (program): a(n) = n!/2-(-2)^(n-2)*(n-2).
  • A186643 (program): The number of divisors d of n which are either d=1 or for which the highest power d^k dividing n has odd exponent k.
  • A186644 (program): The sum of the oex divisors of n.
  • A186646 (program): Every fourth term of the sequence of natural numbers 1,2,3,4,… is halved.
  • A186647 (program): Even numbers whose decimal digits sum to a prime.
  • A186648 (program): Number of walks f length n on a square lattice ending with x > 0 and y > 0.
  • A186679 (program): First differences of A116697.
  • A186680 (program): Total number of positive integers below 10^n requiring 17 positive biquadrates in their representation as sum of biquadrates.
  • A186681 (program): Total number of n-digit numbers requiring 17 positive biquadrates in their representation as sum of biquadrates.
  • A186682 (program): Total number of positive integers below 10^n requiring 18 positive biquadrates in their representation as sum of biquadrates.
  • A186683 (program): Total number of n-digit numbers requiring 18 positive biquadrates in their representation as sum of biquadrates.
  • A186684 (program): Total number of positive integers below 10^n requiring 19 positive biquadrates in their representation as sum of biquadrates.
  • A186685 (program): Total number of n-digit numbers requiring 19 positive biquadrates in their representation as sum of biquadrates.
  • A186688 (program): Semiprimes of the form n^4 + 1.
  • A186689 (program): Numbers n such that n^4 + 1 is a semiprime.
  • A186690 (program): Expansion of - (1/8) theta_3’‘(0, q) / theta_3(0, q) in powers of q.
  • A186697 (program): Next Fibonacci number after n-th prime number.
  • A186698 (program): Next prime after n-th palindrome.
  • A186700 (program): Next palindrome after n-th prime.
  • A186701 (program): Partial sums of Collatz sequence (A008908).
  • A186704 (program): The minimum number of distinct distances determined by n points in the Euclidean plane.
  • A186705 (program): The maximum number of occurrences of the same distance among n points in the plane.
  • A186706 (program): Decimal expansion of the Integral of Dedekind Eta(x*I) from x = 0 … Infinity.
  • A186707 (program): Partial sums of A007202 (crystal ball sequence for hexagonal close-packing).
  • A186711 (program): Greatest common divisor of the n-th and (n+1)st 3-smooth numbers.
  • A186720 (program): As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k^2.
  • A186722 (program): a(n) = numerator of Sum_{k=1..p-1} 1/k^2 for p the n-th prime.
  • A186723 (program): a(n) = n^n! (mod 10)
  • A186731 (program): a(3n) = 2n, a(3n+1) = n, a(3n+2) = n+1.
  • A186738 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-1)*a(n-2) + 1.
  • A186739 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-2)*a(n-2) + 1.
  • A186741 (program): Expansion of f(x^5, x^7) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A186742 (program): Expansion of f(x, x^11) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A186749 (program): a(n) = phi(n - phi(n) + 3).
  • A186752 (program): Length of minimum representation of the permutation [n,n-1,…,1] as the product of transpositions (1,2) and left and right rotations (1,2,…,n).
  • A186755 (program): Number of permutations of {1,2,…,n} having no increasing cycles. A cycle (b(1), b(2), …) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<… .
  • A186760 (program): Number of cycles that are either nonincreasing or of length 1 in all permutations of {1,2,…,n}. A cycle (b(1), b(2), …) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<… .
  • A186762 (program): Number of permutations of {1,2,…,n} having no increasing odd cycles. A cycle (b(1), b(2), …) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<… . A cycle is said to be odd if it has an odd number of entries.
  • A186763 (program): Number of increasing odd cycles in all permutations of {1,2,…,n}.
  • A186768 (program): Number of nonincreasing odd cycles in all permutations of {1,2,…,n}. A cycle (b(1), b(2), …) is said to be increasing if, when written with its smallest element in the first position, it satisfies b(1)<b(2)<b(3)<… . A cycle is said to be odd if it has an odd number of entries.
  • A186773 (program): Odd numbers whose decimal digits sum to a prime.
  • A186776 (program): Stanley Sequence S(0,2).
  • A186783 (program): Diameter of the symmetric group S_n when generated by the transposition (1,2) and both left and right rotations by (1,2,…,n).
  • A186808 (program): Numbers n such that there are a prime number of unlabeled distributive lattices with n elements.
  • A186809 (program): Period 6 sequence [0, 1, 2, 0, -2, -1, …].
  • A186810 (program): Partial sums of A009940.
  • A186812 (program): Expansion of 1/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-x).
  • A186813 (program): a(n) = n if n odd, a(2n) = 3n if n odd, a(4n) = 2n.
  • A186815 (program): Numbers n such that n^2-10 is a prime.
  • A186826 (program): Riordan array (s(x),x*S(x)) where s(x) is the g.f. of the little Schroeder numbers A001003, and S(x) is the g.f. of the large Schroeder numbers A006318.
  • A186827 (program): Riordan array (1-x, x(1-x)/(1+x)).
  • A186828 (program): Diagonal sums of number triangle A186826.
  • A186830 (program): Keith sequence for the number 197.
  • A186852 (program): Number of 3-step knight’s tours on a (n+2)X(n+2) board summed over all starting positions
  • A186862 (program): Number of 3-step king’s tours on an n X n board summed over all starting positions
  • A186924 (program): Expansion of (phi(-q^3) / phi(-q))^2 in powers of q where phi is a Ramanujan theta function.
  • A186925 (program): Coefficient of x^n in (1+n*x+x^2)^n.
  • A186942 (program): a(n)=2(4^n-n*2^n)-1.
  • A186944 (program): Geometric mean of n-th row of A080508.
  • A186947 (program): a(n) = 4^n - n*2^n.
  • A186948 (program): a(n) = 3^n - 2*n.
  • A186949 (program): a(n) = 2^n - 2*(binomial(1,n) - binomial(0,n)).
  • A186950 (program): a(n) = n^2 - 47*n + 479.
  • A186971 (program): Maximal cardinality of a subset of {1, 2, …, n} containing n and having pairwise coprime elements.
  • A186996 (program): G.f. satisfies: A(x) = 1 + x*A(x) + x^2*A(x)^4.
  • A186997 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3 + x^2*A(x)^4.
  • A187003 (program): Expansion of 1/(1-x-2*x^2-3*x^3-3*x^4-2*x^5-x^6).
  • A187004 (program): Expansion of A(x) = (1 + 2*x^2 + 6*x^3 + 9*x^4 + 8*x^5 + 5*x^6) / (1 - x - 2*x^2 - 3*x^3 - 3*x^4 - 2*x^5 - x^6).
  • A187012 (program): Antidiagonal sums of A103516.
  • A187018 (program): Coefficient of x^n in (1 + x + n*x^2)^n.
  • A187019 (program): Coefficient of x^n in expansion of (1+n*x+(n+1)*x^2)^n.
  • A187021 (program): Coefficient of x^n in (1 + (n+1)*x + n*x^2)^n.
  • A187034 (program): Number triangle T(n,k) = (-1)^(n-k) if binomial(k, n-k) > 0, 0 otherwise, with 0 <= k <= n.
  • A187035 (program): Diagonal sums of number triangle A187034.
  • A187036 (program): An eigensequence of A187034.
  • A187038 (program): Row sums of number triangle A187037.
  • A187039 (program): Numbers that have equal counts of even and odd exponents of primes in their factorization.
  • A187044 (program): Row sums of number triangle A070895.
  • A187047 (program): Number of 3-step one or two space at a time bishop’s tours on an n X n board summed over all starting positions
  • A187053 (program): Expansion of (psi(x^2) / psi(x))^3 in powers of x where psi() is a Ramanujan theta function.
  • A187059 (program): The exponent of highest power of 2 dividing the product of the elements of the n-th row of Pascal’s triangle (A001142).
  • A187065 (program): Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3} = {-2,0,1}, n=2*r+p_i, and define a(-2)=1. Then, a(n)=a(2*r+p_i) gives the quantity of H_(7,1,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt(2*cos(Pi/7)).
  • A187066 (program): Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3} = {-2,0,1}, n=2*r+p_i, and define a(-2)=0. Then, a(n)=a(2*r+p_i) gives the quantity of H_(7,2,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt(2*cos(Pi/7)).
  • A187067 (program): Let i be in {1,2,3} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3} = {-2,0,1}, n = 2*r + p_i and define a(-2)=0. Then, a(n) = a(2*r + p_i) gives the quantity of H_(7,3,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x = sqrt(2*cos(Pi/7)).
  • A187068 (program): Let i be in {1,2,3}, let r >= 0 be an integer and n=2*r+i-1. Then a(n)=a(2*r+i-1) gives the quantity of H_(7,1,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt((2*cos(Pi/7))^2-1).
  • A187069 (program): Let i be in {1,2,3}, let r >= 0 be an integer and n=2*r+i-1. Then a(n)=a(2*r+i-1) gives the quantity of H_(7,2,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt((2*cos(Pi/7))^2-1).
  • A187070 (program): Let i be in {1,2,3}, let r >= 0 be an integer and n=2*r+i-1. Then a(n)=a(2*r+i-1) gives the quantity of H_(7,3,0) tiles in a subdivided H_(7,i,r) tile after linear scaling by the factor x^r, where x=sqrt((2*cos(Pi/7))^2-1).
  • A187071 (program): Expansion of d/dx arctan(x*A001003(x)).
  • A187074 (program): a(n) = 0 if and only if n is of the form 3*k or 4*k + 2, otherwise a(n) = 1.
  • A187076 (program): Coefficients of L-series for elliptic curve “144a1”: y^2 = x^3 - 1.
  • A187077 (program): Number of row-convex polyplets with n cells.
  • A187078 (program): 38 followed by n ones.
  • A187090 (program): Smallest multiple of n beginning with 9.
  • A187091 (program): McKay-Thompson series of class 12H for the Monster group with a(0) = 4.
  • A187093 (program): a(0)=0, a(1)=a(2)=1; thereafter, a(n+1) = n^2 - a(n-1).
  • A187100 (program): Expansion of q * (psi(-q^3) * psi(q^6)) / (psi(-q) * phi(-q)) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A187103 (program): Maximum order of explicit Runge-Kutta method with n function evaluations in each step.
  • A187107 (program): Number of nontrivial compositions of differential operations and directional derivative of the n-th order on the space R^9.
  • A187109 (program): Decimal expansion of sqrt(2/11).
  • A187110 (program): Decimal expansion of sqrt(3/8).
  • A187127 (program): Triangular numbers k*(k+1)/2 mod 100, sorted and uniqued.
  • A187129 (program): Consider all pairs of primes (p,q) with p+q = 2n, p <= q; a(n) is the sum of all the q’s.
  • A187130 (program): McKay-Thompson series of class 12I for the Monster group with a(0) = -3.
  • A187143 (program): McKay-Thompson series of class 12I for the Monster group with a(0) = -1.
  • A187144 (program): McKay-Thompson series of class 12I for the Monster group with a(0) = 1.
  • A187145 (program): McKay-Thompson series of class 12I for the Monster group with a(0) = 3.
  • A187146 (program): McKay-Thompson series of class 12B for the Monster group with a(0) = 5.
  • A187147 (program): McKay-Thompson series of class 12B for the Monster group with a(0) = -4.
  • A187148 (program): McKay-Thompson series of class 12B for the Monster group with a(0) = -3.
  • A187150 (program): Expansion of psi(-x)^4 / chi(-x)^2 in powers of x where psi(), chi() are Ramanujan theta functions.
  • A187151 (program): Number of walks of length n starting at origin and ending in first quadrant on a square lattice.
  • A187153 (program): Expansion of q * (psi(q) / psi(q^2)) / (psi(q^3) / psi(q^6))^3 in powers of q where psi() is a Ramanujan theta function.
  • A187154 (program): Expansion of psi(x^4) / phi(-x) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A187156 (program): Number of 3-step one space at a time bishop’s tours on an n X n board summed over all starting positions.
  • A187157 (program): Number of 4-step one space at a time bishop’s tours on an n X n board summed over all starting positions.
  • A187158 (program): Number of 5-step one space at a time bishop’s tours on an n X n board summed over all starting positions.
  • A187163 (program): Number of 2-step self-avoiding walks on an n X n X n cube summed over all starting positions.
  • A187164 (program): Number of 3-step self-avoiding walks on an n X n X n cube summed over all starting positions.
  • A187173 (program): Number of 3-step left-handed knight’s tours (moves only out two, left one) on an n X n board summed over all starting positions.
  • A187174 (program): Number of 4-step left-handed knight’s tours (moves only out two, left one) on an n X n board summed over all starting positions.
  • A187179 (program): Number of nontrivial compositions of differential operations and directional derivative of the n-th order on the space R^10.
  • A187180 (program): Parse the infinite string 0101010101… into distinct phrases 0, 1, 01, 010, 10, …; a(n) = length of n-th phrase.
  • A187181 (program): Parse the infinite string 012012012012… into distinct phrases 0, 1, 2, 01, 20, 12, 012, …; a(n) = length of n-th phrase.
  • A187190 (program): Number of 3-turn rook’s tours on an n X n board summed over all starting positions
  • A187191 (program): Number of 4-turn rook’s tours on an n X n board summed over all starting positions
  • A187206 (program): a(n) = 6*(24*n - 1).
  • A187219 (program): Number of partitions of n that do not contain parts less than the smallest part of the partitions of n-1.
  • A187220 (program): Gullwing sequence (see Comments lines for precise definition).
  • A187221 (program): First differences of A187220.
  • A187224 (program): Rank transform of the sequence floor(3*n/2).
  • A187225 (program): Complement of A187224.
  • A187243 (program): Number of ways of making change for n cents using coins of 1, 5, and 10 cents.
  • A187246 (program): Number of cycles with 2 alternating runs in all permutations of [n] (it is assumed that the smallest element of the cycle is in the first position).
  • A187249 (program): Number of cycles with at most 2 alternating runs in all permutations of [n] (it is assumed that the smallest element of the cycle is in the first position).
  • A187251 (program): Number of permutations of [n] having no cycle with 3 or more alternating runs (it is assumed that the smallest element of a cycle is in the first position).
  • A187252 (program): Number of cycles with at least 3 alternating runs in all permutations of [n] (it is assumed that the smallest element of a cycle is in the first position).
  • A187254 (program): Number of 3-noncrossing RNA structures over 2n vertices with no isolated vertices.
  • A187256 (program): Number of peakless Motzkin paths of length n, assuming that the (1,0)-steps come in 2 colors.
  • A187258 (program): Number of UH^jD’s for some j>0, in all peakless Motzkin paths of length n (here U=(1,1), D=(1,-1) and H=(1,0); can be easily expressed using RNA secondary structure terminology).
  • A187260 (program): Number of uh^jd’s for some j>0, starting at level 0, where u=(1,1), h=(1,0), and d=(1,-1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology).
  • A187263 (program): Number of nonempty subsets of {1, 2, …, n} with <=2 pairwise coprime elements.
  • A187272 (program): a(n) = (n/4)*2^(n/2)*((1+sqrt(2))^2 + (-1)^n*(1-sqrt(2))^2).
  • A187273 (program): a(n) = (n/4)*3^(n/2)*((1+sqrt(3))^2+(-1)^n*(1-sqrt(3))^2).
  • A187274 (program): a(n) = n*4^(n/2 - 1)*(9 + (-1)^n).
  • A187275 (program): a(n) = (n/4)*5^(n/2)*((1+sqrt(5))^2+(-1)^n*(1-sqrt(5))^2).
  • A187277 (program): Let S denote the palindromes in the language {0,1,2,…,n-1}*; a(n) = number of words of length 4 in the language SS.
  • A187285 (program): Smallest multiple of n beginning with 1.
  • A187287 (program): Number of 2-step one or two space at a time rook’s tours on an n X n board summed over all starting positions.
  • A187288 (program): Number of 3-step one or two space at a time rook’s tours on an n X n board summed over all starting positions.
  • A187297 (program): Number of 2-step one space leftwards or up, two space rightwards or down asymmetric rook’s tours on an n X n board summed over all starting positions
  • A187298 (program): Number of 3-step one space leftwards or up, two space rightwards or down asymmetric rook’s tours on an n X n board summed over all starting positions.
  • A187306 (program): Alternating sum of Motzkin numbers A001006.
  • A187307 (program): Hankel transform of an alternating sum of Motzkin numbers.
  • A187318 (program): a(n) = floor(9*n/5).
  • A187320 (program): a(n) = floor((Pi-2)*n); complement of A186544.
  • A187321 (program): a(n) = floor(n/2) + floor(n/4).
  • A187322 (program): a(n) = floor(n/2) + floor(3*n/4).
  • A187323 (program): Floor(n/2)+floor(n/3)+floor(n/4).
  • A187324 (program): a(n) = floor(n/2) + floor(n/3) - floor(n/4).
  • A187325 (program): a(n) = floor(n/2) + floor(n/3) + floor(n/4) + floor(n/5).
  • A187326 (program): Floor(n/4)+floor(n/2)+floor(3n/4).
  • A187327 (program): a(n) = floor(n/5) + floor(2n/5) + floor(3n/5).
  • A187328 (program): a(n) = floor((2-1/sqrt(2))*n); complement of A187338.
  • A187329 (program): Floor((3-sqrt(5))n).
  • A187330 (program): a(n) = floor((4-sqrt(5))*n); complement of A187339.
  • A187331 (program): a(n) = Sum_{k=1..4} floor(k*n/4).
  • A187332 (program): Complement of A187331.
  • A187333 (program): Floor(n/5)+floor(2n/5)+floor(3n/5)+floor(4n/5).
  • A187334 (program): Sum{floor(kn/5), k=1,2,3,4,5}; complement of A187335.
  • A187335 (program): Complement of A187334.
  • A187336 (program): Sum{floor(kn/6), k=1,2,3,4,5}.
  • A187337 (program): Sum{floor(kn/7), k=1,2,3,4,5,6}.
  • A187338 (program): a(n) = 3*n + floor(sqrt(2)*n), complement of A187328.
  • A187339 (program): a(n) = floor((7+sqrt(5))*n/4); complement of A187330.
  • A187340 (program): Hankel transform of A014301(n+1).
  • A187341 (program): Floor((5-sqrt(5))n); complement of A187342.
  • A187342 (program): Floor(((15+sqrt(5))/11)n); complement of A187341.
  • A187357 (program): Catalan trisection: A000108(3*n), n>=0.
  • A187358 (program): Catalan trisection: A000108(3*n+1), n>=0.
  • A187359 (program): Catalan trisection: A000108(3*n + 2)/2, n>=0.
  • A187361 (program): Pell trisection: Pell(3*n+1), n >= 0.
  • A187362 (program): Pell trisection: Pell(3*n+2), n >= 0.
  • A187364 (program): Trisection of A000984 (central binomial coefficients): binomial(2(3n+1),3n+1)/2, n>=0.
  • A187365 (program): Trisection of A000984 (central binomial coefficients): binomial(2(3n+2),3n+2)/3!, n>=0.
  • A187366 (program): One half of a trisection of A001700: binomial(6n+5,3(n+1))/2, n>=0.
  • A187378 (program): Number of 4-step S, NW and NE-moving king’s tours on an n X n board summed over all starting positions
  • A187385 (program): a(n) = floor(r*n), where r=1+sqrt(3)+sqrt(2); complement of A187386.
  • A187386 (program): a(n) = floor(s*n), where s=1+sqrt(3)-sqrt(2); complement of A187385.
  • A187387 (program): Floor(r*n), where r=1+sqrt(6)+sqrt(5); complement of A187388.
  • A187388 (program): Floor(s*n), where s=1+sqrt(6)-sqrt(5); complement of A187387.
  • A187389 (program): a(n) = floor(r*n), where r = 1 + sqrt(7) + sqrt(6); complement of A187390.
  • A187390 (program): a(n) = floor(s*n), where s = 1 + sqrt(7) - sqrt(6); complement of A187389.
  • A187391 (program): Floor(r*n), where r=1+sqrt(8)+sqrt(7); complement of A187392.
  • A187392 (program): Floor(s*n), where s=1+sqrt(8)-sqrt(7); complement of A189391.
  • A187393 (program): a(n) = floor(r*n), where r = 4 + sqrt(8); complement of A187394.
  • A187394 (program): a(n) = floor(s*n), where s = 4 - sqrt(8); complement of A187393.
  • A187395 (program): a(n) = floor(r*n), where r = 4 + sqrt(10); complement of A187396.
  • A187396 (program): a(n) = floor(s*n), where s =-2 + sqrt(10); complement of A187395.
  • A187409 (program): n^2 + nextprime(n^2).
  • A187426 (program): Decimal expansion of (3-phi)^2 = 10 - 5*phi where phi is the golden ratio.
  • A187430 (program): Number of nonnegative walks of n steps with step sizes 1 and 2, starting and ending at 0.
  • A187442 (program): A trisection of A001405 (central binomial coefficients: binomial(3*n,floor(3*n/2)), n>=0.
  • A187443 (program): A trisection of A001405 (central binomial coefficients): binomial(3n+1,floor((3n+1)/2)), n>=0.
  • A187444 (program): A trisection of A001405 (central binomial coefficients): binomial(3n+2,floor((3n+2)/2))/2, n>=0.
  • A187452 (program): Number of right isosceles triangles that can be formed from the n^2 points of n X n grid of points (or geoboard).
  • A187466 (program): a(n) = 9^n mod 11.
  • A187468 (program): Sum of the squares modulo 2^n of the odd numbers less than 2^n.
  • A187476 (program): Rank transform of the sequence floor(3(n-1)/2)); complement of A187477.
  • A187477 (program): Complement of A187476.
  • A187478 (program): Rank transform of the sequence floor(3(n-2)/2)); complement of A187479.
  • A187479 (program): Complement of A187478.
  • A187482 (program): Rank transform of the sequence ceiling(2n/3); complement of A187483.
  • A187483 (program): Complement of A187482.
  • A187484 (program): Rank transform of the sequence A004526=(0,0,1,1,2,2,3,3,4,4,…); complement of A187475.
  • A187485 (program): Positions of 0’s in A123740; complement of A003623.
  • A187486 (program): Distance between first and second positions of A181762(n).
  • A187487 (program): Numerator of n minus n-th harmonic number.
  • A187497 (program): Let i be in {1,2,3,4} and r>=0 an integer. Let p ={p_1,p_2,p_3,p_4} = {-3,0,1,2}, n=3*r+p_i and define a(-3)=0. Then a(n)=a(3*r+p_i) gives the number of H_(9,3,0) tiles in a subdivided H_(9,i,r) tile after linear scaling by the factor Q^r, where Q=sqrt(2*cos(Pi/9)).
  • A187508 (program): Number of 3-step S, E, and NW-moving king’s tours on an n X n board summed over all starting positions
  • A187509 (program): Number of 4-step S, E, and NW-moving king’s tours on an n X n board summed over all starting positions
  • A187532 (program): a(n) = 4^n mod 19.
  • A187535 (program): Central Lah numbers: a(n) = A105278(2*n,n) = A008297(2*n,n).
  • A187536 (program): Partial sums of the central Lah numbers (A187535).
  • A187538 (program): Alternating partial sums of the central Lah numbers (A187535).
  • A187539 (program): Alternated binomial partial sums of central Lah numbers (A187535).
  • A187540 (program): Binomial partial sums of the central Lah numbers.
  • A187541 (program): a(4n+2) = 2n+1, otherwise a(n) = 4n.
  • A187549 (program): Arises in a Diophantine problem with one prime, two squares of primes and s powers of two.
  • A187560 (program): a(n) = 4^(n+1)-2^n-1.
  • A187561 (program): Least number k >= 0 such that prime(n)*(prime(n)-k)-1 is prime.
  • A187562 (program): Least k >= 0 such that prime(n)*(prime(n)-k)+1 is prime.
  • A187568 (program): Rank transform of the sequence round(2n/3); complement of A187569.
  • A187569 (program): Complement of A187568.
  • A187570 (program): Rank transform of the sequence ceiling(n/3); complement of A187571.
  • A187571 (program): Complement of A187570.
  • A187572 (program): Rank transform of the sequence round(n/3); complement of A187473.
  • A187573 (program): Complement of A187572.
  • A187576 (program): Rank transform of the sequence 2*floor((n-1)/2)); complement of A187577.
  • A187577 (program): Complement of A187576.
  • A187580 (program): Rank transform of the sequence 2*floor(n/2); complement of A187581.
  • A187581 (program): Complement of A187580.
  • A187594 (program): G.f. satisfies: 1/A(x) = Sum_{n>=0} (n+1)^2*A000108(n)*x^n*A(x)^n, where A000108(n) = C(2n,n)/(n+1) is the n-th Catalan number.
  • A187601 (program): n/2 times period 6 sequence [1, 2, 3, 4, 3, 2, …].
  • A187607 (program): Number of 3-step one space for components leftwards or up, two space for components rightwards or down asymmetric quasi-bishop’s tours (antidiagonal moves become knight moves) on an n X n board summed over all starting positions.
  • A187615 (program): Expansion of f(-x^17, -x^19) + x^4 * f(-x, -x^35) in powers of x where f(,) is Ramanujan’s general theta function.
  • A187619 (program): Sum of the differences of the parts in each Goldbach partition of 2n, A187129(n) - A185297(n).
  • A187620 (program): a(n) = n^6 - a(n-1), a(0)=1.
  • A187637 (program): T(n,k)=Number of n-step self-avoiding walks on a k-long line summed over all starting positions
  • A187647 (program): Partial sums of the central Stirling numbers of the second kind.
  • A187649 (program): Alternated cumulative sums of the central Stirling numbers of the second kind.
  • A187651 (program): Alternated binomial partial sums of the central Stirling numbers of the second kind.
  • A187653 (program): Binomial cumulative sums of the central Stirling numbers of the second kind (A007820).
  • A187660 (program): Triangle read by rows: T(n,k) = (-1)^(floor(3*k/2))*binomial(floor((n+k)/2),k), 0 <= k <= n.
  • A187673 (program): Partial sums of the tricapped prism numbers A005920.
  • A187677 (program): Primes of the form 8k^2 + 6k - 1 for positive k.
  • A187680 (program): a(n) = (product of divisors of n) mod (sum of divisors of n).
  • A187681 (program): Rank transform of the sequence floor(n/3); complement of A187682.
  • A187682 (program): Complement of A187681.
  • A187683 (program): Rank transform of the sequence floor(2n/3); complement of A187683.
  • A187684 (program): Complement of A187683.
  • A187689 (program): Rank transform of the sequence round(3n/4); complement of A187690.
  • A187690 (program): Complement of A187689.
  • A187691 (program): Rank transform of the sequence ceiling(3n/4); complement of A187692.
  • A187692 (program): Complement of A187691.
  • A187693 (program): G.f.: x^2*(1+4*x-3*x^2)/((1-x)^2*(1-2*x)*(1-3*x)).
  • A187709 (program): a(n) = (7*9^n + 1)/8.
  • A187710 (program): a(n) = n^2 + n + 10.
  • A187715 (program): a(n) = 5*n - (9 + (-1)^n)/2.
  • A187730 (program): Greatest common divisor of Carmichael lambda(n) and n - 1.
  • A187732 (program): Expansion of x/(x^4 - 13x^3 + 36x^2 - 13x + 1).
  • A187734 (program): a(n) is the number of n-walks between the vertices 1 and 3 of the Graph on the chalkboard in ‘Good Will Hunting’, (1997).
  • A187735 (program): G.f.: Sum_{n>=0} (2*n+1)^n * x^n / (1 + (2*n+1)*x)^n.
  • A187738 (program): G.f.: Sum_{n>=0} (3*n+1)^n * x^n / (1 + (3*n+1)*x)^n.
  • A187739 (program): G.f.: Sum_{n>=0} (3*n+2)^n * x^n / (1 + (3*n+2)*x)^n.
  • A187740 (program): G.f.: Sum_{n>=0} (5*n+1)^n * x^n / (1 + (5*n+1)*x)^n.
  • A187741 (program): G.f.: Sum_{n>=0} (1 + n*x)^n * x^n / (1 + x + n*x^2)^n.
  • A187742 (program): G.f.: Sum_{n>=0} (n+x)^n * x^n / (1 + n*x + x^2)^n.
  • A187744 (program): Numbers whose digital sum is a triangular number.
  • A187746 (program): G.f.: Sum_{n>=0} (2*n+x)^n * x^n / (1 + 2*n*x + x^2)^n.
  • A187747 (program): (n-th digit of Pi) - (n-th digit of e).
  • A187748 (program): Determinant of the n X n matrix m_(i,j) = gcd(2^i-1, 2^j-1).
  • A187756 (program): a(n) = n^2 * (4*n^2 - 1) / 3.
  • A187759 (program): Number of ways to write n=x+y (0<x<y<n) with 6x-1, 6x+1, 6y-1 and 6y+1 all prime.
  • A187760 (program): Table T(n,k) read by antidiagonals. T(n,k)=n-k+1, if n>=k, T(n,k)=k-n+2, if n < k.
  • A187765 (program): The (n-1)th decimal place of the fractional part of the square root of n.
  • A187767 (program): Number of bicolored cyclic patterns n X n.
  • A187768 (program): Decimal expansion of square root of 103.
  • A187778 (program): Numbers k dividing psi(k), where psi is the Dedekind psi function (A001615).
  • A187780 (program): Sum_{k=0..n} Lucas(k)^(n-k).
  • A187783 (program): De Bruijn’s triangle, T(m,n) = (m*n)!/(n!^m) read by downward antidiagonals.
  • A187785 (program): Number of ways to write n=x+y (x,y>=0) with {6x-1,6x+1} a twin prime pair and y a triangular number
  • A187791 (program): Repeat n+1 times 2^A005187(n).
  • A187793 (program): Sum of the deficient divisors of n.
  • A187794 (program): Sum of the perfect divisors of n.
  • A187797 (program): Numbers having at least two different ordered partitions p+q and (p+2)+(q-2) where p, q, p+2 and q-2 are all prime.
  • A187798 (program): Decimal expansion of (3-phi)/2, where phi is the golden ratio.
  • A187799 (program): Decimal expansion of 20/phi^2, where phi is the golden ratio. Also (with a different offset), decimal expansion of 3 - sqrt(5).
  • A187801 (program): Pascal’s triangle construction method applied to {1,1,2} as an initial term.
  • A187811 (program): Numbers having at least one prime factor of form 4*k+3.
  • A187816 (program): Triangle read by rows in which row n lists the first 2^(n-1) terms of A006519 in nonincreasing order, n >= 1.
  • A187818 (program): Triangle read by rows in which row n lists the first 2^(n-1) terms of A038712 in nonincreasing order, n >= 1.
  • A187824 (program): a(n) is the largest m such that n is congruent to -1, 0 or 1 mod k for all k from 1 to m.
  • A187830 (program): a(n)=2*a(n-1)+(n+3)*a(n-2)-(n+3)*a(n-3), a(0)=0, a(1)=0, a(2)=1.
  • A187832 (program): Integral from 1/2 to 1 of (1-x)/x dx.
  • A187833 (program): Rank transform of the sequence floor(3n/2-1/2); complement of A187834.
  • A187834 (program): Complement of A187833.
  • A187835 (program): Rank transform of the sequence floor(3n/2-2/3); complement of A187836.
  • A187836 (program): Complement of A187835.
  • A187844 (program): Product of negated digits of n.
  • A187845 (program): Partial sums of A187844.
  • A187848 (program): a(n) is the moment of order n for the probability density function defined by rho(x)=exp(x-1)/((Ei(x-1))^2+Pi^2) over the interval 1..infinity, with Ei the exponential integral.
  • A187873 (program): Second smallest prime after n^2.
  • A187881 (program): Triangle read by rows: the n-th column consists of n n’s followed by 0’s.
  • A187883 (program): Triangle by rows, A003983 * A000012 as infinite lower triangular matrices
  • A187887 (program): Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)).
  • A187888 (program): Riordan matrix (1/sqrt(1-4*x),x/(1-x)).
  • A187890 (program): a(1)=0, a(2)=4, a(n)=a(n-1)+a(n-2)-1.
  • A187891 (program): a(0)=0, a(1)=5, a(n)=a(n-1)+a(n-2)-1.
  • A187892 (program): a(0)=0, a(1)=6, a(n)=a(n-1)+a(n-2)-1.
  • A187893 (program): a(0)=1, a(1)=4, a(n) = a(n-1) + a(n-2) - 1.
  • A187915 (program): a(n) = (1/2)*((n+2)*P(n-1)+(5*n+1)*P(n)) where P() = A000129 are the Pell numbers.
  • A187916 (program): a(n) = C(n) if n is odd, else C(n) - C(n/2); C(n) are Catalan numbers.
  • A187917 (program): a(n) = (1/4)*(5*(n-1)*P(n)+n*P(n-1)) where P() are the Pell numbers A000129.
  • A187918 (program): Largest semiprime < n^2.
  • A187925 (program): Coefficient of x^n in (1+x+x^2+x^3+x^4)^n.
  • A187926 (program): Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/2).
  • A187944 (program): [nr+kr]-[nr]-[kr], where r=(1+sqrt(5))/2, k=3, [ ]=floor.
  • A187945 (program): Positions of 1 in A187944; complement of A101864.
  • A187946 (program): [nr+kr]-[nr]-[kr], where r=(1+sqrt(5))/2, k=5, [ ]=floor.
  • A187947 (program): Positions of 0 in A187946; complement of A134862.
  • A187948 (program): [nr+kr]-[nr]-[kr], where r=(1+sqrt(5))/2, k=6, [ ]=floor.
  • A187949 (program): Positions of 0 in A187948; complement of A187953.
  • A187950 (program): [nr+kr] - [nr] - [kr], where r = (1+sqrt(5))/2, k = 4, [.]=floor.
  • A187951 (program): Positions of 0 in A187950; complement of A187952.
  • A187952 (program): Positions of 1 in A187950; complement of A187951.
  • A187953 (program): Positions of 1 in A187948; complement of A187949.
  • A187956 (program): Half the number of (n+2) X 3 binary arrays with no 3 X 3 subblock having a sum equal to any horizontal or vertical neighbor 3 X 3 subblock sum.
  • A187967 (program): [nr+kr]-[nr]-[kr], where r=sqrt(2), k=2, [ ]=floor.
  • A187968 (program): Positions of 1 in A187967; complement (conjectured) of A098021.
  • A187969 (program): a(n) = [nr+kr]-[nr]-[kr], where r=sqrt(2), k=3, [ ]=floor.
  • A187970 (program): Positions of 0 in A187969; complement of A187971.
  • A187971 (program): Positions of 1 in A187969; complement of A187970.
  • A187972 (program): a(n) = [nr+kr]-[nr]-[kr], where r=sqrt(2), k=4, [ ]=floor.
  • A187973 (program): Positions of 0 in A187972; complement of A187974.
  • A187974 (program): Positions of 1 in A187972; complement of A187973.
  • A187975 (program): Positions of 1 in the zero-one sequence given by s(n)=[nr+5r]-[nr]-[5r], where r=sqrt(2), n>=1, [ ]=floor.
  • A187976 (program): a(n) = [nr+kr]-[nr]-[kr], where r=sqrt(2), k=6, [ ]=floor.
  • A187977 (program): Positions of 0 in A187976; complement of A187978.
  • A187978 (program): Positions of 1 in A187976; complement of A187977.
  • A188003 (program): Number of nondecreasing arrangements of 3 numbers x(i) in -(n+1)..(n+1) with the sum of sign(x(i))*x(i)^2 zero
  • A188009 (program): a(n) = [nr] - [nr-kr] - [kr], where r=(1+sqrt(5))/2, k=2, [ ]=floor.
  • A188010 (program): Positions of 0 in A188009; complement of A101866.
  • A188011 (program): a(n) = floor(n*r) - floor(n*r-k*r) - floor(k*r), where r=(1+sqrt(5))/2, k=3.
  • A188012 (program): Positions of 0 in A188011; complement of A188013.
  • A188013 (program): Positions of 1 in A188011; complement of A188012.
  • A188014 (program): a(n) = [nr]-[nr-kr]-[kr], where r=(1+sqrt(5))/2, k=4, [ ]=floor.
  • A188015 (program): Positions of 0 in A188014; complement of A188016.
  • A188016 (program): Positions of 1 in A188014; complement of A188015.
  • A188017 (program): [nr]-[nr-kr]-[kr], where r=(1+sqrt(5))/2, k=6, [ ]=floor.
  • A188018 (program): Positions of 0 in A188017; complement of A188019.
  • A188019 (program): Positions of 1 in A188017; complement of A188018.
  • A188020 (program): [nr]-[nr-kr]-[kr], where r=(1+sqrt(5))/2, k=7, [ ]=floor.
  • A188021 (program): Expansion of (x^2)/[(1-x)*(1-3*x^2-x^3)].
  • A188022 (program): Expansion of x*(1+x) / (1-3*x^2-x^3).
  • A188023 (program): Triangle by rows, A115361 * A127648
  • A188024 (program): Positions of 0 in A188020; complement of A188025.
  • A188025 (program): Positions of 1 in A188020; complement of A188024.
  • A188026 (program): Positions of 0 in the zero-one sequence given by z(n)=[nr]-[nr-8r]-[8r], where r=(1+sqrt(5))/2, [ ]=floor, n>=1.
  • A188027 (program): [nr]-[nr-kr]-[kr], where r=(1+sqrt(5))/2, k=9, [ ]=floor.
  • A188030 (program): Positions of 1 in the zero-one sequence given by [nr]-[nr-10r]-[10r], where r=(1+sqrt(5))/2, [ ]=floor, n>=1.
  • A188031 (program): [nr]-[nr-kr]-[kr], where r=(1+sqrt(5))/2, k=11, [ ]=floor.
  • A188032 (program): Positions of 0 in A188031; complement of A188033.
  • A188033 (program): Positions of 1 in A188031; complement of A188032.
  • A188034 (program): [nr]-[nr-kr]-[kr], where r=(1+sqrt(5))/2, k=12, [ ]=floor.
  • A188035 (program): Positions of 0 in A188034; complement of A188036.
  • A188036 (program): Positions of 1 in A188034; complement of A188035.
  • A188037 (program): a(n) = floor(nr) - 1 - floor((n-1)r), where r = sqrt(2).
  • A188038 (program): a(n) = [nr]-[kr]-[nr-kr], where r=sqrt(2), k=2, [ ]=floor.
  • A188039 (program): Positions of 0 in A188038; complement of A188040.
  • A188040 (program): Positions of 1 in A188038; complement of A188039.
  • A188041 (program): a(n) = [n*r]-[k*r]-[n*r-k*r], where r=sqrt(2), k=3, [ ]=floor.
  • A188042 (program): Positions of 0 in A188041; complement of A188043.
  • A188043 (program): Positions of 1 in A188041; complement of A188042.
  • A188044 (program): a(n) = [n*r] - [k*r] - [n*r-k*r], where r=sqrt(2), k=4, [ ]=floor.
  • A188045 (program): Positions of 0 in A188044; complement of A188046.
  • A188046 (program): Positions of 1 in A188044; complement of A188045.
  • A188048 (program): Expansion of (1 - x^2)/(1 - 3*x^2 - x^3).
  • A188050 (program): a(n) = A016755(n) - A001845(n).
  • A188053 (program): Stanley Sequence S(0,1,4).
  • A188060 (program): Numerator of 8^(2n-1) |B(2n)| / (2n)!, where B() are the Bernoulli numbers.
  • A188064 (program): Partial sums of wt(n)! where wt(n) is the Hamming weight of n (A000120).
  • A188067 (program): Expansion of x^2*(x^3+2*x^2+x+1)/((x-1)*(x+1))^4.
  • A188068 (program): [nr]-[kr]-[nr-kr], where r=sqrt(3), k=1, [ ]=floor.
  • A188069 (program): Positions of 0 in A188068; complement of A188070.
  • A188070 (program): Positions of 1 in A188068; complement of A188069.
  • A188071 (program): [nr]-[kr]-[nr-kr], where r=sqrt(3), k=2, [ ]=floor.
  • A188072 (program): Positions of 0 in A188071; complement of A188073.
  • A188073 (program): Positions of 1 in A188071; complement of A188072.
  • A188074 (program): Positions of 1 in the zero-one sequence [nr]-[3r]-[nr-3r], where r=sqrt(3), n>=1.
  • A188075 (program): Positions of 0 in the zero-one sequence [nr]-[4r]-[nr-4r], where r=sqrt(3), n>=1.
  • A188076 (program): [nr]-[kr]-[nr-kr], where r=sqrt(3), k=5, [ ]=floor.
  • A188078 (program): Positions of 1 in A188076; complement of A188077.
  • A188079 (program): [nr]-[kr]-[nr-kr], where r=sqrt(3), k=6, [ ]=floor.
  • A188080 (program): Positions of 0 in A188079; complement of A188081.
  • A188081 (program): Positions of 1 in A188079; complement of A188080.
  • A188082 (program): [nr+kr]-[nr]-[kr], where r=sqrt(3), k=1, [ ]=floor.
  • A188083 (program): [nr+kr]-[nr]-[kr], where r=sqrt(3), k=2, [ ]=floor.
  • A188084 (program): Positions of 0 in A188083; complement of A188084.
  • A188085 (program): Positions of 1 in A188083; complement of A188084.
  • A188086 (program): [nr+kr]-[nr]-[kr], where r=sqrt(3), k=3, [ ]=floor.
  • A188087 (program): Positions of 0 in A188086; complement of A188088.
  • A188088 (program): Positions of 1 in A188086; complement of A188087.
  • A188089 (program): Positions of 0 in the zero-one sequence [nr+4r]-[nr]-[4r], where r=sqrt(3), n>=1.
  • A188090 (program): [nr+kr]-[nr]-[kr], where r=sqrt(3), k=5, [ ]=floor.
  • A188091 (program): Positions of 0 in A188090; complement of A188092.
  • A188092 (program): Positions of 1 in A188090; complement of A188091.
  • A188093 (program): [nr+kr]-[nr]-[kr], where r=sqrt(3), k=6, [ ]=floor.
  • A188094 (program): Positions of 0 in A188093; complement of A188095.
  • A188095 (program): Positions of 1 in A188093; complement of A188094.
  • A188108 (program): Triangle T(n,m) read by rows, obtained from [A(x)]^m = Sum_{n>=m} T(n,m)*x^n, where A(x) (the g.f. for A069271) satisfies 2*x^2*A(x)^3 = 1 - 2*x*A(x) - sqrt(1-4*x*A(x)).
  • A188111 (program): Triangle T(n,m) read by rows, [A(x)]^m = Sum_{n>=m} T(n,m)*x^n, where A(x) satisfies A(x) = x/(1-A(x)-A(x)^2).
  • A188123 (program): Number of strictly increasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero.
  • A188128 (program): Expansion of (4-6*x-6*x^2+x^3)/((1+x)*(1-3*x+x^3)).
  • A188129 (program): a(n) = (2^n+3)^2-8.
  • A188131 (program): Primes p == 1 (mod 4) such that 6p+1 is prime.
  • A188132 (program): Primes p such that p == 3 (mod 4) and 6p+1 is prime.
  • A188134 (program): a(4*n) = n, a(1+2*n) = 4+8*n, a(2+4*n) = 2+4*n.
  • A188135 (program): a(n) = 8*n^2 + 2*n + 1.
  • A188137 (program): Riordan array (1, x*(1-x)/(1-3*x+x^2)).
  • A188140 (program): Central coefficient in (1 + x + 2^n*x^2)^n.
  • A188143 (program): Binomial transform of A187848.
  • A188146 (program): Three interleaved 1st-order polynomials: a(3*n) = 1+4*n, a(1+3*n) = 3+4*n, a(2+3*n) = 1+n.
  • A188148 (program): Number of 3-step self-avoiding walks on an n X n square summed over all starting positions.
  • A188149 (program): Number of 4-step self-avoiding walks on an n X n square summed over all starting positions.
  • A188156 (program): If A187211 is written, starting at its fifth term, as a triangle with rows of lengths 2, 4, 8, 16, …, the n-th row begins with the first 2^n-1 terms of the present sequence.
  • A188161 (program): 2*4^n + 3.
  • A188163 (program): Smallest m such that A004001(m) = n.
  • A188164 (program): Number of palindromic structures of length n.
  • A188165 (program): 2^n + 9.
  • A188167 (program): a(2+4*n)=1+2*n, otherwise a(n)=2*n.
  • A188168 (program): a(0) = a(1) = 1; a(n) = 5*a(n-1) + 5*a(n-2).
  • A188169 (program): The number of divisors d of n of the form d == 1 (mod 8).
  • A188170 (program): The number of divisors d of n of the form d == 3 (mod 8).
  • A188171 (program): The number of divisors d of n of the form d == 5 (mod 8).
  • A188172 (program): Number of divisors d of n of the form d == 7 (mod 8).
  • A188182 (program): Number of strictly increasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero
  • A188187 (program): a(n) = [nr]-[kr]-[nr-kr], where r=sqrt(5), k=1, [ ]=floor.
  • A188188 (program): Positions of 0 in A188187; complement of A004958.
  • A188189 (program): [nr]-[kr]-[nr-kr], where r=sqrt(5), k=2, [ ]=floor.
  • A188190 (program): Positions of 0 in A188189; complement of A188191.
  • A188191 (program): Positions of 1 in A188189; complement of A188190.
  • A188192 (program): [nr]-[kr]-[nr-kr], where r=sqrt(5), k=3, [ ]=floor.
  • A188202 (program): Central coefficients in (1 + 2^n*x + x^2)^n.
  • A188203 (program): G.f.: exp( Sum_{n>=1} A188202(n)*x^n/n ) where A188202(n) = [x^n] (1 + 2^n*x + x^2)^n.
  • A188212 (program): Number of nondecreasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero.
  • A188215 (program): Starting with an empty list, n is inserted after the a(n)th element such that the binary representations of the list’s elements are always sorted lexicographically.
  • A188217 (program): Positions of 0 in A188192; complement of A188218.
  • A188218 (program): Positions of 1 in A188192; complement of A188217.
  • A188219 (program): Positions of 0 in the zero-one sequence [nr]-[4r]-[nr-4r], where r=sqrt(5), n>=1.
  • A188220 (program): Positions of 1 in the zero-one sequence [nr]-[5r]-[nr-5r], where r=sqrt(5), n>=1.
  • A188221 (program): [nr+kr]-[nr]-[kr], where r=sqrt(5), k=1, [ ]=floor.
  • A188222 (program): Positions of 0 in A188221; complement of A004976.
  • A188223 (program): G.f.: (1+x^2+x^3)/(1-x-x^2-x^4-x^5)
  • A188225 (program): Number of ways to select 15 knights from n knights sitting at a round table if no adjacent knights are chosen.
  • A188237 (program): Number of nondecreasing arrangements of 4 numbers in -(n+2)..(n+2) with sum zero and not more than two numbers equal.
  • A188257 (program): [nr+kr]-[nr]-[kr], where r=sqrt(5), k=2, [ ]=floor.
  • A188258 (program): Positions of 0 in A188257; complement of A188259.
  • A188259 (program): Positions of 1 in A188257; complement of A188258.
  • A188260 (program): [nr+kr]-[nr]-[kr], where r=sqrt(5), k=3, [ ]=floor.
  • A188261 (program): Positions of 0 in A188260; complement of A188262.
  • A188262 (program): Positions of 1 in A188260; complement of A188261.
  • A188264 (program): Numbers m that are divisible by the product of the factorials of their digits in base 10.
  • A188265 (program): Positions of 1 in A188398; complement of A188399.
  • A188266 (program): Coefficient of x^n in the series 1/F(-1/2,1/2;1;16x), where F(a1,a2;b;x) is the hypergeometric series.
  • A188267 (program): Coefficient of x^n in the series 1/(1-x*F(1/2,1/2;1;16x)), where F(a1,a2;b;x) is the hypergeometric series.
  • A188270 (program): Number of nondecreasing strings of numbers (x(i), i=1..n) in -2..2 with sum x(i)^3 equal to 0.
  • A188285 (program): Riordan matrix ( (1-2x)/(1-2x-x^2}, (x-2x^2)/(1-2x-x^2) ).
  • A188289 (program): Binomial sum related to rooted trees.
  • A188290 (program): Positions of 0 in the zero-one sequence [nr+4r]-[nr]-[4r], where r=sqrt(5) and []=floor.
  • A188291 (program): [nr+kr]-[nr]-[kr], where r=sqrt(5), k=5, [ ]=floor.
  • A188292 (program): Positions of 0 in A188291; complement of A188293.
  • A188293 (program): Positions of 1 in A188291; complement of A188292.
  • A188295 (program): [nr]-[nr-r], where r=1/sqrt(2), [ ]=floor.
  • A188297 (program): a(n) = [n*r] - [k*r] - [n*r-k*r], where r=1/sqrt(2), k=2, [ ]=floor.
  • A188298 (program): Positions of 0 in A188297; complement of A188299.
  • A188299 (program): Positions of 1 in A188297; complement of A188298.
  • A188300 (program): a(n) = [n*r] - [k*r] - [n*r-k*r], where r=1/sqrt(2), k=3, [ ]=floor.
  • A188301 (program): Positions of 0 in A188300; complement of A188302.
  • A188302 (program): Positions of 1 in A188300; complement of A188301.
  • A188313 (program): A (25,-29) Somos-4 sequence.
  • A188315 (program): A (25,-29) Somos-4 sequence.
  • A188316 (program): Riordan array (1/(1-x^2), x/((1-x)*(1-x^2))).
  • A188318 (program): a(n) = [n*r] - [k*r] - [n*r-k*r], where r=1/sqrt(2), k=4, [ ]=floor.
  • A188319 (program): Positions of 0 in A188318; complement of A188320.
  • A188320 (program): Positions of 1 in A188318; complement of A188319.
  • A188334 (program): Number of nondecreasing arrangements of 4 nonzero numbers in -(n+2)..(n+2) with sum zero
  • A188340 (program): Decimal expansion of 1 - 1/Pi.
  • A188341 (program): Numbers having no 0’s and not more than one 1 in their representation in base 3.
  • A188365 (program): a(n) = n! * [x^n] exp((1 - 2*x)/(1 - 3*x + x^2) - 1).
  • A188371 (program): a(n) = [n*r] - [k*r] - [n*r-k*r], where r=1/sqrt(2), k=6, [ ]=floor.
  • A188372 (program): Positions of 0 in A188371; complement of A188373.
  • A188373 (program): Positions of 1 in A188371; complement of A188372.
  • A188374 (program): [nr+kr]-[nr]-[kr], where r=1/sqrt(2), k=2, [ ]=floor.
  • A188375 (program): Positions of 0 in A188374; complement of A188376.
  • A188376 (program): Positions of 1 in A188374; complement of A188375.
  • A188377 (program): a(n) = n^3 - 4n^2 + 6n - 2.
  • A188378 (program): Partial sums of A005248.
  • A188382 (program): Primes of the form 8*n^2 + 2*n + 1.
  • A188383 (program): Positions of 1 in the zero-one sequence [nr+3r]-[nr]-[3r], where r=1/sqrt(2).
  • A188385 (program): Highest exponent in the prime factorization of n^n
  • A188386 (program): a(n) = numerator(H(n+2)-H(n-1)), where H(n) = Sum_{k=1..n} 1/k is the n-th harmonic number.
  • A188387 (program): Central coefficient in (1 + (2^n+1)*x + 2^n*x^2)^n for n>=0.
  • A188395 (program): a(n) = [n*r +k*r]-[n*r]-[k*r], where r=1/sqrt(2), k=4, [ ]=floor.
  • A188396 (program): Positions of 0 in A188395; complement of A188397.
  • A188397 (program): Positions of 1 in A188395; complement of A188396.
  • A188398 (program): a(n) = [n*r+k*r] - [n*r] - [k*r], where r=1/sqrt(2), k=5, [ ]=floor.
  • A188399 (program): Positions of 0 in A188398; complement of A188265.
  • A188424 (program): Number of primes of the form k^2 + k + 2n - 1 for k = 0..2n-1.
  • A188427 (program): Position of 5^n in A051037 (5-smooth numbers).
  • A188432 (program): Fixed point of the morphism 0->001, 1->01.
  • A188433 (program): a(n) = [2r]-[nr]-[2r-nr], where r=(1+sqrt(5))/2 and [.]=floor.
  • A188434 (program): Positions of 0 in A188433; complement of A188435.
  • A188435 (program): Positions of 1 in A188433; complement of A188434.
  • A188436 (program): [3r]-[nr]-[3r-nr], where r=(1+sqrt(5))/2 and [.]=floor.
  • A188437 (program): Positions of 0 in A188436; complement of A188438.
  • A188438 (program): Positions of 1 in A188436; complement of A188437.
  • A188440 (program): Triangle T(n,k) read by rows: number of size-k antisymmetric subsets of {1,2,…,n}.
  • A188441 (program): Partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
  • A188442 (program): Expansion of -(sqrt(-3*x^2-2*x+1)-x-1)/(2*sqrt(-3*x^2-2*x+1)+2*x).
  • A188458 (program): Expansion of e.g.f. exp(x)/cosh(2*x).
  • A188460 (program): Diagonal sums of number triangle A119308.
  • A188464 (program): Diagonal sums of triangle A188463.
  • A188467 (program): [4r]-[nr]-[4r-nr], where r=(1+sqrt(5))/2 and [.]=floor.
  • A188468 (program): Positions of 0 in A188467.
  • A188469 (program): Positions of 1 in A188467; complement of A188468.
  • A188470 (program): a(n) = [5r]-[nr]-[5r-nr], where r=(1+sqrt(5))/2 and []=floor.
  • A188471 (program): Positions of 0 in A188470.
  • A188472 (program): a(n) = [6r]-[nr]-[6r-nr], where r=(1+sqrt(5))/2 and []=floor.
  • A188473 (program): Positions of 1 in A188472.
  • A188475 (program): a(n) = (2*n^3 + 3*n^2 + n + 3)/3.
  • A188476 (program): Diagonal sums of number triangle A188474.
  • A188480 (program): a(n) = (n^4 + 16*n^3 + 65*n^2 + 26*n + 12)/12.
  • A188481 (program): Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/(2*sqrt(1-4x)).
  • A188482 (program): Diagonal sums of the Riordan matrix (1/(1-4x),(1-sqrt(1-4x))/(2*sqrt(1-4x)) (A188481).
  • A188485 (program): Decimal expansion of (3+sqrt(17))/4, which has periodic continued fractions [1,1,3,1,1,3,1,1,3,…] and [3/2, 3, 3/2, 3, 3/2, …].
  • A188501 (program): Number of n X 2 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.
  • A188509 (program): Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) is the maximal number of colors in a vertex coloring of the cube graph Q_n such that no subgraph Q_k is a rainbow.
  • A188510 (program): Expansion of x*(1 + x^2)/(1 + x^4) in powers of x.
  • A188511 (program): a(n) = floor(7*n/10).
  • A188512 (program): Lengths of successive runs of identical terms in A188511.
  • A188514 (program): Expansion of exp( Sum_{n >= 1} A188458(n)*x^n/n ).
  • A188516 (program): Number of nX2 binary arrays without the pattern 1 1 0 diagonally, vertically or horizontally
  • A188525 (program): a(n) = rad(rad(n)^2+1), where rad = A007947 (squarefree kernel).
  • A188526 (program): a(n) = 3^(2*n + 3) + 2^n.
  • A188527 (program): a(n) = A188526(n) / 7.
  • A188530 (program): 2^(2n+1)-5*2^(n-1)-1.
  • A188538 (program): Row sums of triangle A156070.
  • A188542 (program): Number of primes between n^3-n and n^3+n.
  • A188549 (program): Numbers n such that 8*n^2+1 is a prime.
  • A188551 (program): Numbers located at angle turns in a pentagonal spiral.
  • A188552 (program): Prime numbers at locations of angle turns in pentagonal spiral.
  • A188553 (program): T(n,k) = Number of n X k binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.
  • A188554 (program): Number of 3Xn binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally
  • A188555 (program): Number of 4 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.
  • A188556 (program): Number of 5 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.
  • A188557 (program): Number of 6 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.
  • A188558 (program): Number of 7 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.
  • A188559 (program): Number of 8 X n binary arrays without the pattern 0 1 diagonally, vertically, antidiagonally or horizontally.
  • A188568 (program): Enumeration table T(n,k) by descending antidiagonals. The order of the list - if n is odd: T(n,1), T(2,n-1), T(n-2,3), …, T(n-1,2), T(1,n); if n is even: T(1,n), T(n-1,2), T(3,n-2), …, T(2,n-1), T(n,1).
  • A188570 (program): Coefficients of the absolute term in (1 + sqrt(2) + sqrt(3))^n sequence, denoted as C1(n).
  • A188571 (program): Coefficients of the term by sqrt(2) in (1 + sqrt(2) + sqrt(3))^n sequence, denoted as C2(n).
  • A188572 (program): Coefficients of the term by sqrt(3) in (1 + sqrt(2) + sqrt(3))^n sequence, denoted as C3(n).
  • A188573 (program): Coefficient of the sqrt(6) term in (1 + sqrt(2) + sqrt(3))^n, denoted as C6(n).
  • A188578 (program): Expansion of (1 - x^3) * (1 - x^5) * (1 - x^6) / (1 - x^15) in powers of x.
  • A188580 (program): Number of words of length n over an alphabet of size 5 which do not contain a run of 5 identical letters.
  • A188581 (program): Inverse Moebius transform of A000688, the number of factorizations of n into prime powers greater than 1.
  • A188582 (program): Decimal expansion of sqrt(2) - 1.
  • A188588 (program): Row sums of 1-Euler triangle A188587.
  • A188589 (program): Expansion of (1-3*x+6*x^2-3*x^3)/((1-x)^2*(1-2*x)).
  • A188590 (program): [(n+1)*r] - [n*r], where r = 3/2 + sqrt(13)/2 and […] denotes the floor function.
  • A188593 (program): Decimal expansion of (diagonal)/(shortest side) of a golden rectangle.
  • A188594 (program): Decimal expansion of (circumradius)/(inradius) of side-golden right triangle.
  • A188599 (program): Expansion of x/(1-6*x+25*x^2).
  • A188614 (program): Decimal expansion of (circumradius)/(inradius) of side-silver right triangle.
  • A188615 (program): Decimal expansion of Brocard angle of side-silver right triangle.
  • A188619 (program): Decimal expansion of (diagonal)/(shortest side) of 2nd electrum rectangle.
  • A188622 (program): Row sums of the Riordan matrix (1/sqrt(1-4*x), x/(1-x)) (A187888).
  • A188623 (program): Number of reachable configurations in a chip-firing game on a triangle starting with n chips on one vertex.
  • A188626 (program): a(n) = n + (n-1)*2^(n-2).
  • A188633 (program): Numbers of the form 2^k * m, with k > 1 and m an odd composite number.
  • A188636 (program): Decimal expansion of length/width of a metasilver rectangle.
  • A188638 (program): Decimal expansion of length/width of a meta-1st electrum rectangle.
  • A188639 (program): Decimal expansion of length/width of a 2nd electrum rectangle.
  • A188644 (program): Array of (k^n + k^(-n))/2 where k = (sqrt(x^2-1) + x)^2 for integers x >= 1.
  • A188645 (program): Array of ((k^n)+(k^(-n)))/2 where k=(sqrt(x^2+1)+x)^2 for integers x>=1.
  • A188646 (program): Array of a(n)=a(n-1)*k-((k-1)/(k^n)) where a(0)=1 and k=(sqrt(x^2-1)+x)^2 for integers x>=1.
  • A188647 (program): Array read by antidiagonals of a(n) = a(n-1)*k-((k-1)/(k^n)) where a(0)=1 and k=(sqrt(x^2+1)+x)^2 for integers x>=1.
  • A188648 (program): Binomial sums a(n) = Sum_{k=0..n} (binomial(2n-k,k))^2.
  • A188651 (program): Products of two primes (i.e., “semiprimes”) that are the sum of three consecutive primes.
  • A188652 (program): First differences of A000463.
  • A188653 (program): Second differences of A000463; first differences of A188652.
  • A188654 (program): Numbers such that in canonical prime factorization the maximal exponent does not equal the number of positive exponents.
  • A188655 (program): Decimal expansion of (2+sqrt(13))/3.
  • A188656 (program): Decimal expansion of (1+sqrt(65))/8.
  • A188657 (program): Decimal expansion of (3+sqrt(73))/8.
  • A188658 (program): Decimal expansion of (1+sqrt(101))/10.
  • A188659 (program): Decimal expansion of (1+sqrt(26))/5.
  • A188662 (program): Binomial coefficients: a(n) = binomial(3*n,n)^2.
  • A188666 (program): Largest m <= n such that lcm(m, m+1, …, n) = lcm(1, 2, …, n).
  • A188667 (program): Ordered (2,2)-selections from the multiset {1,1,2,2,3,3,…,n,n}.
  • A188669 (program): a(n) = ceiling(binomial(2*n-1,n-1)/n).
  • A188675 (program): Partial sums of the binomial coefficients binomial(3*n,n) (A005809).
  • A188676 (program): Alternate partial sums of the binomial coefficients binomial(3*n,n).
  • A188678 (program): Alternate partial sums of binomial(3*n,n)/(2*n+1).
  • A188679 (program): Partial sums of binomial(3n,n)^2.
  • A188680 (program): Alternate partial sums of binomial(3n,n)^2.
  • A188681 (program): a(n) = binomial(3n,n)^2/(2n+1).
  • A188682 (program): Partial sums of binomials bin(3n,n)^2/(2n+1).
  • A188683 (program): Alternate partial sums of binomial(3n,n)^2/(2n+1).
  • A188684 (program): Partial sums of binomials binomial(3n,n)^2/(2n+1)^2.
  • A188685 (program): Partial alternating sums of binomial(3n,n)^2/(2n+1)^2.
  • A188686 (program): Binomial transform of the sequence of binomial(3n,n).
  • A188687 (program): Partial binomial sums of binomial(3n,n)/(2n+1) = A001764(n).
  • A188696 (program): G.f.: (1+x^2)/(1-26*x+x^2-26*x^3+2*x^4).
  • A188697 (program): Expansion of (1+2*x^2)/(1-26*x+2*x^2-52*x^3+4*x^4).
  • A188700 (program): Number of n X 3 binary arrays without the pattern 0 0 diagonally or vertically.
  • A188707 (program): Number of 3 X n binary arrays without the pattern 0 0 diagonally or vertically.
  • A188708 (program): Number of 4 X n binary arrays without the pattern 0 0 diagonally or vertically.
  • A188713 (program): Primes of the form 2^x + 2^y - 1.
  • A188714 (program): G.f.: (1+x+x^2+x^3)/(1-3*x-3*x^2-3*x^3).
  • A188716 (program): a(n) = n + (n-1)*(2^n-2).
  • A188729 (program): Decimal expansion of (3+sqrt(109))/10.
  • A188730 (program): Decimal expansion of (2+sqrt(29))/5.
  • A188731 (program): Decimal expansion of (5+sqrt(41))/4.
  • A188732 (program): Decimal expansion of (5+sqrt(61))/6.
  • A188733 (program): Decimal expansion of (9+sqrt(145))/8.
  • A188734 (program): Decimal expansion of (7+sqrt(65))/4.
  • A188735 (program): Decimal expansion of (9+sqrt(97))/4.
  • A188736 (program): Decimal expansion of (3+sqrt(34))/5.
  • A188737 (program): Decimal expansion of (7+sqrt(85))/6.
  • A188754 (program): Primes in A031344.
  • A188765 (program): Number of binary strings of length n with no substrings equal to 00000 or 00100.
  • A188766 (program): Numbers n such that the number of decompositions of 2n into sum of two primes (counting 1 as a prime) is 1 or a composite.
  • A188778 (program): Number of 3-turn bishop’s tours on an n X n board summed over all starting positions
  • A188785 (program): Number of 2-step self-avoiding walks on an n X n X n X n 4-cube summed over all starting positions.
  • A188786 (program): Number of 3-step self-avoiding walks on an n X n X n X n 4-cube summed over all starting positions.
  • A188793 (program): Start with 1 and 5, then repeatedly adjoin the smallest number that is greater than the last term and not equal to the sum of a subset of the existing terms.
  • A188802 (program): Expansion of (x^2+1)/(x^4+2*x^3-2*x+1).
  • A188805 (program): The n-th derivative of 1/(1-x-x^2), evaluated at x=1.
  • A188819 (program): Number of n X 3 binary arrays without the pattern 0 1 diagonally or antidiagonally.
  • A188820 (program): Number of n X 5 binary arrays without the pattern 0 1 diagonally or antidiagonally.
  • A188821 (program): Number of n X 6 binary arrays without the pattern 0 1 diagonally or antidiagonally.
  • A188825 (program): Number of 3Xn binary arrays without the pattern 0 1 diagonally or antidiagonally
  • A188826 (program): Number of 4 X n binary arrays without the pattern 0 1 diagonally or antidiagonally.
  • A188828 (program): Number of 6 X n binary arrays without the pattern 0 1 diagonally or antidiagonally.
  • A188838 (program): Number of n X 4 binary arrays without the pattern 0 1 diagonally or vertically.
  • A188859 (program): Decimal expansion of 2 - log(4).
  • A188860 (program): Number of n X n binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
  • A188861 (program): Number of n X 4 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
  • A188862 (program): Number of n X 5 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
  • A188868 (program): Number of nX3 binary arrays without the pattern 0 0 0 antidiagonally or horizontally
  • A188882 (program): Decimal expansion of (5+sqrt(34))/3.
  • A188887 (program): Decimal expansion of sqrt(2 + sqrt(3)).
  • A188899 (program): Third row of array in A187617.
  • A188902 (program): Numerator of the base n logarithm of the product of the divisors of n.
  • A188914 (program): a(n) = n*n! + 1 = (n+1)! - n! + 1.
  • A188916 (program): Where squares occur in the union of squares and powers of 2.
  • A188917 (program): Where powers of 2 occur in the union of squares and powers of 2.
  • A188918 (program): Alternate partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
  • A188922 (program): Decimal expansion of (sqrt(3) + sqrt(7))/2.
  • A188924 (program): Decimal expansion of sqrt(4+sqrt(15)).
  • A188934 (program): Decimal expansion of (1+sqrt(17))/4.
  • A188935 (program): Decimal expansion of (1+sqrt(37))/6.
  • A188938 (program): Decimal expansion of (7-sqrt(33))/4.
  • A188939 (program): Decimal expansion of (7+sqrt(33))/4.
  • A188940 (program): Decimal expansion of (9-sqrt(65))/4.
  • A188941 (program): Decimal expansion of (9+sqrt(65))/4.
  • A188942 (program): Decimal expansion of (7-sqrt(13))/6.
  • A188943 (program): Decimal expansion of (7 + sqrt(13))/6.
  • A188944 (program): Decimal expansion of (4-sqrt(7))/3.
  • A188945 (program): Decimal expansion of (4+sqrt(7))/3.
  • A188946 (program): Binomial partial sums of binomial(2n,n)*binomial(3n,n) (A006480).
  • A188947 (program): a(n) = n^3 - 2*n^2 + 2*n + 1.
  • A188967 (program): Zero-one sequence based on (3n-2): a(A016777(k))=a(k); a(A007494(k))=1-a(k); a(1)=0.
  • A188968 (program): Positions of 0 in A188967; complement of A188968.
  • A188969 (program): Positions of 1 in A188967; complement of A188968.
  • A188970 (program): Zero-one sequence based on (4n-3): a(A016813(k))=a(k); a(A004772(k))=1-a(k); a(1)=0.
  • A188971 (program): Positions of 0 in A188970; complement of A188972.
  • A188972 (program): Positions of 1 in A188970; complement of A188971.
  • A188973 (program): Zero-one sequence based on squares: a(A000290(k))=a(k); a(A000037(k))=1-a(k); a(1)=0.
  • A188974 (program): Positions of 0 in A188973; complement of A188975.
  • A188975 (program): Positions of 1 in A188973; complement of A188974.
  • A188986 (program): Number of n X 3 binary arrays without the pattern 0 0 1 antidiagonally or horizontally.
  • A189001 (program): a(n) = Sum_{i=0..n} (i+1)*n^i.
  • A189007 (program): Number of ON cells after n generations of the 2D cellular automaton described in the comments.
  • A189011 (program): Zero-one sequence based on triangular numbers: a(A000217(k))=a(k); a(A014132(k))=1-a(k); a(1)=0.
  • A189012 (program): Positions of 0 in A189011; complement of A189013.
  • A189013 (program): Positions of 1 in A189011; complement of A189012.
  • A189021 (program): Apostol’s second order Möbius (or Moebius) function mu_2(n).
  • A189022 (program): Apostol’s third-order Möbius function mu_3(n).
  • A189024 (program): Number of primes in the range (n - sqrt(n), n].
  • A189028 (program): Zero-one sequence based on the sequence (5n-4): a(A016861(k))=a(k); a(A047203(k))=1-a(k); a(1)=0.
  • A189029 (program): Positions of 0 in A189028; Complement of A189030.
  • A189030 (program): Positions of 1 in A189028; complement of A189029.
  • A189031 (program): Zero-one sequence based on the sequence (6n-5): a(A016921(k))=a(k); a(A114024(k))=1-a(k); a(1)=0.
  • A189032 (program): Positions of 0 in A189031; complement of A189033.
  • A189033 (program): Positions of 1 in A189031; complement of A189032.
  • A189034 (program): Positions of 0 in the zero-one sequence s based on the sequence lower Wythoff sequence p: s(p(k))=s(k); s(q(k))=1-s(k); s(1)=0, q=(upper Wythoff sequence).
  • A189035 (program): Positions of 1 in the zero-one sequence s based on the sequence lower Wythoff sequence p: s(p(k))=s(k); s(q(k))=1-s(k); s(1)=0, q=(upper Wythoff sequence).
  • A189036 (program): a(n)= lcm(n,n’)/gcd(n,n’), where n’ is the arithmetic derivative of n.
  • A189037 (program): Decimal expansion of (9-sqrt(17))/8.
  • A189038 (program): Decimal expansion of (9+sqrt(17))/8.
  • A189046 (program): a(n) = lcm(n,n+1,n+2,n+3,n+4,n+5)/60.
  • A189049 (program): Denominators of expansion of Sum_{k=1..n} 1/k - log(n(1+1/(2n)) - gamma.
  • A189050 (program): a(n) = if n even then P((n-2)/2)+P(n/2) otherwise 3*P((n+1)/2)+P((n-1)/2) where P(i) are the Pell numbers (A000129).
  • A189052 (program): a(n) is the number of inversions in all compositions of n.
  • A189053 (program): Expansion of d/dx log(1/(1-x/sqrt(1-4*x^2))).
  • A189054 (program): E.g.f. exp(x/sqrt(1-4*x^2)).
  • A189071 (program): The n-th derivative of x^10 evaluated at x=2.
  • A189073 (program): Triangle read by rows: T(n,k) is the number of inversions in k-compositions of n for n >= 3, 2 <= k <= n-1.
  • A189097 (program): Zero-one sequence based on the sequence (3k-1): a(A016789(k))=a(k); a(A032766(k))=1-a(k), a(1)=0.
  • A189098 (program): Positions of 0 in A189097; complement of A189099.
  • A189099 (program): Positions of 1 in A189097; complement of A189098.
  • A189100 (program): a(n) = lcm(n!,n!’)/gcd(n!,n!’), where n!’ is the arithmetic derivative of n! (A068311).
  • A189101 (program): G.f.: 1/(1-(x+x^2+x^3+x^4+x^6+x^7)).
  • A189102 (program): Greatest common divisor of n! and its arithmetic derivative.
  • A189103 (program): Least common multiple of n! and its arithmetic derivative.
  • A189120 (program): Sum of squares of nonprime divisors of n.
  • A189122 (program): a(n) = Sum_{i=0..n} (i+1)^2*n^i.
  • A189126 (program): Zero-one sequence based on the sequence (4n-2): a(A016825(k))=a(k); a(A042965(k))=1-a(k), a(1)=0.
  • A189127 (program): Positions of 0 in A189126; complement of A189128.
  • A189128 (program): Positions of 1 in A189126; complement of A189127.
  • A189129 (program): Zero-one sequence based on the sequence (5n-3): a(A016873(k))=a(k); a(A047207(k))=1-a(k), a(1)=0.
  • A189130 (program): Positions of 0 in A189129; complement of A189131.
  • A189131 (program): Positions of 1 in A189129; complement of A189130.
  • A189135 (program): Zero-one sequence based on the central polygonal numbers n^2-n+1: a(A002061(k))=a(k); a(A135668(k))=1-a(k), a(1)=0.
  • A189136 (program): Positions of 0 in A189135; complement of A189137.
  • A189137 (program): Positions of 1 in A189135; complement of A189136.
  • A189141 (program): Zero-one sequence based on the primes: a(A000040(k))=a(k); a(A002808(k))=1-a(k), a(1)=0.
  • A189142 (program): Positions of 0 in A189141; complement of A189143.
  • A189143 (program): Positions of 1 in A189141; complement of A189142.
  • A189144 (program): a(n) = lcm(n,n+1,n+2,n+3,n+4,n+5,n+6)/420.
  • A189145 (program): Number of n X 2 array permutations with each element making zero or one knight moves.
  • A189151 (program): Numbers n such that n < floor(sqrt(n)) * ceiling(sqrt(n)).
  • A189154 (program): Number of n X 2 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally
  • A189155 (program): Number of nX3 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally
  • A189162 (program): The maximum possible value for the apex of a triangle of numbers whose base consists of a permutation of the numbers 1 to n, and each number in a higher row is the sum of the two numbers directly below it.
  • A189173 (program): Integers m such that m^3 is the sum of squares of m consecutive integers.
  • A189175 (program): Riordan matrix (1+x/sqrt(1-4*x),(1-sqrt(1-4*x))/2).
  • A189176 (program): Row sums of the Riordan matrix (1+x/sqrt(1-4*x),(1-sqrt(1-4*x))/2) (A189175).
  • A189177 (program): Diagonal sums of the Riordan matrix (1+x/sqrt(1-4*x),(1-sqrt(1-4*x))/2) (A189175).
  • A189179 (program): Number of n X 2 array permutations with each element making a single king move.
  • A189215 (program): Zero-one sequence based on the sequence (3n): a(A008585(k))=a(k); a(A001651(k))=1-a(k), a(1)=0, a(2)=1.
  • A189219 (program): Zero-one sequence based on the octagonal numbers: a(A000567(k))=a(k); a(A183220(k))=1-a(k), a(1)=0.
  • A189220 (program): Positions of 0 in A189219; complement of A189221.
  • A189221 (program): Positions of 1 in A189219; complement of A189220.
  • A189222 (program): Zero-one sequence based on the sequence (3n): a(A008585(k))=a(k); a(A001651(k))=1-a(k), a(1)=0, a(2)=0.
  • A189223 (program): Positions of 0 in A189222; complement of A189224.
  • A189224 (program): Positions of 1 in A189222; complement of A189223.
  • A189230 (program): Complementary Catalan triangle read by rows.
  • A189242 (program): Numbers n such that 24*n+17 is not prime.
  • A189247 (program): Number of n X 2 array permutations with each element making zero or one king moves
  • A189274 (program): Number of nX3 array permutations with each element not moved or moved diagonally or antidiagonally by one
  • A189287 (program): Positions of 0 in A189215; complement of A189288.
  • A189288 (program): Positions of 1 in A189215; complement of A189287.
  • A189289 (program): Zero-one sequence based on the sequence (4n): a(A008586(k))=a(k); a(A042968(k))=1-a(k), a(1)=0, a(2)=0, a(3)=0.
  • A189290 (program): Positions of 0 in A189289, complement of A189291.
  • A189291 (program): Positions of 1 in A189289; complement of A189290.
  • A189292 (program): Zero-one sequence based on the sequence (4n): a(A008586(k))=a(k); a(A042968(k))=1-a(k), a(1)=0, a(2)=0, a(3)=1.
  • A189293 (program): Positions of 0 in A189292; complement of A189294.
  • A189294 (program): Positions of 1 in A189292; complement of A189293.
  • A189295 (program): Zero-one sequence based on the sequence (4n): a(A008586(k))=a(k); a(A042968(k))=1-a(k), a(1)=0, a(2)=1, a(3)=0.
  • A189296 (program): Positions of 0 in A189295; complement of A189297.
  • A189297 (program): Positions of 1 in A189295; complement of A189286.
  • A189298 (program): Zero-one sequence based on the sequence (4n): a(A008586(k))=a(k); a(A042968(k))=1-a(k), a(1)=0, a(2)=1, a(3)=1.
  • A189299 (program): Positions of 0 in A189298; complement of A189300.
  • A189300 (program): Positions of 1 in A189298; complement of A189299.
  • A189305 (program): Number of n X 2 array permutations with each element moving zero or one space diagonally, horizontally or vertically.
  • A189315 (program): Expansion of 5*(1-3*x+x^2)/(1-5*x+5*x^2).
  • A189316 (program): Expansion of 5*(1-x-x^2)/((1+x)*(1-3*x+x^2))
  • A189317 (program): Expansion of 5*(1-6*x+x^2)/(1-10*x+5*x^2)
  • A189318 (program): Expansion of 5*(1-2*x)/(1-3*x-2*x^2+4*x^3)
  • A189320 (program): Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding four
  • A189321 (program): Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding four.
  • A189327 (program): Number of nondecreasing arrangements of 4 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding four
  • A189334 (program): Expansion of (1-6*x+x^2)/(1-10*x+5*x^2)
  • A189336 (program): Number of nX2 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally
  • A189337 (program): Number of nX3 binary arrays without the pattern 1 0 0 1 diagonally, vertically, antidiagonally or horizontally
  • A189345 (program): Number of ways to choose four points in an n X n grid (or geoplane).
  • A189348 (program): Number of n X 2 array permutations with each element moving one space diagonally, horizontally or vertically.
  • A189356 (program): a(n) gives y-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2 for positive x.
  • A189361 (program): a(n) = n + floor(n*s/r) + floor(n*t/r); r=1, s=sqrt(2), t=sqrt(3).
  • A189362 (program): a(n) = n + floor(n*r/s) + floor(n*t/s); r=1, s=sqrt(2), t=sqrt(3).
  • A189363 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sqrt(2), t=sqrt(3).
  • A189364 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=sqrt(2), t=(1+sqrt(5))/2.
  • A189366 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sqrt(2), t=(1+sqrt(5))/2.
  • A189367 (program): a(n) = n + [n*s/r] + [n*t/r]; r=2, s=sqrt(2), t=sqrt(3).
  • A189368 (program): a(n) = n + [n*r/s] + [n*t/s]; r=2, s=sqrt(2), t=sqrt(3).
  • A189369 (program): a(n) = n + [n*r/t] + [n*s/t]; r=2, s=sqrt(2), t=sqrt(3).
  • A189370 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=sqrt(2), t=sqrt(5).
  • A189371 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sqrt(2), t=sqrt(5).
  • A189374 (program): Expansion of 1/((1-x)^5*(x^2+x+1)^3).
  • A189375 (program): Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^3).
  • A189376 (program): Expansion of 1/((1-x)^5*(x^3+x^2+x+1)^2).
  • A189377 (program): a(n) = n + floor(ns/r) + floor(nt/r) with r=2, s=(-1+sqrt(5))/2, t=(1+sqrt(5))/2.
  • A189378 (program): a(n) = n + [nr/s] + [nt/s]; r=2, s=(-1+sqrt(5))/2, t=(1+sqrt(5))/2.
  • A189379 (program): n+[nr/t]+[ns/t]; r=2, s=(-1+sqrt(5))/2, t=(1+sqrt(5))/2.
  • A189380 (program): a(n) = n + floor(n*s/r) + floor(n*t/r); r=1, s=-1+sqrt(2), t=1+sqrt(2).
  • A189381 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=-1+sqrt(2), t=1+sqrt(2).
  • A189382 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=-1+sqrt(2), t=1+sqrt(2).
  • A189383 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=1/sqrt(2), t=1/sqrt(3).
  • A189384 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=1/sqrt(2), t=1/sqrt(3).
  • A189385 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=1/sqrt(2), t=1/sqrt(3).
  • A189386 (program): a(n) = n+[ns/r]+[nt/r]; r=1, s=sqrt(2), t=1/sqrt(3), []=floor.
  • A189387 (program): a(n) = n+[nr/s]+[nt/s]; r=1, s=sqrt(2), t=1/sqrt(3).
  • A189388 (program): a(n) = n+[nr/t]+[ns/t]; r=1, s=sqrt(2), t=1/sqrt(3).
  • A189390 (program): The maximum possible value for the apex of a triangle of numbers whose base consists of a permutation of the numbers 0 to n, and each number in a higher row is the sum of the two numbers directly below it.
  • A189391 (program): The minimum possible value for the apex of a triangle of numbers whose base consists of a permutation of the numbers 0 to n, and each number in a higher row is the sum of the two numbers directly below it.
  • A189393 (program): a(n) = phi(n^4).
  • A189395 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=1/sqrt(2), t=sqrt(3).
  • A189396 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=1/sqrt(2), t=sqrt(3).
  • A189397 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=1/sqrt(2), t=sqrt(3).
  • A189405 (program): n+[ns/r]+[nt/r]; r=1, s=-1+sqrt(3), t=1+sqrt(3).
  • A189406 (program): n+[nr/s]+[nt/s]; r=1, s=-1+sqrt(3), t=1+sqrt(3).
  • A189407 (program): n+[nr/t]+[ns/t]; r=1, s=-1+sqrt(3), t=1+sqrt(3).
  • A189409 (program): a(n) = prime(n)#^2 + 1, where prime(n)# is the n-th primorial (A002110).
  • A189411 (program): Odd primes p such that sigma(p)/2 is a power of an odd prime.
  • A189426 (program): Expansion of (x^2)/(1-2*x-x^2+x^3)^2
  • A189427 (program): Expansion of (x^2)/((1-x)*(1-2*x-x^2+x^3)^2)
  • A189429 (program): Number of n X 3 array permutations with each element not moving, or moving one space N, SW or SE.
  • A189436 (program): Number of 4 X n array permutations with each element not moving, or moving one space N, SW or SE.
  • A189442 (program): a(n) = A140230(n) / A016116(n-1).
  • A189450 (program): Number of 2 X n array permutations with each element moving zero or one space horizontally or diagonally.
  • A189457 (program): a(n) = n+[ns/r]+[nt/r]; r=2, s=sqrt(2), t=1+sqrt(2).
  • A189458 (program): a(n) = n+[nr/s]+[nt/s]; r=2, s=sqrt(2), t=1+sqrt(2).
  • A189459 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=1+sqrt(2), t=1/2+sqrt(2).
  • A189460 (program): n+[ns/r]+[nt/r]; r=2, s=sqrt(5), t=1+sqrt(5).
  • A189461 (program): n+[nr/s]+[nt/s]; r=2, s=sqrt(5), t=1+sqrt(5).
  • A189462 (program): n+[nr/t]+[ns/t]; r=2, s=sqrt(5), t=1+sqrt(5).
  • A189463 (program): a(n) = [3*n*r] - 3*[n*r], where r=sqrt(5).
  • A189464 (program): Positions of 0 in A189463.
  • A189465 (program): Positions of 1 in A189463.
  • A189467 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=1+sqrt(2), t=1/2+sqrt(2).
  • A189469 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=1+sqrt(2), t=1+sqrt(3).
  • A189476 (program): Fixed point of the morphism 0->01, 1->100.
  • A189477 (program): Positions of 0 in A189476; complement of A189478.
  • A189478 (program): Positions of 1 in A189476; complement of A189477.
  • A189479 (program): Fixed point starting with 0 of the morphism 0->01, 1->101.
  • A189480 (program): [4rn]-4[rn], where r=sqrt(5) and [ ]=floor.
  • A189489 (program): E.g.f. A(x) satisfies A(x)=x*exp(A(x)*exp(A(x))+A(x)^2*exp(2*A(x)))
  • A189510 (program): Digital root of n^n.
  • A189572 (program): Fixed point of the morphism 0->01, 1->001.
  • A189573 (program): Positions of 0 in A189572; complement of A080652 (conjectured).
  • A189574 (program): Partial sums of A189572.
  • A189575 (program): Partial sums of A189476.
  • A189576 (program): Fixed point of the morphism 0->01, 1->110.
  • A189577 (program): Positions of 0 in A189576; complement of A189578.
  • A189578 (program): Positions of 1 in A189576; complement of A189577.
  • A189579 (program): Partial sums of A189576.
  • A189593 (program): Number of permutations of 1..n with displacements restricted to {-6,-5,-4,-3,-2,0,1}.
  • A189600 (program): Number of permutations of 1..n with displacements restricted to {-7,-6,-5,-4,-3,-2,0,1}.
  • A189604 (program): Number of n X 3 array permutations with each element not moving, or moving one space E, S or NW.
  • A189624 (program): Fixed point of the morphism 0->001, 1->10.
  • A189625 (program): Positions of 0 in A189624; complement of A189626.
  • A189626 (program): Positions of 1 in A189624; complement of A189625.
  • A189627 (program): Partial sums of A189624.
  • A189628 (program): Fixed point of the morphism 0->001, 1->010.
  • A189629 (program): Positions of 0 in A189628; complement of A189630.
  • A189630 (program): Positions of 1 in A189628; complement of A189629.
  • A189631 (program): Partial sums of A189628.
  • A189632 (program): Fixed point starting with 0 of the morphism 0->001, 1->100.
  • A189633 (program): Positions of 0 in A189632; complement of A189634.
  • A189634 (program): Positions of 1 in A189632; complement of A189633.
  • A189635 (program): Partial sums of A189632.
  • A189636 (program): Positions of 0 in A116178; complement of A189637.
  • A189637 (program): Positions of 1 in A116178; complement of A189636.
  • A189638 (program): Partial sums of A116178.
  • A189640 (program): Fixed point of the morphism 0->001, 1->101.
  • A189641 (program): Partial sums of A189640.
  • A189642 (program): Numerator of H(n+4) - H(n), where H(n) = Sum_{k=1..n} 1/k.
  • A189657 (program): Start with n, apply k->2k+1 until a semiprime is reached; sequence gives the semiprimes.
  • A189658 (program): Positions of 0 in A064990; complement of A189659.
  • A189659 (program): Positions of 1 in A064990; complement of A189658.
  • A189660 (program): Partial sums of A064990.
  • A189661 (program): Fixed point of the morphism 0->010, 1->10 starting with 0.
  • A189662 (program): Positions of 0 in A189661; complement of A026356.
  • A189663 (program): Partial sums of A189661.
  • A189664 (program): Fixed point of the morphism 0->010, 1->001.
  • A189665 (program): Positions of 0’s in A189664; complement of A189666.
  • A189666 (program): Positions of 1 in A189664; complement of A189665.
  • A189667 (program): Partial sums of A189664.
  • A189668 (program): Fixed point of the morphism 0->010, 1->100.
  • A189669 (program): Positions of 0 in A189668; complement of A189679.
  • A189670 (program): Positions of 1 in A189668; complement of A189669.
  • A189671 (program): Partial sums of A189668.
  • A189672 (program): Partial sums of A080846.
  • A189673 (program): Fixed point of the morphism 0->010, 1->110.
  • A189674 (program): Partial sums of A189673.
  • A189676 (program): a(n) = n + [nr/s] + [nt/s]; r=Pi/2, s=arcsin(3/5), t=arcsin(4/5).
  • A189680 (program): a(n) = n + [nr/t] + [ns/t]; r=Pi/2, s=arcsin(3/5), t=arcsin(4/5).
  • A189681 (program): (A189676)/2; from a 3-way partition of the positive integers.
  • A189682 (program): (A189680)/2; from a 3-way partition of the positive integers.
  • A189687 (program): Fixed point of the morphism 0->011, 1->01.
  • A189688 (program): Partial sums of A189687.
  • A189702 (program): Fixed point of the morphism 0->011, 1->10.
  • A189703 (program): Positions of 0 in A189702; complement of A189704.
  • A189704 (program): Positions of 1 in A189702; complement of A189703.
  • A189705 (program): Partial sums of A189702.
  • A189706 (program): Fixed point of the morphism 0->011, 1->001.
  • A189707 (program): Positions of 0 in A189706; complement of A189708.
  • A189708 (program): Positions of 1 in A189706; complement of A189707.
  • A189709 (program): Partial sums of A189706.
  • A189715 (program): Numbers k such that A156595(k-1) = 0; complement of A189716.
  • A189716 (program): Numbers k such that A156595(k-1) = 1; complement of A189715.
  • A189717 (program): Partial sums of A156595.
  • A189718 (program): Fixed point of the morphism 0->011, 1->100.
  • A189719 (program): Positions of 0 in A189718; complement of A189720.
  • A189720 (program): Positions of 1 in A189718; complement of A189719.
  • A189721 (program): Partial sums of A189718.
  • A189723 (program): Fixed point of the morphism 0->011, 1->101.
  • A189724 (program): Positions of 0 in A189723; complement of A189725.
  • A189725 (program): Positions of 1 in A189723; complement of A189724.
  • A189726 (program): Partial sums of A189723.
  • A189727 (program): Fixed point of the morphism 0->011, 1->110.
  • A189728 (program): Positions of 0 in A189727; complement of A189729.
  • A189729 (program): Positions of 1 in A189727; complement of A189728.
  • A189730 (program): Partial sums of A189727.
  • A189731 (program): a(n) = numerator of B(0,n) where B(n,n) = 0, B(n-1,n) = 1/n, and B(m,n) = B(m-1,n+1) - B(m-1,n).
  • A189732 (program): a(1)=1, a(2)=5, a(n) = a(n-1) + 5*a(n-2).
  • A189733 (program): Denominator of B(0,n) where B(n,n)=0, B(n-1,n) = (-1)^(n+1)/n, and B(m,n) = B(m+1,n-1) + B(m,n-1), n >= 0, m >= 0, is an array of fractions.
  • A189734 (program): a(1)=2, a(2)=5, a(n)=2*a(n-1) + 5*a(n-2).
  • A189735 (program): a(1)=3, a(2)=1, a(n) = 3*a(n-1) + a(n-2).
  • A189736 (program): a(1)=3, a(2)=2, a(n)=3*a(n-1) + 2*a(n-2)
  • A189737 (program): a(1)=3, a(2)=3, a(n)=3*a(n-1) + 3*a(n-2)
  • A189738 (program): a(1)=3, a(2)=4, a(n)=3a(n-1) + 4a(n-2)
  • A189739 (program): a(1)=3, a(2)=5, a(n)=3a(n-1) + 5a(n-2)
  • A189740 (program): Partial sums of tetranacci numbers (A000288).
  • A189741 (program): a(1)=4, a(2)=2, a(n) = 4*a(n-1) + 2*a(n-2).
  • A189742 (program): a(1)=4, a(2)=3, a(n)=4*a(n-1) + 3*a(n-2)
  • A189743 (program): a(1)=4, a(2)=4, a(n)=4*a(n-1) + 4*a(n-2)
  • A189744 (program): a(1)=4, a(2)=5, a(n) = 4*a(n-1) + 5*a(n-2).
  • A189745 (program): a(n) = 5*a(n-1) + a(n-2); with a(1)=5, a(2)=1.
  • A189746 (program): a(1)=5, a(2)=2, a(n)=5*a(n-1) + 2*a(n-2)
  • A189747 (program): a(1)=5, a(2)=3, a(n)=5*a(n-1) + 3*a(n-2)
  • A189748 (program): a(n) = 5*a(n-1) + 4*a(n-2) with a(1)=5, a(2)=4.
  • A189749 (program): a(1)=5, a(2)=5, a(n)=5*a(n-1) + 5*a(n-2).
  • A189753 (program): n+[ns/r]+[nt/r]; r=1, s=arctan(1/3), t=arctan(3).
  • A189761 (program): Numbers n for which the set of residues {Fibonacci(k) mod n, k=0,1,2,….} is minimal.
  • A189766 (program): Trace of the inverse of the n-th order Hilbert matrix.
  • A189772 (program): The n-th derivative of exp(2*arctan(x) - Pi/2), evaluated at x=1.
  • A189781 (program): a(n) = n + [nr/s] + [nt/s]; r=Pi/2, s=arcsin(8/17), t=arcsin(15/17).
  • A189782 (program): a(n) = n + [nr/t] + [ns/t]; r=Pi/2, s=arcsin(8/17), t=arcsin(15/17).
  • A189783 (program): (A189781)/2.
  • A189784 (program): (A189782)/2.
  • A189785 (program): a(n) = n+floor(n*r/s)+floor(nt/s); r=Pi/2, s=arcsin(5/13), t=arcsin(12/13).
  • A189786 (program): a(n) = n + [nr/t] + [ns/t]; r=Pi/2, s=arcsin(5/13), t=arcsin(12/13).
  • A189787 (program): a(n) = A189785(n)/2.
  • A189790 (program): Number of ways to place n nonattacking bishops on an n X n toroidal board.
  • A189791 (program): Number of ways to place n nonattacking bishops on an 2n x 2n toroidal board.
  • A189792 (program): n + [nr/s] + [nt/s] with r = 1, s = (sin(1))^2, t = (cos(1))^2.
  • A189793 (program): n+[nr/t]+[ns/t]; r=1, s=(sin(1))^2, t=(cos(1))^2.
  • A189794 (program): (A189792)/2.
  • A189795 (program): (A189793)/2.
  • A189796 (program): n+[ns/r]+[nt/r]; r=2, s=(sin(1))^2, t=(cos(1))^2.
  • A189797 (program): n+[nr/s]+[nt/s]; r=2, s=(sin(1))^2, t=(cos(1))^2.
  • A189798 (program): n+[nr/t]+[ns/t]; r=2, s=(sin(1))^2, t=(cos(1))^2.
  • A189800 (program): a(n) = 6*a(n-1) + 8*a(n-2), with a(0)=0, a(1)=1.
  • A189801 (program): a(n) = 6*a(n-1) + 9*a(n-2), with a(0)=0, a(1)=1.
  • A189806 (program): Denominators of coefficients in the series expansion of ((2 - m) EllipticK(m) - 2 EllipticE(m))/(Pi * m).
  • A189807 (program): Number of right triangles on an (n+1) X 3 grid.
  • A189816 (program): a(3*k-2)=0, a(3*k-1)=1-a(k), a(3*k)=1-a(k); k>0, a(1)=0.
  • A189817 (program): Positions of 0 in A189816; complement of A189818.
  • A189818 (program): Positions of 1 in A189816; complement of A189817.
  • A189819 (program): Partial sums of A189816.
  • A189820 (program): a(3*k-2) = a(k), a(3*k-1) = a(k), a(3*k) = 1 for k >= 1, starting with a(1) = 0.
  • A189822 (program): Positions of 1 in A189820; complement of A003278.
  • A189824 (program): Decimal expansion of Pogson’s ratio 100^(1/5).
  • A189826 (program): a(n) = (3^n-n)*(n-1) - 2^n*(n-2).
  • A189827 (program): a(n) = d(n-1) + d(n+1), where d(k) is the number of divisors of k.
  • A189832 (program): Expansion of 2/((x+3)*sqrt(-3*x^2-2*x+1)+3*x^2+2*x-1).
  • A189833 (program): a(n) = n^2 + 8.
  • A189834 (program): a(n) = n^2 + 9.
  • A189835 (program): Number of representations of n as a*b + b*c + c*d + d*e where a, b, d, e>0, c>=0 are integers.
  • A189836 (program): a(n) = n^2 + 11.
  • A189849 (program): a(0)=1, a(1)=0, a(n) = 4*n*(n-1)*(a(n-1) + 2*(n-1)*a(n-2)).
  • A189883 (program): Numbers n such that the square part of n is one greater than the squarefree part of n.
  • A189886 (program): a(n) is the number of compositions of the set {1, 2, …, n} into blocks, each of size 1, 2 or 3 (n >= 0).
  • A189887 (program): Dimension of homogeneous component of degree n in x in the Malcev-Poisson superalgebra S^tilde(M).
  • A189889 (program): Maximum number of nonattacking kings on an n X n toroidal board.
  • A189890 (program): a(n) = (n^3 - 2*n^2 + 3*n + 2)/2.
  • A189891 (program): Complement of A085104.
  • A189892 (program): a(n) = n*prime(n) - sum_{i=1..n-1} prime(i).
  • A189894 (program): Number of isosceles right triangles on a 2n X (n+1) grid.
  • A189911 (program): Row sums of the extended Catalan triangle A189231.
  • A189912 (program): Extended Motzkin numbers, Sum_{k>=0} C(n,k)C(k), C(k) the extended Catalan number A057977(k).
  • A189913 (program): Triangle read by rows: T(n,k) = binomial(n, k) * k! / (floor(k/2)! * floor((k+2)/2)!).
  • A189915 (program): Sequence for finding the day of the week for the first day of the month in a common (non-leap) year.
  • A189916 (program): Sequence for finding the day of the week for the first day of the month in leap years.
  • A189918 (program): Sum of tetrahedral numbers A000292(k), with k in the reduced residue system modulo n.
  • A189922 (program): Jordan function J_{-4} multiplied by n^4.
  • A189923 (program): Jordan function J_{-5}(n) multiplied by n^5.
  • A189924 (program): a(n) = abs(Stirling1(n+2,2)) - abs(Stirling1(n+2,3)).
  • A189925 (program): Expansion of theta_4/theta_3 in powers of q.
  • A189932 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=(sin(Pi/5))^2, t=(cos(Pi/5))^2, where [] denotes the floor function.
  • A189933 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=(sin(Pi/5))^2, t=(cos(Pi/5))^2.
  • A189934 (program): a(n) = A189932(n)/2.
  • A189935 (program): a(n) = A189933(n)/2.
  • A189940 (program): Number of connected components in all simple labeled graphs with n nodes having degrees at most one.
  • A189959 (program): Decimal expansion of (4+5*sqrt(2))/4.
  • A189960 (program): Decimal expansion of (9+27*sqrt(2))/17.
  • A189961 (program): Decimal expansion of (5+7*sqrt(5))/10.
  • A189962 (program): Decimal expansion of 3*(1 + 3*sqrt(5))/11.
  • A189963 (program): Decimal expansion of (5+9*sqrt(5))/12.
  • A189966 (program): Decimal expansion of (3+sqrt(33))/4, which has periodic continued fractions [2,5,2,1,2,5,2,1,…] and [3/2, 1, 3/2, 1, …].
  • A189967 (program): Decimal expansion of (7+sqrt(105))/4, which has periodic continued fractions [4,3,4,1,4,3,4,1…] and [7/2, 1, 7/2, 1, …].
  • A189968 (program): Decimal expansion of (5+sqrt(85))/6, which has periodic continued fractions [2,2,1,2,2,1,…] and [5/2, 1, 5/2, 1, …].
  • A189969 (program): Decimal expansion of (7 + sqrt(133))/6, which has periodic continued fractions [3,11,3,1,3,11,3,1,…] and [7/3, 1, 7/3, 1, …].
  • A189970 (program): Decimal expansion of (1 + x + sqrt(14+10*x))/4, where x=sqrt(5).
  • A189975 (program): Numbers with prime factorization pqr^3.
  • A189976 (program): a(n) is the number of incongruent two-color bracelets of n beads, 8 of them black (A005514), having a diameter of symmetry.
  • A189980 (program): a(n) is the number of incongruent two-color bracelets of n beads, 10 from them are black (A005515), having a diameter of symmetry.
  • A189986 (program): Numbers of the form 4k+1 having exactly 4 divisors.
  • A189988 (program): Numbers with prime factorization p^2*q^4.
  • A189990 (program): Numbers with prime factorization p^2*q^6.
  • A189991 (program): Numbers with prime factorization p^4*q^4.
  • A189996 (program): Bott periodicity: the homotopy groups of the stable orthogonal group are periodic with period 8 and repeat like [2, 2, 1, 0, 1, 1, 1, 0].
  • A189997 (program): Partial sums of A061742.
  • A189998 (program): Numerator of h(n+5) - h(n) where h(n) = Sum_{k=1..n} (1/k) are the Harmonic numbers.
  • A190002 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=(sinh(1))^2, t=(cosh(1))^2.
  • A190003 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=(sinh(1))^2, t=(cosh(1))^2.
  • A190004 (program): A190002/2.
  • A190005 (program): a(n) = 6*a(n-1) + 10*a(n-2), with a(0)=0, a(1)=1.
  • A190007 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sin(Pi/3), t=csc(Pi/3).
  • A190008 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sin(Pi/3), t=csc(Pi/3).
  • A190035 (program): Number of nondecreasing arrangements of n+2 numbers in 0..3 with the last equal to 3 and each after the second equal to the sum of one or two of the preceding three.
  • A190036 (program): Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding three.
  • A190037 (program): Number of nondecreasing arrangements of n+2 numbers in 0..5 with the last equal to 5 and each after the second equal to the sum of one or two of the preceding three.
  • A190038 (program): Number of nondecreasing arrangements of n+2 numbers in 0..6 with the last equal to 6 and each after the second equal to the sum of one or two of the preceding three.
  • A190039 (program): Number of nondecreasing arrangements of n+2 numbers in 0..7 with the last equal to 7 and each after the second equal to the sum of one or two of the preceding three.
  • A190048 (program): Expansion of (8+6*x)/(1-x)^5
  • A190049 (program): Expansion of (16+24*x+2*x^2)/(x-1)^6.
  • A190050 (program): Expansion of ((1-x)*(3*x^2-3*x+1))/(1-2*x)^3
  • A190051 (program): Expansion of (1-x)*(10*x^4-20*x^3+16*x^2-6*x+1)/(1-2*x)^5
  • A190055 (program): a(n) = n + [n*r/t] + [n*s/t]; r=2, s=sin(Pi/3), t=csc(Pi/3).
  • A190057 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1/2, s=sin(Pi/3), t=csc(Pi/3).
  • A190058 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1/2, s=sin(Pi/3), t=csc(Pi/3).
  • A190062 (program): a(n) = n*Fibonacci(n) - Sum_{i=0..n-1} Fibonacci(i).
  • A190079 (program): n + [n*s/r] + [n*t/r]; r=1, s=cos(Pi/5), t=sec(Pi/5).
  • A190080 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=cos(Pi/5), t=sec(Pi/5).
  • A190088 (program): Triangle of binomial coefficients binomial(3*n-k+1,3*n-3*k+1).
  • A190089 (program): Row sums of the triangular matrix A190088.
  • A190090 (program): Diagonal sums of the triangular matrix A190088.
  • A190091 (program): Number of rhombuses on a (n+1) X 3 grid.
  • A190105 (program): a(n) = (3*A002145(n) - 1)/4.
  • A190116 (program): a(n) = n*n’, where n’ is the arithmetic derivative (A003415) of n.
  • A190117 (program): a(n) = Sum_{k=1..n} k*k’, where n’ is the arithmetic derivative of n.
  • A190118 (program): a(n) = Sum_{k=1..n} k/gcd(k,k’), where n’ is arithmetic derivative of n.
  • A190119 (program): a(n) = Sum_{k=1..n} lcm(k,k’)/k, where k’ is arithmetic derivative of k.
  • A190120 (program): a(n) = Sum_{k=1..n} lcm(k,k’)/gcd(k,k’), where n’ is arithmetic derivative of n.
  • A190121 (program): Partial sums of the arithmetic derivative function A003415.
  • A190122 (program): a(n) = Sum_{k=1..n} k*lcm(k,k’)/gcd(k,k’), where k’ is arithmetic derivative of k.
  • A190125 (program): If n = product(p_i^e_i), a(n) = product((p_i^e_i)^(p_i^e_i)).
  • A190136 (program): Largest prime factor of n*(n+1)*(n+2)*(n+3).
  • A190138 (program): Final number of terms obtained with Euler’s recurrence formula when computing the sum of divisors of n.
  • A190139 (program): a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4), a(-2)=0, a(-1)=0, a(0)=1, a(1)=1.
  • A190140 (program): a(n) = 2*a(n-1) + a(n-2) + 3*a(n-3), a(0)=1.
  • A190152 (program): Triangle of binomial coefficients binomial(3*n-k,3*n-3*k).
  • A190153 (program): Row sums of the triangle A190152.
  • A190154 (program): Diagonal sums of the triangle A190152.
  • A190157 (program): Decimal expansion of (1+sqrt(-1+2*sqrt(5)))/2.
  • A190158 (program): Positions of 2 in A189463.
  • A190159 (program): Number of peakless Motzkin paths of length n and having no uhh…hd’s starting at level 0, where u = (1, 1), h = (1, 0) and d = (1, -1).
  • A190171 (program): Number of peakless Motzkin paths of length n having no UHD’s starting at level 0; here U=(1,1), H=(1,0), and D=(1,-1).
  • A190173 (program): a(n) = Sum_{1 <= i < j <= n} F(i)*F(j), where F(k) is the k-th Fibonacci number.
  • A190176 (program): a(n) = n^4 + 2^4 + (n+2)^4.
  • A190177 (program): Decimal expansion of (1+sqrt(2)+sqrt(7+6*sqrt(2)))/2.
  • A190179 (program): Decimal expansion of (1+sqrt(-3+4*sqrt(2)))/2.
  • A190181 (program): Decimal expansion of (15+sqrt(465))/12.
  • A190214 (program): Expansion of (1-x)/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-2*x).
  • A190222 (program): Noncomposite numbers all of whose decimal digits are noncomposite numbers (1,2,3,5,7).
  • A190224 (program): a(n) = [n*u + n*v] - [n*u] - [n*v], where u=sin(Pi/3), v=cos(Pi/3), and []=floor.
  • A190225 (program): Positions of 0 in A190224; complement of A190226.
  • A190226 (program): Positions of 1 in A190224; complement of A190225.
  • A190236 (program): a(n) = [n*u + n*v] -[n*u] -[n*v], where u=1/2, v=(1+sqrt(5))/2, and []=floor.
  • A190237 (program): Positions of 0 in A190236; complement of A190238.
  • A190238 (program): Positions of 1 in A190236; complement of A190237.
  • A190248 (program): a(n) = [nu+nv+nw]-[nu]-[nv]-[nw], where u=(1+sqrt(5))/2, v=u^2, w=u^3, []=floor.
  • A190249 (program): Positions of 0 in A190248.
  • A190250 (program): Positions of 1 in A190248.
  • A190251 (program): Positions of 2 in A190248.
  • A190258 (program): Decimal expansion of (x + sqrt(2 + 4x))/2, where x=sqrt(2).
  • A190260 (program): Decimal expansion of (1 + sqrt(1 + 2*x))/2, where x=sqrt(2).
  • A190262 (program): Decimal expansion of (3 + sqrt(9 + 12x))/6, where x=sqrt(3).
  • A190264 (program): Decimal expansion of (sqrt(89) - 6)/2.
  • A190274 (program): Numbers n such that n’= p^2 -1, with n = semiprime = p*q, n’ is the arithmetic derivative of n. Also: semiprimes of the form p*(p^2-p-1)
  • A190275 (program): Semiprimes of the form p*(p^2 - p + 1).
  • A190276 (program): Numbers n such that tau(2n-1) = tau(2n+1) where tau(n) = A000005(n).
  • A190277 (program): Number of trails between opposite vertices in a triangle strip.
  • A190278 (program): Number of decimal digits in LCM of Fibonacci sequence {F_1, …, F_n}.
  • A190281 (program): Decimal expansion of (1+sqrt(1+r))/r, where r=sqrt(2).
  • A190283 (program): Decimal expansion of 1+sqrt(1+sqrt(2)).
  • A190285 (program): Decimal expansion of (3+sqrt(9+4r))/2, where r=sqrt(3).
  • A190289 (program): Decimal expansion of (3+sqrt(21))/4.
  • A190290 (program): Decimal expansion of (3+sqrt(21))/3.
  • A190295 (program): A055134(n,k)*k
  • A190297 (program): Bisection of A013697.
  • A190298 (program): Numbers less than or equal to sum of the triangular number of each of their decimal digits.
  • A190299 (program): Squarefree semiprimes of the form 4k+1.
  • A190301 (program): Smallest number h such that n*h is a repunit (A002275), or 0 if no such h exists.
  • A190302 (program): Smallest number h such that the decimal expansion of n*h starts with 1.
  • A190311 (program): Number of nonzero digits when writing n in base where place values are positive cubes, cf. A000433.
  • A190314 (program): The number of cycles in the digraph representation of all endofunctions on {1,2,…,n}.
  • A190321 (program): Number of nonzero digits when writing n in base where place values are squares, cf. A007961.
  • A190322 (program): a(1) = 1, a(2) = 9, a(3) = 17; for n>3, a(n) = a(n-3) + 2.
  • A190329 (program): a(n) = n + [n*s/r] + [n*t/r]; r=1, s=sqrt(2), t=1/s.
  • A190330 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sqrt(2), t=1/s.
  • A190331 (program): a(n) = 8*a(n-1) + 2*a(n-2), with a(0)=0, a(1)=1.
  • A190332 (program): n + [n*s/r] + [n*t/r]; r=1, s=sqrt(3), t=1/s.
  • A190333 (program): n + [n*r/s] + [n*t/s]; r=1, s=sqrt(3), t=1/s.
  • A190334 (program): a(n) = n + floor(n*r/t) + floor(n*s/t) where r=1, s=sqrt(3), t=1/s.
  • A190335 (program): a(n) = n + [n*s/r] + [n*t/r]; r=2, s=sqrt(2), t=1/s.
  • A190336 (program): a(n) = n + [n*r/s] + [n*t/s]; r=2, s=sqrt(2), t=1/s.
  • A190337 (program): a(n) = n + [n*r/t] + [n*s/t]; r=2, s=sqrt(2), t=1/s.
  • A190340 (program): Number of (n+1)X(n+1) symmetric binary matrices without the pattern 1 1 antidiagonally
  • A190343 (program): a(n) = floor(n^((n-1)/2)).
  • A190346 (program): a(n) = n + [n*r/t] + [n*s/t]; r=1, s=sqrt(5/2), t=sqrt(2/5).
  • A190357 (program): Decimal expansion of 1/4 - 2/Pi^2.
  • A190360 (program): Number of one-sided n-step prudent walks, avoiding 4 or more consecutive east steps.
  • A190362 (program): a(n) = n + [n*r/s] + [n*t/s]; r=1, s=sqrt(5/4), t=sqrt(4/5).
  • A190365 (program): n + [n*r/s] + [n*t/s] + [n*u/s]; r=sqrt(2), s=1/r, t=sqrt(3), u=1/t.
  • A190367 (program): n + [n*r/u] + [n*s/u] + [n*t/u]; r=sqrt(2), s=1/r, t=sqrt(3), u=1/t.
  • A190377 (program): Numbers with prime factorization p^2q^2r^2s^2
  • A190395 (program): Number of ways to place 3 nonattacking grasshoppers on a chessboard of size n x n.
  • A190419 (program): Number of (n+2)X(n+2) symmetric binary matrices without the pattern 1 1 1 diagonally
  • A190425 (program): Number of one-sided prudent walks from (0,0) to (n,n), with floor(n/2)+n east steps, floor(n/2) west steps and n north steps.
  • A190427 (program): a(n) = [(b*n+c)*r] - b*[n*r] - [c*r], where (r,b,c)=(golden ratio,2,1) and []=floor.
  • A190428 (program): Positions of 0 in A190427.
  • A190429 (program): Positions of 1 in A190427.
  • A190430 (program): Positions of 2 in A190427.
  • A190431 (program): a(n) = [(b*n+c)*r] - b*[n*r] - [c*r], where (r,b,c)=(golden ratio,3,1) and []=floor.
  • A190432 (program): Positions of 0 in A190431.
  • A190433 (program): Positions of 1 in A190431.
  • A190434 (program): Positions of 2 in A190431.
  • A190435 (program): Positions of 3 in A190431.
  • A190436 (program): a(n) = [(b*n+c)*r] - b*[n*r] - [c*r], where (r,b,c)=(golden ratio,3,2) and []=floor.
  • A190437 (program): Positions of 0 in A190436.
  • A190438 (program): Positions of 1 in A190436.
  • A190439 (program): Positions of 2 in A190436.
  • A190440 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,0) and []=floor.
  • A190441 (program): a(n) = 4*a(n-1) + 39*a(n-2), with a(0)=0, a(1)=1.
  • A190442 (program): Positions of 1 in A190440.
  • A190443 (program): Positions of 2 in A190440.
  • A190444 (program): E.g.f. exp(x+x^2+x^4).
  • A190445 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,1) and []=floor.
  • A190446 (program): Positions of 0 in A190445.
  • A190447 (program): Positions of 1 in A190445.
  • A190448 (program): Positions of 2 in A190445.
  • A190449 (program): Positions of 3 in A190445.
  • A190450 (program): Positions of 4 in A190445.
  • A190451 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,2) and []=floor.
  • A190452 (program): E.g.f. exp(x+x^2/2+x^4/24).
  • A190453 (program): Positions of 1 in A190451.
  • A190454 (program): Positions of 2 in A190451.
  • A190455 (program): Positions of 3 in A190451.
  • A190456 (program): Positions of 4 in A190451.
  • A190457 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,3) and []=floor.
  • A190458 (program): Positions of 0 in A190457.
  • A190459 (program): Positions of 1 in A190457.
  • A190460 (program): Positions of 2 in A190457.
  • A190461 (program): Positions of 3 in A190457.
  • A190463 (program): Positions of 4 in A190457.
  • A190465 (program): Numbers with prime factorization p^5q^5.
  • A190469 (program): Numbers with prime factorization p^2q^2r^6.
  • A190471 (program): Numbers with prime factorization p^2q^4r^4.
  • A190480 (program): Concatenation of first n digits in the concatenation of first n primes written in base 2.
  • A190482 (program): Convex, obtuse, hexagonal lattice numbers
  • A190483 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),2,1) and []=floor.
  • A190484 (program): Positions of 0 in A190483.
  • A190485 (program): Positions of 1 in A190483.
  • A190486 (program): Positions of 2 in A190483.
  • A190487 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,0) and []=floor.
  • A190488 (program): Positions of 0 in A190487.
  • A190489 (program): Positions of 1 in A190487.
  • A190490 (program): Positions of 2 in A190487.
  • A190491 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,1) and []=floor.
  • A190492 (program): Positions of 0 in A190491.
  • A190493 (program): Positions of 1 in A190491.
  • A190494 (program): Positions of 2 in A190491.
  • A190495 (program): Positions of 3 in A190491.
  • A190496 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,2) and []=floor.
  • A190497 (program): Positions of 0 in A190496.
  • A190498 (program): Positions of 1 in A190496.
  • A190499 (program): Positions of 2 in A190496.
  • A190500 (program): Positions of 3 in A190496.
  • A190505 (program): n+[nr/s]+[nt/s]+[nu/s]; r=golden ratio, s=r+1, t=r+2, u=r+3.
  • A190506 (program): n+[nr/t]+[ns/t]+[nu/t]; r=golden ratio, s=r+1, t=r+2, u=r+3.
  • A190508 (program): n+[ns/r]+[nt/r]+[nu/r]; r=golden ratio, s=r^2, t=r^3, u=r^4.
  • A190509 (program): a(n) = n + [nr/s] + [nt/s] + [nu/s] where r=golden ratio, s=r^2, t=r^3, u=r^4, and [] represents the floor function.
  • A190510 (program): a(n) = 8*a(n-1) + 4*a(n-2), with a(0)=0, a(1)=1.
  • A190511 (program): n+[nr/u]+[ns/u]+[nt/u]; r=golden ratio, s=r^2, t=r^3, u=r^4.
  • A190512 (program): Number of one-sided n-step prudent walks, avoiding single west step only, i.e., two or more consecutive west steps are permitted.
  • A190525 (program): Number of n-step one-sided prudent walks, avoiding exactly two consecutive west steps (can have three or more west steps).
  • A190526 (program): Number of words of length n on alphabet {1,2,…,n} with no adjacent 1’s.
  • A190528 (program): Number of n-step one-sided prudent walks avoiding exactly three consecutive West steps.
  • A190531 (program): Number of idempotents in Identity Difference Partial Transformation semigroup.
  • A190535 (program): Number of (n+2) X (n+2) symmetric binary matrices without the pattern 0 1 1 diagonally.
  • A190540 (program): 7^n - 2^n.
  • A190541 (program): 7^n - 3^n.
  • A190542 (program): 7^n - 4^n.
  • A190543 (program): a(n) = 8^n - 3^n.
  • A190544 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,0) and []=floor.
  • A190545 (program): Positions of 0 in A190544.
  • A190546 (program): Positions of 1 in A190544.
  • A190547 (program): Positions of 2 in A190544.
  • A190548 (program): Positions of 3 in A190544.
  • A190549 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,1) and []=floor.
  • A190550 (program): Positions of 0 in A190549.
  • A190551 (program): Positions of 1 in A190549.
  • A190552 (program): Positions of 2 in A190549.
  • A190553 (program): Positions of 3 in A190549.
  • A190554 (program): Positions of 4 in A190549.
  • A190555 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,2) and []=floor.
  • A190556 (program): Positions of 0 in A190555.
  • A190557 (program): Positions of 1 in A190555.
  • A190558 (program): Positions of 2 in A190555.
  • A190559 (program): Positions of 3 in A190555.
  • A190560 (program): a(n) = 8*a(n-1) + 6*a(n-2), with a(0)=0, a(1)=1.
  • A190561 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,3) and []=floor.
  • A190563 (program): Positions of 1 in A190561.
  • A190564 (program): Positions of 2 in A190561.
  • A190565 (program): Positions of 3 in A190561.
  • A190568 (program): Number of squares between powers of 2, floor(sqrt(2^(n+1))) - floor(sqrt(2^n))
  • A190569 (program): Number of n-step one-sided prudent walks, avoiding single west steps and single east steps.
  • A190570 (program): Number of n-step one-sided prudent walks, avoiding exactly two consecutive west steps and two consecutive east steps.
  • A190571 (program): Number of n-step one-sided prudent walks, avoiding exactly three consecutive west steps and three consecutive east steps.
  • A190576 (program): a(n) = n^2 + 5*n - 5.
  • A190577 (program): a(n) = n*(n+2)*(n+4)*(n+6).
  • A190578 (program): a(n) = n^7 + n.
  • A190582 (program): Generalized McCarthy function: a(n) = n - s if n > c; otherwise, a(n) = a(a(n+t)) with d = t - s > 0, with parameters t=15, s=9, c=21.
  • A190584 (program): Bisection of A013697.
  • A190590 (program): Expansion of series reversion of x/(1 + x + 2*x^4).
  • A190592 (program): Maximal digit in base-3 expansion of n.
  • A190593 (program): Maximal digit in base-4 expansion of n.
  • A190594 (program): Maximal digit in base-5 expansion of n.
  • A190595 (program): Maximal digit in base-6 expansion of n.
  • A190596 (program): Maximal digit in base-7 expansion of n.
  • A190597 (program): Maximal digit in base-8 expansion of n.
  • A190598 (program): Maximal digit in base-9 expansion of n.
  • A190599 (program): Maximal digit in base-11 expansion of n.
  • A190604 (program): Number of (n+2)X(n+2) symmetric binary matrices without the pattern 1 0 1 diagonally
  • A190608 (program): a(1)=a(2)=1; thereafter a(n) = 2*(a(ceiling(n/2))-a(floor(n/2))).
  • A190609 (program): a(1)=a(2)=1; thereafter a(n) = 3*(a(ceiling(n/2))-a(floor(n/2))).
  • A190610 (program): a(1)=a(2)=1; thereafter a(n) = a(ceiling(n/2))-a(floor(n/2)).
  • A190611 (program): Expansion of f(q^3) * f(-q^8) * chi(-q^12) / chi(q) in powers of q where f(), chi() are Ramanujan theta functions.
  • A190613 (program): a(n) = Sum_{k=1..n} (-1)^(n-floor(n/k)) * floor(n/k).
  • A190614 (program): Values of n where A190613(n) < 0.
  • A190615 (program): Expansion of f(x^2) * f(x^3) / (chi(x) * chi(x^6)) in powers of x where f(), chi() are Ramanujan theta functions.
  • A190619 (program): Binary expansions of odd numbers with a single zero in their binary expansion.
  • A190620 (program): Odd numbers with a single zero in their binary expansion.
  • A190621 (program): a(n) = n if n is not divisible by 4, otherwise 0.
  • A190623 (program): Mobius transform of A008457.
  • A190636 (program): a(n)=(n^3+3*n^7)/4.
  • A190640 (program): Numbers whose base-3 expansion ends in 2 and does not contain any 1’s.
  • A190641 (program): Numbers having exactly one non-unitary prime factor.
  • A190642 (program): Numbers 3n+2 written in base 3.
  • A190650 (program): Product of iterated integral part of square root.
  • A190660 (program): Number of triangular numbers T(k) between powers of 2, 2^(n-1) < T(k) <= 2^n.
  • A190666 (program): Number of walks from (0,0) to (n+3,n) which take steps from {E, N, NE}.
  • A190667 (program): Expansion of (1+2*x)/(1-x^4-2*x^3-2*x^2-x).
  • A190669 (program): a(n) = [(b*n+c)*r] - b*[n*r] - [c*r], where (r,b,c)=(sqrt(3),2,0) and [ ] = floor.
  • A190670 (program): Positions of 0 in A190669; complement of A190671.
  • A190671 (program): Positions of 1 in A190669; complement of A190670.
  • A190672 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),2,1) and [ ]=floor.
  • A190673 (program): Positions of 0 in A190672.
  • A190674 (program): Positions of 1 in A190672.
  • A190675 (program): Positions of 2 in A190672.
  • A190676 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,0) and [ ]=floor.
  • A190677 (program): Positions of 0 in A190676.
  • A190678 (program): Positions of 1 in A190676.
  • A190679 (program): Positions of 2 in A190676.
  • A190683 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,1) and [ ]=floor.
  • A190684 (program): Positions of 0 in A190683.
  • A190685 (program): Positions of 1 in A190683.
  • A190686 (program): Positions of 2 in A190683.
  • A190687 (program): Positions of 3 in A190683.
  • A190688 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),3,2) and [ ]=floor.
  • A190689 (program): Positions of 0 in A190688.
  • A190690 (program): Positions of 1 in A190688.
  • A190691 (program): Positions of 2 in A190688.
  • A190692 (program): Positions of 3 in A190688.
  • A190693 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,0) and [ ]=floor.
  • A190694 (program): Positions of 0 in A190693.
  • A190695 (program): Positions of 1’s in A190693.
  • A190696 (program): Positions of 2 in A190693.
  • A190697 (program): Positions of 3 in A190693.
  • A190698 (program): a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,1) and [ ]=floor.
  • A190699 (program): Positions of 0 in A190698.
  • A190700 (program): Positions of 1 in A190698.
  • A190701 (program): Positions of 2 in A190698.
  • A190702 (program): Positions of 3 in A190698.
  • A190703 (program): Positions of 4 in A190698.
  • A190704 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,2) and [ ]=floor.
  • A190705 (program): a(n) = 6*n^2*(2*n + 1).
  • A190706 (program): Positions of 1 in A190704.
  • A190707 (program): Positions of 2 in A190704.
  • A190708 (program): Positions of 3 in A190704.
  • A190709 (program): Positions of 4 in A190704.
  • A190710 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,3) and [ ]=floor.
  • A190711 (program): Positions of 0 in A190710.
  • A190712 (program): Positions of 1 in A190710.
  • A190713 (program): Positions of 2 in A190710.
  • A190714 (program): Positions of 3 in A190710.
  • A190716 (program): a(2*n) = 2*n and a(2*n-1) = A054569(n).
  • A190717 (program): Triplicated tetrahedral numbers A000292.
  • A190718 (program): Quadruplicated tetrahedral numbers A000292
  • A190719 (program): Numbers that are congruent to {0, 1, 3, 5, 7, 8, 11} mod 12.
  • A190723 (program): Numbers m for which A055778(m) > A055778(m-1).
  • A190724 (program): Row sums of Riordan matrix A118384.
  • A190725 (program): Diagonal sums of Riordan matrix A118384.
  • A190726 (program): Central coefficients of Riordan matrix A118384.
  • A190727 (program): Product of (digits of n each incremented by 1) - 2.
  • A190728 (program): Least m>1 such that m^3 mod n^2 is 1.
  • A190729 (program): E.g.f. exp(x+1/6*x^3+1/24*x^4)
  • A190730 (program): Let b(n,0) = n and b(n,k) = 2*b(n,k-1) + 1 for k > 0. Then a(n) = b(n,1) + b(n,2) + … + b(n,n).
  • A190733 (program): Expansion of (4*x+2)/(1+sqrt(1-4*x-4*x^2)).
  • A190734 (program): Central coefficients of the Riordan matrix A121576.
  • A190737 (program): Diagonal sums of the Riordan matrix A104259.
  • A190738 (program): Central coefficients of the Riordan matrix A104259.
  • A190762 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),2,1) and [ ]=floor.
  • A190763 (program): Positions of 0 in A190762.
  • A190764 (program): Positions of 1 in A190762.
  • A190765 (program): Positions of 2 in A190762.
  • A190766 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),3,0) and [ ]=floor.
  • A190767 (program): Positions of 0 in A190766.
  • A190768 (program): Positions of 1 in A190766.
  • A190769 (program): Positions of 2 in A190766.
  • A190770 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),3,1) and [ ]=floor.
  • A190771 (program): Positions of 0 in A190770.
  • A190772 (program): Positions of 1 in A190770.
  • A190773 (program): Positions of 2 in A190770.
  • A190774 (program): Positions of 3 in A190770.
  • A190775 (program): [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),3,2) and [ ]=floor.
  • A190776 (program): Positions of 0 in A190775.
  • A190777 (program): Positions of 1 in A190775.
  • A190778 (program): Positions of 2 in A190775.
  • A190779 (program): Positions of 3 in A190775.
  • A190785 (program): Numbers that are congruent to {0, 2, 3, 5, 7, 9, 11} mod 12.
  • A190787 (program): Odd powers of 2 and 9 times odd powers of 2, sorted.
  • A190788 (program): Expansion of ((x-1)*sqrt(1-4*x^2))/((x-1)*sqrt(1-4*x^2)+x).
  • A190798 (program): Maximum value of k^2 * (n-k).
  • A190812 (program): Increasing sequence generated by these rules: a(1)=1, and if x is in a then 2x+1 and 3x+2 are in a.
  • A190813 (program): Positions of 0 in A189480.
  • A190815 (program): A bisection of A049690.
  • A190816 (program): a(n) = 5*n^2 - 4*n + 1.
  • A190818 (program): E.g.f: 1/(1-2*tanh(x))
  • A190843 (program): [2ne]-2[ne], where [ ]=floor.
  • A190847 (program): Positions of 0 in A190843; complement of A190860.
  • A190860 (program): Positions of 1 in A190843; complement of A190847.
  • A190864 (program): Expansion of 1/(1-x*sqrt(1+4*x^2)).
  • A190865 (program): E.g.f. exp(x+x^3/6).
  • A190867 (program): Count of the 3-full divisors of n.
  • A190869 (program): a(n) = 10*a(n-1) - 2*a(n-2), a(0)=0, a(1)=1.
  • A190870 (program): a(n) = 11*a(n-1) - 22*a(n-2), a(0)=0, a(1)=1.
  • A190871 (program): a(n) = 11*a(n-1) - 11*a(n-2), a(0)=0, a(1)=1.
  • A190872 (program): a(n) = 11*a(n-1) - 9*a(n-2), a(0)=0, a(1)=1.
  • A190873 (program): a(n) = 12*a(n-1) - 12*a(n-2), a(0)=0, a(1)=1.
  • A190875 (program): E.g.f. exp(x+x^4)
  • A190876 (program): Numbers 1 through 8 together with numbers congruent to 9 mod 10.
  • A190877 (program): Expansion of e.g.f. exp(x+x^5).
  • A190878 (program): E.g.f. exp(x/(1-x-x^4)).
  • A190883 (program): Positions of 1 in A189480.
  • A190884 (program): Positions of 2 in A189480.
  • A190885 (program): Positions of 3 in A189480.
  • A190886 (program): a(n) = [5nr]-5[nr], where r=sqrt(5).
  • A190887 (program): Positions of 0 in A190886.
  • A190888 (program): Positions of 1 in A190886.
  • A190889 (program): Positions of 2 in A190886.
  • A190890 (program): Positions of 3 in A190886.
  • A190891 (program): Positions of 4 in A190886.
  • A190893 (program): a(n) = [3en] - 3[en], where [ ] = floor.
  • A190894 (program): Auxiliary c(n) sequence used to prove some properties about Rowland’s sequence. c(n) has the following recursive definition: c(1) = 5, c_(n+1) = c(n) + lfp(c(n)) - 1, where lpf(.) denotes the lowest prime factor of a number.
  • A190895 (program): Auxiliary r(n) sequence used to prove some properties about Rowland’s sequence: r(1) = 1, and r(n) = 1/2*(c(n)+1), where c(n) is A190894, for n>1.
  • A190901 (program): a(n) = Product_{k in M_n} k; M_n = {k | 1 <= k <= 2n and k mod 2 = n mod 2}.
  • A190902 (program): Product_{ d divides n } d*mu(n/d).
  • A190903 (program): a(n) = Product_{k in M_n} k, M_n = {k | 1 <= k <= 3n and k mod 3 = n mod 3}.
  • A190906 (program): a(n) = gcd(n! / floor(n/2)!^2, 3^n).
  • A190907 (program): Triangle read by rows: T(n,k) = binomial(n+k, n-k) k! / (floor(k/2)! * floor((k+2)/2)!).
  • A190908 (program): a(n) = Sum{0<=k<=n} binomial(n+k, n-k) * k! / (floor(k/2)! * floor((k+2)/2)!).
  • A190909 (program): Triangle read by rows: T(n,k) = binomial(n+k,n-k) * k! / floor(k/2)!^2.
  • A190910 (program): a(n) = Sum{0<=k<=n} binomial(n+k,n-k) * k! / (floor(k/2)!)^2.
  • A190911 (program): Least number coprime to n and n+3.
  • A190912 (program): Partial sums of pentanacci numbers (A000322).
  • A190913 (program): Sequence A190914 evaluated at the negative index -n.
  • A190914 (program): Expansion of ( 5-9*x^2-2*x^3 ) / ( (1+x-x^2)*(1-x-x^2-x^3) ).
  • A190941 (program): Partial sums of A190592.
  • A190943 (program): a(n) = 8*a(n-1) + 27*a(n-2), with a(0)=0, a(1)=1.
  • A190944 (program): Multiples of 3 written in base 2.
  • A190949 (program): Odd Fibonacci numbers with odd index.
  • A190953 (program): a(n) = 8*a(n-1) + 10*a(n-2), with a(0)=0, a(1)=1.
  • A190954 (program): a(n) = 10*a(n-1) + 4*a(n-2), with a(0)=0, a(1)=1.
  • A190955 (program): a(n) = 10*a(n-1) + 5*a(n-2), with a(0)=0, a(1)=1.
  • A190956 (program): a(n) = 10*a(n-1) + 6*a(n-2), with a(0)=0, a(1)=1.
  • A190957 (program): a(n) = 10*a(n-1) + 8*a(n-2), with a(0)=0, a(1)=1.
  • A190958 (program): a(n) = 2*a(n-1) - 10*a(n-2), with a(0) = 0, a(1) = 1.
  • A190959 (program): a(n) = 3*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
  • A190960 (program): a(n) = 3*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.
  • A190961 (program): a(n) = 3*a(n-1) - 7*a(n-2), with a(0)=0, a(1)=1.
  • A190962 (program): a(n) = 3*a(n-1) - 8*a(n-2), with a(0)=0, a(1)=1.
  • A190963 (program): a(n) = 3*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
  • A190964 (program): a(n) = 3*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=1.
  • A190965 (program): a(n) = 4*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.
  • A190966 (program): a(n) = 4*a(n-1) - 8*a(n-2), with a(0)=0, a(1)=1.
  • A190967 (program): a(n) = 4*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
  • A190968 (program): a(n) = 4*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=1.
  • A190969 (program): a(n) = 5*a(n-1) - 8*a(n-2), with a(0)=0, a(1)=1.
  • A190970 (program): a(n) = 5*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
  • A190971 (program): a(n) = 5*a(n-1) - 10*a(n-2), with a(0)=0, a(1)=1.
  • A190972 (program): a(n) = 7*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.
  • A190973 (program): a(n) = 7*a(n-1) - 4*a(n-2), with a(0) = 0, a(1) = 1.
  • A190974 (program): a(n) = 7*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
  • A190975 (program): a(n) = 8*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.
  • A190976 (program): a(n) = 8*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.
  • A190977 (program): a(n) = 8*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
  • A190978 (program): a(n) = 8*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.
  • A190979 (program): a(n) = 9*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.
  • A190980 (program): a(n) = 9*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.
  • A190981 (program): a(n) = 9*a(n-1) - 4*a(n-2), with a(0)=0, a(1)=1.
  • A190982 (program): a(n) = 9*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
  • A190983 (program): a(n) = 9*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.
  • A190984 (program): a(n) = 9*a(n-1) - 7*a(n-2), with a(0)=0, a(1)=1.
  • A190985 (program): a(n) = 10*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.
  • A190986 (program): a(n) = 10*a(n-1) - 4*a(n-2), with a(0)=0, a(1)=1.
  • A190987 (program): a(n) = 10*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
  • A190988 (program): a(n) = 10*a(n-1) - 6*a(n-2), with a(0)=0, a(1)=1.
  • A190989 (program): a(n) = 10*a(n-1) - 7*a(n-2), with a(0)=0, a(1)=1.
  • A190990 (program): a(n) = 10*a(n-1) - 8*a(n-2), with a(0)=0, a(1)=1.
  • A190991 (program): a(n) = 13*n + 1.
  • A190992 (program): Square excess of squarefree semiprimes.
  • A190993 (program): Square excess of Fibonacci numbers.
  • A190994 (program): a(n) = a(n-1) + a(n-2), for n>=2, with a(0)=27, a(1)=2.
  • A190995 (program): Fibonacci sequence beginning 9, 7.
  • A190996 (program): Fibonacci sequence beginning 10, 7.
  • A190998 (program): Digital root of concatenation of all divisors of n (A037278).
  • A190999 (program): a(n) = 2^(n^2)*(2^(2*n+1) - 1).
  • A191002 (program): Completely multiplicative function with a(prime(k)) = prime(k)*prime(k+1).
  • A191006 (program): Number of n X n symmetric binary matrices with each 1 adjacent to exactly 1 diagonally neighboring 1
  • A191007 (program): a(n) = n*2^(n+1) + (2^(n+3)+(-1)^n)/3.
  • A191008 (program): a(n) = (n*3^(n+1)+((5*3^(n+1)+(-1)^(n))/4))/4.
  • A191009 (program): The remainder of (sum of proper divisors of n) mod (largest proper divisor of n).
  • A191010 (program): a(n) = (n*4^(n+1) + (6*4^(n+1)+(-1)^n)/5)/5.
  • A191011 (program): E.g.f. log(1 + sin(arctan(x))).
  • A191012 (program): a(n) = n^5 - n^4 + n^3 - n^2 + n.
  • A191014 (program): a(n) = 10*a(n-1) + 2*a(n-2), with a(0)=0, a(1)=1.
  • A191018 (program): Primes p with Jacobi symbol (p|3*5) = 1.
  • A191019 (program): Rational primes that decompose in the quadratic field Q(sqrt(-19)).
  • A191022 (program): Primes that are squares mod 29.
  • A191024 (program): Primes that are squares mod 31.
  • A191059 (program): Primes p that have Kronecker symbol (p|6) = -1.
  • A191060 (program): Primes that are not squares mod 11.
  • A191062 (program): Primes p that have Kronecker symbol (p|15) = -1.
  • A191063 (program): Primes that are not squares mod 19.
  • A191067 (program): Primes that are not squares mod 31.
  • A191099 (program): 5th differences of Bell numbers.
  • A191103 (program): Positions of 0 in A190893.
  • A191104 (program): Positions of 1 in A190893.
  • A191105 (program): Positions of 2 in A190893.
  • A191106 (program): Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 3x are in a.
  • A191107 (program): Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 3x+1 are in a.
  • A191108 (program): Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x-2 and 3x+2 are in a.
  • A191109 (program): a(1)=1, and if x is a term then 3x-1 and 3x+2 are terms too.
  • A191110 (program): Increasing sequence generated by these rules: a(1)=1, and if x is in a then 3x and 3x+2 are in a.
  • A191111 (program): Describe 10^n. Also called the “Say What You See” or “Look and Say” sequence LS(10^n).
  • A191152 (program): [4n*e]-2[2n*e], where [ ]=floor.
  • A191153 (program): a(n) = floor(2*n*Pi) - 2*floor(n*Pi).
  • A191156 (program): a(n) = [6*n*Pi] - 2*[3*n*Pi], where [ ]=floor.
  • A191159 (program): Positions of 0 in A191153; complement of A191164.
  • A191160 (program): Positions of 0 in A191156; complement of A191176.
  • A191161 (program): Hypersigma(n), definition 2: sum of the divisors of n plus the recursive sum of the divisors of the proper divisors.
  • A191162 (program): a(n) = [4*n*Pi] - 2*[2*n*Pi], where [ ]=floor.
  • A191164 (program): Positions of 1 in A191153; complement of A191159.
  • A191176 (program): Positions of 1 in A191156; complement of A191160.
  • A191188 (program): a(n) = floor(8*n*Pi) - 2*floor(4*n*Pi).
  • A191194 (program): Positions of 0 in A191188; complement of A191202.
  • A191202 (program): Positions of 1 in A191188; complement of A191194.
  • A191214 (program): Positions of 0 in A191162; complement of A191215.
  • A191215 (program): Positions of 1 in A191162; complement of A191214.
  • A191217 (program): Numbers n such that sigma(n) is congruent to 2 modulo 4
  • A191218 (program): Odd numbers n such that sigma(n) is congruent to 2 modulo 4.
  • A191230 (program): Positions of 0 in A191152; complement of A191231.
  • A191231 (program): Positions of 1 in A191152; complement of A191230.
  • A191237 (program): E.g.f. exp(x+x^3+x^5)
  • A191239 (program): Triangle T(n,k) = coefficient of x^n in expansion of (x+x^2+2*x^3)^k.
  • A191252 (program): Positions of 1 in A191250.
  • A191253 (program): Positions of 2 in A191250.
  • A191254 (program): Fixed point of the morphism 0 -> 01, 1 -> 02, 2 -> 01.
  • A191255 (program): Fixed point of the morphism 0 -> 01, 1 -> 02, 2 -> 03, 3 -> 01.
  • A191257 (program): a(n) = A067368(n)/2.
  • A191262 (program): Positions of 0 in A191261.
  • A191263 (program): Positions of 1 in A191261.
  • A191264 (program): Positions of 2 in A191261.
  • A191269 (program): Fixed point of the morphism 0 -> 001, 1 -> 02, 2 -> 01.
  • A191270 (program): Positions of 1 in A191269.
  • A191271 (program): Positions of 2 in A191269.
  • A191272 (program): Expansion of x*(4+5*x)/( (1-4*x)*(1 + x + x^2) ).
  • A191275 (program): Numbers that are congruent to {0, 1, 3, 5, 7, 9, 11} mod 12.
  • A191276 (program): Numbers that are congruent to {0, 1, 4, 5, 7, 9, 11} mod 12.
  • A191277 (program): Expansion of e.g.f. 1/(1 - sinh(x)*cosh(x)).
  • A191292 (program): Numbers k such that k-1 and k+1 are both digitally balanced.
  • A191296 (program): Least k such that k-1 and k+1 in binary representation have same number n of 0’s as 1’s.
  • A191307 (program): Sum of the heights of the first peaks in all dispersed Dyck paths of length n (i.e., in Motzkin paths of length n with no (1,0)-steps at positive heights).
  • A191309 (program): Number of peaks at height >= 2 in all dispersed Dyck paths of length n (i.e., Motzkin paths of length n with no (1,0) steps at positive heights).
  • A191313 (program): Sum of the abscissae of the first returns to the horizontal axis (assumed to be 0 if there are no such returns) in all dispersed Dyck paths of length n (i.e., Motzkin paths of length n with no (1,0) steps at positive heights).
  • A191319 (program): Sum of pyramid weights of all dispersed Dyck paths of length n (i.e., of all Motzkin paths of length n with no (1,0) steps at positive heights).
  • A191321 (program): Number of dispersed Dyck paths of length n (i.e., Motzkin paths of length n with no (1,0) steps at positive heights) having only ascents of even length (an ascent is a maximal sequence of consecutive (1,1)-steps).
  • A191329 (program): (Lower Wythoff sequence mod 2)+(Upper Wythoff sequence mod 2).
  • A191330 (program): Positions of 0 in A191329.
  • A191331 (program): Positions of 2 in A191329.
  • A191336 (program): (A022838 mod 2)+(A054406 mod 2)
  • A191337 (program): Positions of 0 in A191336.
  • A191338 (program): Positions of 1 in A191336.
  • A191339 (program): Positions of 2 in A191336.
  • A191341 (program): a(n) = 4^n - 2*2^n + 3.
  • A191349 (program): Binomial sums a(n) = sum(binomial(n-k,2*k)^2,k=0..floor(n/3)).
  • A191352 (program): Numbers n with property that 9*n is a sum of two distinct positive cubes.
  • A191355 (program): Indices of terms in A069748 with two decimal digits 1 and all others 0.
  • A191360 (program): Number of the diagonal of the Wythoff array that contains n.
  • A191361 (program): Number of the diagonal of the Wythoff difference array that contains n.
  • A191362 (program): Number of the diagonal of the dispersion of the even positive integers that contains n.
  • A191370 (program): a(n) = 2*(1+(-1)^n)/3 + 2*A010892(n-1).
  • A191373 (program): Sum of binomial coefficients C(i+j,i) modulo 2 over all pairs (i,j) of positive integers satisfying 5i+j=n.
  • A191386 (program): Number of ascents of length 1 in all dispersed Dyck paths of length n (i.e., in all Motzkin paths of length n with no (1,0) steps at positive heights). An ascent is a maximal sequence of consecutive (1,1)-steps.
  • A191389 (program): Number of valleys at level 0 in all dispersed Dyck paths of length n (i.e., in all Motzkin paths of length n with no (1,0) steps at positive heights).
  • A191391 (program): Number of horizontal segments in all dispersed Dyck paths of length n (i.e., in all Motzkin paths of length n with no (1,0)-steps at positive heights; a horizontal segment is a maximal sequence of consecutive (1,0)-steps).
  • A191394 (program): Number of base pyramids in all dispersed Dyck paths of length n (i.e., in all Motzkin paths of length n with no (1,0)-steps at positive heights).
  • A191396 (program): Sum of the heights of the base pyramids in all dispersed Dyck paths of length n (i.e., in all Motzkin paths of length n with no (1,0)-steps at positive heights). A base pyramid is a factor of the form U^j D^j (j>0), starting at the horizontal axis. Here U=(1,1) and D=(1,-1).
  • A191402 (program): a(n) = A000201(n) + A000201(n+1).
  • A191403 (program): a(n) = A000201(n) + A000201(n+2).
  • A191404 (program): a(n) = A000201(n) + A000201(n+3).
  • A191405 (program): A001951(n)+A001951(n+1).
  • A191406 (program): A001951(n)+A001951(n+2).
  • A191407 (program): A001951(n)+A001951(n+3).
  • A191413 (program): a(n) = 3*n^2 - 2*n + 7.
  • A191414 (program): Unitary Jordan function J_2^*(n).
  • A191448 (program): Dispersion of the odd integers greater than 1, by antidiagonals.
  • A191449 (program): Dispersion of (3,6,9,12,15,…), by antidiagonals.
  • A191450 (program): Dispersion of (3n-1), read by antidiagonals.
  • A191451 (program): Dispersion of (3n-2), for n>=2, by antidiagonals.
  • A191452 (program): Dispersion of (4,8,12,16,…), by antidiagonals.
  • A191465 (program): 9^n - 2^n.
  • A191466 (program): 9^n - 5^n.
  • A191467 (program): 9^n - 7^n.
  • A191468 (program): 8^n - 5^n.
  • A191472 (program): a(n) = 2*prime(n+2) - prime(n+1) - prime(n).
  • A191475 (program): Values of i of the numbers 2^i*3^j (A033845).
  • A191476 (program): Values of j of the numbers 2^i*3^j (A033845).
  • A191483 (program): Even discriminants of imaginary quadratic fields, negated.
  • A191484 (program): Number of compositions of even natural numbers into 5 parts <= n.
  • A191487 (program): The row sums of the Sierpinski-Stern triangle A191372.
  • A191488 (program): A companion to Gould’s sequence A001316.
  • A191489 (program): Number of compositions of even natural numbers into 6 parts <= n.
  • A191494 (program): Number of compositions of even natural numbers in 7 parts <= n.
  • A191495 (program): Number of compositions of even natural numbers into 8 parts <= n.
  • A191496 (program): Number of compositions of even numbers into 9 parts <= n.
  • A191497 (program): a(n+1) = 2*a(n) + A014017(n+5), a(0) = 0.
  • A191520 (program): Number of UUU’s in all the dispersed Dyck paths of semilength n (i.e., in all Motzkin paths of length n (U=(1,1)).
  • A191522 (program): Number of valleys in all left factors of Dyck paths of length n. A valley is a (1,-1)-step followed by a (1,1)-step.
  • A191524 (program): Number of double rises in all left factors of Dyck paths of length n (a double rise consists of two consecutive (1,1)-steps).
  • A191526 (program): Number left factors of Dyck paths of length n and having no hills; a hill is a (1,1)-step starting at level 0 and followed by a (1,-1)-step.
  • A191527 (program): Number of turns in all left factors of Dyck paths of length n.
  • A191528 (program): Triangle read by rows: T(n,k) is the number of left factors of Dyck paths of length n that have k returns to the axis.
  • A191529 (program): Number of dispersed Dyck paths of length n (i.e., Motzkin paths of length n with no (1,0) steps at positive heights) with no initial and no final (1,0)-steps.
  • A191531 (program): Sum of lengths of initial and final horizontal segments over all dispersed Dyck paths of semilength n (i.e., over all Motzkin paths of length n with no (1,0)-steps at positive heights).
  • A191532 (program): Triangle T(n,k) read by rows: T(n,n) = 2n+1, T(n,k)=k for k<n.
  • A191558 (program): a(n) = 0 if n prime, otherwise n.
  • A191561 (program): a(n) = 2^n mod 3*n
  • A191562 (program): a(n) = 7^n mod 3*n.
  • A191566 (program): a(n) = 7*a(n-1) + (-1)^n*6*2^(n-1).
  • A191567 (program): Four interlaced 2nd order polynomials: a(4*k) = k*(1+2*k); a(1+2*k) = 2*(1+2*k)*(3+2*k); a(2+4*k) = 4*(1+k)*(1+2*k).
  • A191582 (program): Riordan matrix (1/(1-3*x^2),x/(1-x)).
  • A191583 (program): Sum of the distinct prime divisors of prime(n) + prime(n+1).
  • A191584 (program): Diagonal sums of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).
  • A191585 (program): Central coefficients of the Riordan matrix (1/(1-3*x^2),x/(1-x)) (A191582).
  • A191586 (program): Binomial row sums of the Riordan matrix (1/(1-x),x/(1-x^2)) (A046854).
  • A191588 (program): T(m,n) is the number of ways to split two strings of length m and n, respectively, into the same number of nonempty parts such that at least one of the corresponding parts has length 1 and such that the parts have at most size 2.
  • A191589 (program): Primes of the form 3*n^4+12*n^2+2, n > 0.
  • A191590 (program): a(n) is the genus of the modular curve associated to the principal congruence subgroup of level p(n), where p(n) is the n-th prime number.
  • A191593 (program): Number of partitions of 12*n into parts < 5.
  • A191596 (program): Expansion of (1+x)^4/(1-x)^7.
  • A191597 (program): Expansion of x*(1+3*x)/ ( (1-4*x)*(1+x+x^2)).
  • A191610 (program): Possible number of trailing zeros in n!.
  • A191616 (program): a(1) = 1; a(n) is the largest number m such that m-A085392(m) = a(n-1).
  • A191621 (program): a(n) = ((n+1)^n-(n-1)^n)/2+1.
  • A191627 (program): a(n) = floor(3^n/(3n-1)).
  • A191628 (program): a(n) = floor((3^n)/(3*n - 2)).
  • A191629 (program): a(n) = floor((2^n)/(3*n - 1)).
  • A191630 (program): a(n) = floor((-1 + 2^n)/(1 + 2*n)).
  • A191631 (program): a(n) = floor((2^n)/(2n-1)).
  • A191632 (program): a(n) = floor((3^n)/(2*n - 1)).
  • A191633 (program): a(n) = floor((1 + 2^n)/(1 + 2*n)).
  • A191634 (program): a(n) = floor((1 + 3^n)/(1 + 3*n)).
  • A191636 (program): a(n) = floor((-1 + 4^n)/(-1 + 2*n)).
  • A191637 (program): a(n) = floor((1 + 4^n)/(1 + 2*n)).
  • A191638 (program): a(n) = floor((-1 + 4^n)/(-1 + 3*n)).
  • A191639 (program): a(n) = floor((1 + 4^n)/(1 + 3*n)).
  • A191640 (program): a(n) = floor((-1 + 4^n)/(-1 + 4*n)).
  • A191641 (program): a(n) = floor((1 + 4^n)/(1 + 4*n)).
  • A191655 (program): Dispersion of (2,5,8,11,14,17,…), by antidiagonals.
  • A191656 (program): Dispersion of (2,4,5,7,8,10,…), by antidiagonals.
  • A191659 (program): First differences of A000219.
  • A191660 (program): Second differences of A000219.
  • A191661 (program): Third differences of A000219.
  • A191662 (program): a(n) = n! / A000034(n-1).
  • A191663 (program): Dispersion of A042948 (numbers >3, congruent to 0 or 1 mod 4), by antidiagonals.
  • A191664 (program): Dispersion of A014601 (numbers >2, congruent to 0 or 3 mod 4), by antidiagonals.
  • A191665 (program): Dispersion of A042963 (numbers >1, congruent to 1 or 2 mod 4), by antidiagonals.
  • A191666 (program): Dispersion of A042964 (numbers congruent to 2 or 3 mod 4), by antidiagonals.
  • A191667 (program): Dispersion of A016813 (4k+1, k>1), by antidiagonals.
  • A191668 (program): Dispersion of A016825 (4k+2, k>0), by antidiagonals.
  • A191669 (program): Dispersion of A004767 (4k+3, k>=0), by antidiagonals.
  • A191670 (program): Dispersion of A042968 (>1 and congruent to 1 or 2 or 3 mod 4), by antidiagonals.
  • A191671 (program): Dispersion of A004772 (>1 and congruent to 0 or 2 or 3 mod 4), by antidiagonals.
  • A191672 (program): Dispersion of A042965 (>1 and congruent to 0 or 1 or 3 mod 4), by antidiagonals.
  • A191673 (program): Dispersion of A004773 (>1 and congruent to 0 or 1 or 2 mod 4), by antidiagonals.
  • A191677 (program): Numbers n such that 1^(n-1)+2^(n-1)+…+n^(n-1) == 0 (mod n)
  • A191680 (program): Number of compositions of odd natural numbers into 9 parts <= n.
  • A191681 (program): a(n) = (9^n - 1)/2.
  • A191682 (program): Twice A113473.
  • A191686 (program): a(n) = n^(n-1) - (n-1)^(n-1) - … - 2^(n-1) - 1^(n-1).
  • A191687 (program): Table T(n,k)=[Ceiling[1/2*((k+1)^n+(1+(-1)^k)/2)] read by antidiagonals
  • A191690 (program): a(n) = n^n-n^(n-1)-n^(n-2)-…-n^2-n-1.
  • A191694 (program): a(n) = floor((3^n - 2^n)/n).
  • A191695 (program): a(n) = floor((5^n)/(3^n - 2^n)).
  • A191696 (program): a(n) = floor((5^n)/(3^n + 2^n)).
  • A191697 (program): a(n) = r1^n + r2^n + r3^n where r1, r2, r3 are the three roots of x^3 - 2*x - 2 = 0.
  • A191698 (program): a(n) = (122n^3 + 140n^2 + 45n + 3n(-1)^n)/8.
  • A191702 (program): Dispersion of A008587 (5,10,15,20,25,30,…), by antidiagonals.
  • A191703 (program): Dispersion of A016861, (5k+1), by antidiagonals.
  • A191704 (program): Dispersion of A016873, (5k+2), by antidiagonals.
  • A191705 (program): Dispersion of A016873, (5k+3), by antidiagonals.
  • A191706 (program): Dispersion of A016873, (5k+4), by antidiagonals.
  • A191707 (program): Dispersion of A016873, (numbers >1 and congruent to 1, 2, 3, or 4 mod 5), by antidiagonals.
  • A191708 (program): Dispersion of A047202, (numbers >1 and congruent to 0, 2, 3, or 4 mod 5), by antidiagonals.
  • A191709 (program): Dispersion of A047202, (numbers >1 and congruent to 0, 1, 3, or 4 mod 5), by antidiagonals.
  • A191710 (program): Dispersion of A032763, (numbers >1 and congruent to 0, 1, 2, or 4 mod 5), by antidiagonals.
  • A191711 (program): Dispersion of A001068, (numbers >1 and congruent to 0, 1, 2, or 3 mod 5), by antidiagonals.
  • A191721 (program): Permutations in S_n avoiding the patterns {4321, 34512, 45123, 35412, 43512, 45132, 45213, 53412, 45312, 45231}.
  • A191723 (program): Dispersion of A047215, (numbers >1 and congruent to 0 or 2 mod 5), by antidiagonals.
  • A191724 (program): Dispersion of A047218, (numbers >1 and congruent to 0 or 3 mod 5), by antidiagonals.
  • A191727 (program): Dispersion of A047219, (numbers >1 and congruent to 1 or 3 mod 5), by antidiagonals.
  • A191728 (program): Dispersion of A047209, (numbers >1 and congruent to 1 or 4 mod 5), by antidiagonals.
  • A191730 (program): Dispersion of A047211, (numbers >1 and congruent to 2 or 4 mod 5), by antidiagonals.
  • A191733 (program): Dispersion of A047206, (numbers >1 and congruent to 1 or 3 or 4 mod 5), by antidiagonals.
  • A191734 (program): Dispersion of A032793, (numbers >1 and congruent to 1 or 2 or 4 mod 5), by antidiagonals.
  • A191737 (program): Dispersion of A047212, (numbers >1 and congruent to 0 or 2 or 4 mod 5), by antidiagonals.
  • A191738 (program): Dispersion of A047222, (numbers >1 and congruent to 0 or 2 or 3 mod 5), by antidiagonals.
  • A191740 (program): Dispersion of A047220, (numbers >1 and congruent to 0 or 1 or 3 mod 5), by antidiagonals.
  • A191745 (program): a(n) = 12*n^3 + 9*n^2 + 2*n.
  • A191746 (program): Partial sums of product of twin primes.
  • A191747 (program): Concatenation of row entries of the n X n identity matrices.
  • A191748 (program): Sequence of all m in {1,2,3,…} such that A191747(m) = 1.
  • A191750 (program): Dirichlet convolution of A000012 with A007947.
  • A191759 (program): Least significant decimal digit of (2n-1)^2.
  • A191760 (program): Digital root of the n-th odd square.
  • A191761 (program): Last digit of (2*n)^2. Also period 5: repeat [0, 4, 6, 6, 4].
  • A191762 (program): Digital roots of the nonzero even squares.
  • A191763 (program): Integers that cannot be partitioned into a sum of an odd square, an even square and a triangular number.
  • A191764 (program): Integers that do not have a partition into a sum of an odd square and two (not necessarily distinct) triangular numbers.
  • A191770 (program): Lim f(f(…f(n)…)) where f(n) is the fractal sequence A022446.
  • A191771 (program): Positions of 1 in A191770.
  • A191772 (program): Positions of 2 in A191770.
  • A191773 (program): Positions of 3 in A191770.
  • A191777 (program): Positions of 1 in A020903; complement of A020904.
  • A191778 (program): a(1) = 1; a(n)= 2*lcm(n, a(n - 1)).
  • A191782 (program): Sum of the lengths of the first ascents in all n-length left factors of Dyck paths.
  • A191790 (program): Number of base pyramids in all length n left factors of Dyck paths.
  • A191796 (program): Number of DUU’s in all length n left factors of Dyck paths; here U=(1,1) and D=(1,-1).
  • A191797 (program): a(n) = binomial(F(n), 2) where F(n) = A000045(n).
  • A191819 (program): (A178477(n)-1)/9.
  • A191820 (program): A178478(n)/9.
  • A191821 (program): a(n) = n*(2^n - n + 1) + 2^(n-1)*(n^2 - 3*n + 2).
  • A191829 (program): a(n) = Sum_{i+j+k=n, i,j,k >= 1} tau(i)*tau(j)*tau(k), where tau() = A000005().
  • A191830 (program): Expansion of x^2*(2-3*x)/(1-x-x^2)^2.
  • A191831 (program): a(n) = Sum_{i+j=n, i,j >= 1} tau(i)*sigma(j), where tau() = A000005(), sigma() = A000203().
  • A191836 (program): The slowest growing sequence that satisfies: a(1) = 1, a(n) is a multiple of n and a(n-1), and a(n) > a(n-1).
  • A191869 (program): First differences of the dying rabbits sequence A000044.
  • A191871 (program): a(n) = numerator(n^2 / 2^n).
  • A191873 (program): A problem of Zarankiewicz: maximal number of 1’s in an n X n matrix of 0’s and 1’s with 0’s on the main diagonal and no “rectangle” with 1’s at the four corners.
  • A191897 (program): Coefficients of the Z(n,x) polynomials; Z(0,x) = 1, Z(1,x) = x and Z(n,x) = x*Z(n-1,x) - 2*Z(n-2,x), n >= 2.
  • A191899 (program): Number of compositions of odd natural numbers into 8 parts <=n
  • A191900 (program): Number of compositions of odd natural numbers into 7 parts <=n
  • A191901 (program): Number of compositions of odd natural numbers into 6 parts <= n.
  • A191902 (program): Number of compositions of odd positive integers into 5 parts <= n.
  • A191903 (program): Number of compositions of odd natural numbers into 4 parts <= n.
  • A191904 (program): Square array read by antidiagonals up: T(n,k) = 1-k if k divides n, else 1.
  • A191906 (program): The remainder of (product of proper divisors of n) mod (sum of proper divisors of n).
  • A191907 (program): Square array read by antidiagonals up: T(n,k) = -(n-1) if n divides k, else 1.
  • A191909 (program): Decimal expansion of the limit of the square root of the ratio of consecutive Padovan numbers.
  • A191910 (program): Triangle read by rows: T(n,n)=n; T(n,k) = k-1 if k divides n and k < n, otherwise -1.
  • A191967 (program): n * (numbers that are not divisible by 3).
  • A191968 (program): a(n) = Fibonacci(8n+5) mod Fibonacci(8n+1).
  • A191969 (program): Numbers that are indices of deficient oblong numbers (A002378).
  • A191985 (program): Monotonically ordered sequence nonnegative 2^(i-1)-3*2^(j-1), for i>=1, j>=1.
  • A191986 (program): Monotonically ordered sequence nonnegative 3*2^(i-1)-2^(j-1), for i>=1, j>=1.
  • A191992 (program): Concatenation of n and the n-th composite number.
  • A191993 (program): a(n) = 3^(n-1) + C(2*n, n)/2.
  • A191994 (program): (Sum of first n Fibonacci numbers) times (product of first n Fibonacci numbers).
  • A192000 (program): Sum of binomial numbers A000332(k+3), with k in the reduced residue system modulo n.
  • A192001 (program): Triangle with sums of nonnegative integer powers of positive first n integers in the columns.
  • A192002 (program): Counting sequence for Wythoff AB-numbers smaller than n.
  • A192004 (program): Alternating row sums of array A187360: minimal polynomial of 2*cos(Pi/n) evaluated for x=-1.
  • A192013 (program): a(n) = Sum_{d|n} Kronecker(-6, d).
  • A192015 (program): Arithmetic derivative of prime powers: a(n) = A003415(A000961(n)).
  • A192016 (program): Second arithmetic derivative of prime powers: a(n) = A068346(A000961(n)).
  • A192020 (program): Triangle read by rows: T(n,k) is the number of unordered pairs of nodes at distance k in the binomial tree of order n (1 <= k <= 2n-1; entries in row n are the coefficients of the corresponding Wiener polynomial).
  • A192021 (program): The Wiener index of the binomial tree of order n.
  • A192023 (program): The Wiener index of the comb-shaped graph |_|_|…|_| with 2n (n>=1) nodes. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices in the graph.
  • A192025 (program): The Wiener index of the double-comb graph \/_\/_\/…\/_\/ with 3n (n>=1) nodes. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices in the graph.
  • A192026 (program): Square array read by antidiagonals: W(n,m) (n >= 3, m >= 1) is the Wiener index of the graph G(n,m) obtained from an n-wheel graph by adjoining m pendant edges at each node of the cycle.
  • A192030 (program): Square array read by antidiagonals: W(n,p) (n>=1, p>=1) is the Wiener index of the graph G(n,p) obtained in the following way: consider n copies of a star tree with p-1 edges, add a vertex to their union, and connect this vertex with the roots of the star trees.
  • A192032 (program): Square array read by antidiagonals: W(m,n) (m >= 0, n >= 0) is the Wiener index of the graph G(m,n) obtained in the following way: connect by an edge the center of an m-edge star with the center of an n-edge star. The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices in the graph.
  • A192033 (program): Expansion of x*(3*x^2+x+1)/((x-1)*(2*x-1)*(x+1)).
  • A192065 (program): Expansion of Product_{k>=1} Q(x^k)^k where Q(x) = Product_{k>=1} (1 + x^k).
  • A192066 (program): Sum of the odd unitary divisors of n.
  • A192068 (program): a(n) = Fibonacci(2*n) - (n mod 2).
  • A192069 (program): (A192249)/5.
  • A192070 (program): (A192251)/2.
  • A192080 (program): Expansion of 1/((1-x)^6-x^6).
  • A192082 (program): Let f=A038554(n)+delta(n,1), where delta is the Kronecker symbol. Then a(n) is the fixed point that arises from iterating f (a(n)=0 or 1).
  • A192083 (program): Arithmetic derivative of squares of prime powers: a(n)=A003415(A056798(n)).
  • A192084 (program): Second arithmetic derivative of squares of prime powers: a(n)=A068346(A056798(n)).
  • A192085 (program): Number of ones in the binary expansion of n^3.
  • A192096 (program): Maximum number of tatami tilings of any m-by-m square region with exactly n horizontal dimers and m monomers.
  • A192106 (program): Decimal expansion of square root of 102.
  • A192107 (program): Sum of all the n-digit numbers whose digits are all odd.
  • A192109 (program): Numbers k that divide 2^(k-1) - 2.
  • A192113 (program): Monotonic ordering of nonnegative differences 4^i-2^j, for 40>=i>=0, j>=0.
  • A192121 (program): Monotonic ordering of nonnegative differences 8^i - 2^j, for 40 >= i >= 0, j >= 0.
  • A192132 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3 + x*(A(x) - 1)^3.
  • A192133 (program): Difference of base and exponent of prime powers (cf. A000961).
  • A192136 (program): a(n) = (5*n^2 - 3*n + 2)/2.
  • A192142 (program): 1-sequence of reduction of (n^2+n+1) by x^2 -> x+1.
  • A192143 (program): 0-sequence of reduction of hexagonal numbers sequence by x^2 -> x+1.
  • A192144 (program): 1-sequence of reduction of hexagonal numbers sequence by x^2 -> x+1.
  • A192145 (program): 0-sequence of reduction of pentagonal numbers sequence by x^2 -> x+1.
  • A192146 (program): 1-sequence of reduction of pentagonal numbers sequence by x^2 -> x+1.
  • A192158 (program): Monotonic ordering of nonnegative differences 9^i-3^j, for 40>= i>=0, j>=0.
  • A192186 (program): a(n) = binomial(2*n, floor(n*sqrt(2))).
  • A192192 (program): Numbers whose second arithmetic derivative (A068346) is prime; Polynomial-like numbers of degree 3.
  • A192217 (program): a(1)=1; a(n) = n*lcm(n, a(n-1)) for n > 1.
  • A192232 (program): Constant term of the reduction of n-th Fibonacci polynomial by x^2 -> x+1. (See Comments.)
  • A192234 (program): a(n) = 2*(a(n-1) + a(n-2) + a(n-3)) - a(n-4) for n >= 4, with initial terms 0,1,0,1.
  • A192235 (program): Constant term of the reduction of the n-th 2nd-kind Chebyshev polynomial by x^2 -> x+1.
  • A192236 (program): Coefficient of x in the reduction of the n-th 2nd-kind Chebyshev polynomial by x^2 -> x+1.
  • A192237 (program): a(n) = 2*(a(n-1) + a(n-2) + a(n-3)) - a(n-4) for n >= 4, with initial terms 0,0,0,1.
  • A192238 (program): Constant term in the reduction of the polynomial x(x+1)(x+2)…(x+n-1) by x^2 -> x+1.
  • A192239 (program): Coefficient of x in the reduction of the polynomial x(x+1)(x+2)…(x+n-1) by x^2 -> x+1.
  • A192240 (program): Constant term in the reduction of the polynomial (x+3)^n by x^2 -> x+1.
  • A192243 (program): 0-sequence of reduction of Lucas sequence by x^2 -> x+1.
  • A192244 (program): 0-sequence of reduction of triangular number sequence by x^2 -> x+1.
  • A192245 (program): 1-sequence of reduction of triangular number sequence by x^2 -> x+1.
  • A192246 (program): 0-sequence of reduction of tetrahedral number sequence by x^2 -> x+1.
  • A192247 (program): 1-sequence of reduction of tetrahedral number sequence by x^2 -> x+1.
  • A192248 (program): 0-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.
  • A192249 (program): 1-sequence of reduction of binomial coefficient sequence B(n,4)=A000332 by x^2 -> x+1.
  • A192250 (program): 0-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.
  • A192251 (program): 1-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.
  • A192252 (program): 0-sequence of reduction of (n!) by x^2 -> x+1.
  • A192253 (program): 1-sequence of reduction of (n!) by x^2 -> x+1.
  • A192254 (program): 0-sequence of reduction of (n^2) by x^2 -> x+1.
  • A192255 (program): 1-sequence of reduction of (n^2) by x^2 -> x+1.
  • A192256 (program): 0-sequence of reduction of (n^3) by x^2 -> x+1.
  • A192257 (program): 1-sequence of reduction of (n^3) by x^2 -> x+1.
  • A192263 (program): a(n) = abs(a(n-1) - 3*a(n-2)) with a(1)=a(2)=1.
  • A192278 (program): Numbers n whose product of their anti-divisors divides the product of their divisors.
  • A192280 (program): Characteristic function of numbers that are the product of consecutive primes.
  • A192299 (program): 0-sequence of reduction of (n^2+n+1) by x^2 -> x+1.
  • A192300 (program): 0-sequence of reduction of the lower Wythoff sequence by x^2 -> x+1.
  • A192301 (program): 1-sequence of reduction of the lower Wythoff sequence by x^2 -> x+1.
  • A192302 (program): 0-sequence of reduction of the upper Wythoff sequence by x^2 -> x+1.
  • A192303 (program): 1-sequence of reduction of the upper Wythoff sequence by x^2 -> x+1.
  • A192304 (program): 0-sequence of reduction of (2n-1) by x^2 -> x+1.
  • A192305 (program): 0-sequence of reduction of (2n) by x^2 -> x+1.
  • A192306 (program): 1-sequence of reduction of (2n) by x^2 -> x+1.
  • A192307 (program): 0-sequence of reduction of (3n) by x^2 -> x+1.
  • A192308 (program): 1-sequence of reduction of (3n) by x^2 -> x+1.
  • A192309 (program): 0-sequence of reduction of (3n-1) by x^2 -> x+1.
  • A192310 (program): 1-sequence of reduction of (3n-1) by x^2 -> x+1.
  • A192311 (program): 0-sequence of reduction of (3n-2) by x^2 -> x+1.
  • A192312 (program): 1-sequence of reduction of (3n-2) by x^2 -> x+1.
  • A192313 (program): Constant term of the reduction of n-th polynomial at A157751 by x^2->x+1.
  • A192316 (program): G.f.: A(x) = Sum_{n>=0} x^n * (1+x)^A038722(n), where A038722(n) = floor(sqrt(2*n)+1/2)^2 - n + 1.
  • A192323 (program): Expansion of theta_3(q^3) * theta_3(q^5) in powers of q.
  • A192324 (program): Sequence of numbers formed as remainder of Mersenne numbers divided by primes.
  • A192326 (program): Remainders of primes divided by odd numbers.
  • A192327 (program): a(n) = prime(n) mod 2*n.
  • A192328 (program): Numbers of the form 20*k+7 which are three times a square.
  • A192330 (program): Minimum number of endpoints of a tree so that there exists a zero-entropy map defined on it having a period n orbit.
  • A192333 (program): Numbers that are “unsafe” when playing the game Dollar Nim, which is a Nim game where users can remove 1, 5, 10, or 25 cents from an initial pile of money. The most common version of the game is played with an initial amount of $1, hence the name.
  • A192337 (program): Coefficient of x in the reduction of n-th polynomial at A157751 by x^2->x+1.
  • A192338 (program): Constant term of the reduction of n-th polynomial at A157751 by x^2->x+2.
  • A192339 (program): Coefficient of x in the reduction of n-th polynomial at A157751 by x^2->x+2.
  • A192344 (program): Constant term of the reduction of n-th polynomial at A161516 by x^2->x+1.
  • A192345 (program): Constant term of the reduction of n-th polynomial at A161516 by x^2->x+1.
  • A192346 (program): Constant term of the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
  • A192347 (program): Coefficient of x in the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
  • A192348 (program): Constant term of the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
  • A192349 (program): Coefficient of x in the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
  • A192350 (program): Constant term of the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
  • A192351 (program): Coefficient of x in the reduction (by x^2->x+1) of polynomial p(n,x) identified in Comments.
  • A192352 (program): Constant term of the reduction of the polynomial p(n,x)=(1/2)((x+1)^n+(x-1)^n) by x^2->x+1.
  • A192353 (program): Constant term of the reduction of the polynomial p(n,x)=(1/2)((x+2)^n+(x-2)^n) by x^2->x+1.
  • A192354 (program): Coefficients of x in the reduction of the polynomial p(n,x)=(1/2)((x+2)^n+(x-2)^n) by x^2->x+1.
  • A192355 (program): Constant term of the reduction of the polynomial p(n,x)=(1/2)((x+2)^n+(x-2)^n) by x^2->x+2.
  • A192356 (program): Coefficients of x in the reduction of the polynomial p(n,x) = ((x+2)^n + (x-2)^n)/2 by x^2->x+2.
  • A192357 (program): Constant term of the reduction of the polynomial p(n,x)=(1/2)((x+3)^n+(x-3)^n) by x^2->x+1.
  • A192358 (program): Coefficients of x in the reduction of the polynomial p(n,x)=(1/2)((x+3)^n+(x-3)^n) by x^2->x+1.
  • A192359 (program): Numerator of h(n+6) - h(n), where h(n) = Sum_{k=1..n} 1/k.
  • A192370 (program): Sum of all the n-digit numbers whose digits are all even and nonzero: 2,4,6,8.
  • A192373 (program): Constant term in the reduction of the polynomial p(n,x) defined at A162517 and below in Comments.
  • A192374 (program): Coefficient of x in the reduction of the polynomial p(n,x) defined at A162517 and below in Comments.
  • A192375 (program): A192374(n)/2.
  • A192376 (program): Constant term of the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192377 (program): Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192378 (program): (A192377)/2.
  • A192379 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192380 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192381 (program): (A192380)/2.
  • A192382 (program): Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192383 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192384 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192385 (program): (A192384)/2.
  • A192386 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192387 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192388 (program): (A192387)/2.
  • A192389 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192395 (program): Main (or principal) sequence for a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) + 2*a(n-4).
  • A192396 (program): Square array T(n,k) = floor(((k+1)^n-(1+(-1)^k)/2)/2) read by antidiagonals.
  • A192398 (program): a(n) = n^4 + 3*n^3 - 3*n.
  • A192415 (program): G.f. satisfies: A(x) = (1 + x*A(x))*(1 + x^3*A(x)^2).
  • A192418 (program): Molecular topological indices of the complete bipartite graphs K_{n,n}.
  • A192421 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192422 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined below in Comments.
  • A192423 (program): Constant term of the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192424 (program): (A192423)/2.
  • A192425 (program): Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192426 (program): Constant term of the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192427 (program): Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192428 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192429 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192430 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192431 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192438 (program): Number of bases <= n in which n has no digits exceeding 9.
  • A192440 (program): Coefficient of x^floor(n/2) in the expansion of (1+x+x^3)^n.
  • A192441 (program): Coefficient of x^(2*n) in the expansion of (1 + x^3 + x^4)^n.
  • A192442 (program): Coefficient of x^n in the expansion of (1+x^3+x^4)^n.
  • A192447 (program): a(n) = n*(n-1)/2 if this is even, otherwise (n*(n-1)/2) + 1.
  • A192450 (program): Numbers k such that -1 is not a square mod k.
  • A192451 (program): Number of primes between successive hexagonal numbers.
  • A192452 (program): Numbers n such that -1 is not a 4th power mod n.
  • A192453 (program): Numbers k such that -1 is a 4th power mod k.
  • A192457 (program): Constant term of the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192458 (program): a(n) = A192457(n)/2.
  • A192459 (program): Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x) defined below in Comments.
  • A192460 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192461 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192462 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192463 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) = (x+1) * (2x+1) * … *(nx+1).
  • A192464 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) = 1 + x^n + x^(2n).
  • A192465 (program): Constant term of the reduction by x^2->x+2 of the polynomial p(n,x)=1+x^n+x^(2n).
  • A192466 (program): Coefficient of x in the reduction by x^2->x+2 of the polynomial p(n,x)=1+x^n+x^(2n).
  • A192467 (program): (A192466)/2.
  • A192468 (program): Constant term of the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).
  • A192469 (program): Coefficient of x in the reduction by x^2->x+3 of the polynomial p(n,x)=1+x^n+x^(2n).
  • A192470 (program): (A192469)/2.
  • A192471 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^n+x^(2n+1).
  • A192472 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^n+x^(2n+2).
  • A192473 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^n+x^(2n+2).
  • A192474 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^(n+1)+x^(2n).
  • A192475 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=1+x^(n+1)+x^(2n).
  • A192479 (program): a(n) = 2^n*C(n-1) - A186997(n-1), where C(n) are the Catalan numbers (A000108).
  • A192480 (program): a(n) = n + A000108(n-1) for n > 1; a(0)=0, a(1)=1.
  • A192489 (program): Numbers m such that A099427(m) = 2.
  • A192491 (program): Molecular topological indices of the complete tripartite graphs K_{n,n,n}.
  • A192543 (program): Let r be the largest real zero of x^n - x^(n-1) - x^(n-2) - … - 1 = 0. Then a(n) is the value of k which satisfies the equation 0.5/10^k < 2 - r < 5/10^k.
  • A192544 (program): Number bases n such that all integers m having the commuting property r(m)^2=r(m^2), where r is cyclic replacement of digits d->(d+1) mod n, are of the form m=A^k*B, where B=n/2, A=B-1, and 0<=k<=n-3.
  • A192550 (program): a(n) = sum(stirling2(n+1,k+1)*k!^2,k=0..n).
  • A192552 (program): a(n) = sum(stirling2(n,k)*(-1)^(n-k)*k!^2,k=0..n).
  • A192555 (program): a(n) = sum(stirling2(n+1,k+1)*(-1)^(n-k)*k!^2,k=0..n).
  • A192570 (program): a(n) = floor(sqrt(Bell(n)))
  • A192571 (program): a(n) = sum(floor(sqrt(Bell(k))),k=0..n).
  • A192572 (program): a(n) = sum((-1)^(n-k)*floor(sqrt(Bell(k))),k=0..n).
  • A192576 (program): a(n) = sum(binomial(n,k)*floor(sqrt(Bell(k))),k=0..n).
  • A192616 (program): Constant term in the reduction of the n-th Fibonacci polynomial by x^3->x^2+x+1. See Comments.
  • A192617 (program): Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+x+1.
  • A192633 (program): Partial sums of the Floor-Sqrt transform of Catalan numbers.
  • A192638 (program): Numbers n such that 4n + 3 and 16n + 15 are prime.
  • A192651 (program): Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+x+1. See Comments.
  • A192654 (program): Alternating partial sums of the Floor-Sqrt transform of Catalan numbers.
  • A192655 (program): Floor-Sqrt transform of central binomial coefficients (A000984).
  • A192656 (program): Partial sums of the Floor-Sqrt transform of central binomial coefficients.
  • A192659 (program): Alternating partial sums of the Floor-Sqrt transform of central binomial coefficients.
  • A192660 (program): Floor-Sqrt transform of Lucas numbers (A000032).
  • A192661 (program): Floor-Sqrt transform of central Stirling numbers of the second kind (A007820).
  • A192663 (program): Floor-Sqrt transform of the binomial coefficients bin(3*n,n) (A005809).
  • A192664 (program): Floor-Sqrt transform of the binomial coefficients bin(2*n+1,n) (A001700).
  • A192665 (program): Floor-Sqrt transform of the numbers bin(3*n,n)/(2*n+1) (A001764).
  • A192668 (program): Floor-Sqrt transform of superfactorials (A000178).
  • A192669 (program): Floor-Sqrt transform of Motzkin numbers (A001006).
  • A192670 (program): Floor-Sqrt transform of central trinomial coefficients (A002426).
  • A192671 (program): Floor-Sqrt transform of Riordan numbers (A005043).
  • A192672 (program): Floor-Sqrt transform of little Schroeder numbers (A001003).
  • A192673 (program): Floor-Sqrt transform of large Schroder numbers (A006318).
  • A192674 (program): Floor-Sqrt transform of large central Delannoy numbers (A001850).
  • A192676 (program): Floor-Sqrt transform of derangement numbers (A000166).
  • A192677 (program): Floor-Sqrt transform of involution numbers (A000085).
  • A192678 (program): Floor-Sqrt transform of idempotent endomap numbers (A000248).
  • A192679 (program): Floor-Sqrt transform of ordered Bell numbers (A000670).
  • A192680 (program): Floor-Sqrt transform of Sylvester continuants (A002801).
  • A192681 (program): Floor-sqrt transform of Lah partition numbers (A000262).
  • A192682 (program): Floor-Sqrt transform of numbers of A078678 (Grand Dyck paths with no zigzags).
  • A192684 (program): Floor-Sqrt transform of numbers of A004148 (secondary structures).
  • A192685 (program): Floor-Sqrt transform of numbers of A051286.
  • A192687 (program): Male-female differences: a(n) = A005378(n) - A005379(n).
  • A192717 (program): Positive integers of the form (p^e)(k^2) for p prime congruent to 3 (mod 8), e congruent to 1 (mod 4), and k an odd integer coprime to p.
  • A192720 (program): High-water marks of A062357: record values of prime(n)-n*(prime(n+1)-prime(n)).
  • A192727 (program): a(n) = Fibonacci(n-2) + 2*a(n-2) - (n mod 2).
  • A192735 (program): Left edge of the triangle in A033291.
  • A192736 (program): Right edge of the triangle in A033291.
  • A192742 (program): Number of matchings in the n-antiprism graph.
  • A192744 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192745 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192746 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined below in Comments.
  • A192747 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192748 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192749 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192750 (program): Define a pair of sequences c_n, d_n by c_0=0, d_0=1 and thereafter c_n = c_{n-1}+d_{n-1}, d_n = c_{n-1}+4*n+2; sequence here is d_n.
  • A192751 (program): Define a pair of sequences c_n, d_n by c_0=0, d_0=1 and thereafter c_n = c_{n-1}+d_{n-1}, d_n = c_{n-1}+4*n+2; sequence here is c_n.
  • A192752 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192753 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192754 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192755 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192756 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192757 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192758 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192759 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192760 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192761 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192762 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
  • A192772 (program): Constant term in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2x+1.
  • A192773 (program): Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2x+1.
  • A192774 (program): Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2x+1.
  • A192775 (program): The numbers n^2 as n runs through the numbers which are palindromes in base 2.
  • A192776 (program): Squares of binary palindromes.
  • A192777 (program): Constant term in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1. See Comments.
  • A192778 (program): Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1.
  • A192779 (program): Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+3x+1.
  • A192780 (program): Constant term in the reduction of the n-th Fibonacci polynomial by x^3->x^2+1. See Comments.
  • A192781 (program): Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+1.
  • A192782 (program): Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+1.
  • A192790 (program): Molecular topological index of the Andrasfai graphs
  • A192791 (program): Molecular topological index of the n-antiprism graph.
  • A192793 (program): Molecular topological indices of the crossed prism graphs
  • A192794 (program): Numbers n such that n + 2 and n^2 + 4 are primes.
  • A192796 (program): Molecular topological indices of the crown graphs
  • A192797 (program): Molecular topological indices of the cycle graphs
  • A192798 (program): Constant term in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2. See Comments.
  • A192799 (program): Coefficient of x in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.
  • A192800 (program): Coefficient of x^2 in the reduction of the n-th Fibonacci polynomial by x^3->x^2+2.
  • A192801 (program): Constant term in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1. See Comments.
  • A192802 (program): Coefficient of x in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.
  • A192803 (program): Coefficient of x^2 in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.
  • A192804 (program): Constant term in the reduction of the polynomial 1+x+x^2+…+x^n by x^3->x^2+x+1. See Comments.
  • A192805 (program): Constant term in the reduction of the polynomial 1+x+x^2+…+x^n by x^3->x^2+2x+1. See Comments.
  • A192806 (program): a(n) = 7*a(n-1) - 5*a(n-2) + a(n-3), with initial values a(0) = a(1) = 1, a(2)=4.
  • A192807 (program): Coefficient of x in the reduction of the polynomial (x^2 + x + 1)^n by x^3 -> x^2 + x + 1.
  • A192808 (program): Constant term in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2. See Comments.
  • A192809 (program): Coefficient of x in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.
  • A192810 (program): Coefficient of x^2 in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.
  • A192811 (program): a(n) = A192809(n)/2.
  • A192812 (program): Constant term in the reduction of the polynomial x^(2*n) + x^n + 1 by x^3 -> x + 1. See Comments.
  • A192813 (program): Coefficient of x in the reduction of the polynomial x^(2*n) + x^n + 1 by x^3 -> x + 1.
  • A192814 (program): Constant term in the reduction of the polynomial (2*x+1)^n by x^3 -> x^2 + x + 1. See Comments.
  • A192815 (program): Coefficient of x in the reduction of the polynomial (2*x + 1)^n by x^3 -> x^2 + x + 1.
  • A192816 (program): a(n) = A192815(n)/2.
  • A192817 (program): Numbers that are coprime to their 9’s complement.
  • A192827 (program): Molecular topological indices of the gear graphs
  • A192830 (program): Molecular topological indices of the halved cube graphs.
  • A192831 (program): Molecular topological indices of the hypercube graphs.
  • A192832 (program): Molecular topological indices of the lattice graphs.
  • A192833 (program): Molecular topological indices of the Moebius ladders.
  • A192834 (program): Molecular topological indices of the Mycielski graphs.
  • A192836 (program): Molecular topological indices of the pan graphs.
  • A192838 (program): Molecular topological indices of the prism graphs Y_n.
  • A192839 (program): Molecular topological indices of the square graphs.
  • A192845 (program): Molecular topological indices of the sun graphs.
  • A192846 (program): Molecular topological indices of the sunlet graphs.
  • A192847 (program): Molecular topological indices of the tetrahedral graphs.
  • A192848 (program): Molecular topological indices of the graph join C_n + C_n of cycle graphs.
  • A192849 (program): Molecular topological indices of the triangular graphs.
  • A192850 (program): Molecular topological indices of the web graphs.
  • A192858 (program): Hosoya indices of the 2n-wheel graphs W_{2n}.
  • A192861 (program): Flat numbers: odd n such that n+1 is a squarefree number times a power of two.
  • A192862 (program): Flat primes: odd primes p such that p+1 is a squarefree number times a power of two.
  • A192863 (program): Lower flat numbers: odd numbers k such that k-1 is a squarefree number times a power of two.
  • A192864 (program): Lower flat primes: odd primes p such that p-1 is a squarefree number times a power of two.
  • A192868 (program): Thin numbers: odd numbers k > 1 such that k+1 is a prime times a power of two.
  • A192872 (program): Constant term in the reduction by (x^2 -> x+1) of the polynomial p(n,x) given in Comments.
  • A192873 (program): Coefficient of x in the reduction by (x^2->x+1) of the polynomial p(n,x) given in Comments.
  • A192874 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments.
  • A192875 (program): Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments.
  • A192876 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments.
  • A192877 (program): Coefficient of x in the reduction by (x^2->x+1) of the polynomial p(n,x) given in Comments.
  • A192878 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments.
  • A192879 (program): Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments.
  • A192880 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) given in Comments.
  • A192881 (program): Number of terms for the shortest Egyptian fraction representation of 1 starting with 1/n.
  • A192882 (program): Coefficient of x in the reduction by (x^2 -> x+1) of the polynomial p(n,x) given in Comments.
  • A192883 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial F(n+3)*x^n, where F = A000045 (Fibonacci sequence).
  • A192885 (program): A071963(n) - n, where A071963(n) is the largest prime factor of p(n), the n-th partition number A000041(n).
  • A192893 (program): Number of symmetric 11-ary factorizations of the n-cycle (12…n).
  • A192894 (program): Number of symmetric 13-ary factorizations of the n-cycle (12…n).
  • A192896 (program): Prime factor addition sequence: For the term n, add all the prime factors of n to n. If n is a prime then add n to it. Start with n = 3
  • A192904 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192905 (program): Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192906 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192907 (program): Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192908 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192909 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192910 (program): Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
  • A192911 (program): Constant term in the reduction by (x^3 -> x + 1) of the polynomial F(n+1)*x^n, where F(n)=A000045 (Fibonacci sequence).
  • A192912 (program): Coefficient of x in the reduction by (x^3 -> x + 1) of the polynomial F(n+1)*x^n, where F(n)=A000045 (Fibonacci sequence).
  • A192913 (program): Coefficient of x^2 in the reduction by (x^3 -> x + 1) of the polynomial F(n+1)*x^n, where F(n)=A000045 (Fibonacci sequence).
  • A192914 (program): Constant term in the reduction by (x^2 -> x + 1) of the polynomial C(n)*x^n, where C=A000285.
  • A192915 (program): Triangle read by rows: T(n,k) = Sum_{j=0..3} binomial(n+3, k+j), 0 <= k <= n.
  • A192916 (program): Constant term in the reduction by (x^2 -> x+1) of the polynomial C(n)*x^n, where C=A022095.
  • A192917 (program): Coefficient of x in the reduction by (x^2 -> x+1) of the polynomial C(n)*x^n, where C=A022095.
  • A192918 (program): The decimal expansion of the real root of r^3 + r^2 + r - 1.
  • A192919 (program): Constant term in the reduction by (x^2 -> x+1) of the polynomial F(n+4)*x^n, where F=A000045 (Fibonacci sequence).
  • A192920 (program): Coefficient of x in the reduction by (x^2 -> x+1) of the polynomial F(n+4)*x^n, where F=A000045 (Fibonacci sequence).
  • A192921 (program): Constant term in the reduction by (x^2->x+1) of the polynomial p(n,x) defined below at Comments.
  • A192922 (program): Constant term in the reduction by (x^2->x+1) of the polynomial p(n,x) defined below at Comments.
  • A192923 (program): Coefficient of x in the reduction by (x^2->x+1) of the polynomial p(n,x) defined below at Comments.
  • A192932 (program): Squares of numbers in Perrin sequence
  • A192936 (program): Constant term of the reduction by x^2 -> x + 1 of the polynomial p(n,x) = Product_{k=1..n} (x+k).
  • A192937 (program): a(n) = 100*a(n-1) - (n-1) with a(1)=100.
  • A192938 (program): Decimal expansion of the real positive root of the equation: 4*d^4 + 12*d^3 + 8*d^2 - 1 = 0.
  • A192939 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x)=(x+2)(x+4)…(x+2n).
  • A192940 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x)=(x+2)(x+4)…(x+2n).
  • A192941 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x)=(2x+1)(2x+2)…(2x+n).
  • A192942 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x)=(2x+1)(2x+2)…(2x+n).
  • A192945 (program): G.f. satisfies: A(x) = 1 + x*Sum_{n>=0} (A(x)^2 - 1)^n.
  • A192949 (program): E.g.f. satisfies: A(x) = 1 + x*Sum_{n>=0} (A(x)^2 - 1)^n/n!.
  • A192950 (program): a(n) = A192942(n)/2.
  • A192951 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192952 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192953 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192954 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192955 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192956 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192957 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192958 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192959 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192960 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192961 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192962 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192963 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192964 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A192965 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192966 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192967 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192968 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192969 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192970 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192971 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192972 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192973 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192974 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192975 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192976 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192978 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192979 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192980 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192981 (program): Constant term of the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192982 (program): Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments.
  • A192986 (program): Numerator of Sum_{i=0..n-1} B(i)/B(n), where B(i) = A000110(i) are the Bell numbers.
  • A192987 (program): Denominator of Sum_{i=0..n-1} B(i)/B(n), where B(i) = A000110(i) are the Bell numbers.
  • A192989 (program): Expansion of e.g.f.: exp((1+x)^3 - 1).
  • A193004 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193005 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193006 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193007 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193008 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193010 (program): Decimal expansion of the constant term of the reduction of e^x by x^2->x+1.
  • A193026 (program): Decimal expansion of the constant term of the reduction of e^(-x) by x^2->x+1.
  • A193029 (program): Decimal expansion of the constant term of the reduction of e^(x/2) by x^2->x+1.
  • A193030 (program): Decimal expansion of the coefficient of x in the reduction of e^(x/2) by x^2->x+1.
  • A193041 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193042 (program): Natural fractal sequence of A194126.
  • A193043 (program): Listed by antidiagonals, array A[k,n] = digital root of n-th nonzero k-gonal number.
  • A193044 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193045 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193046 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193047 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193048 (program): Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193049 (program): Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined at Comments.
  • A193052 (program): a(n) = 5^n - 4^n - 3^n.
  • A193053 (program): a(n) = (14*n*(n+3) + (2*n-5)*(-1)^n + 21)/16.
  • A193068 (program): Generating primitive Pythagorean triangles by using (n, n+1) gives perimeters for each n. This sequence list the sum of these perimeters for each n triangles.
  • A193070 (program): Odd numbers N for which sigma(N^2) is prime.
  • A193071 (program): Odd numbers N for which sigma(N^2) is not prime.
  • A193090 (program): Digital roots of the nonzero pentagonal numbers.
  • A193091 (program): Augmentation of the triangular array A158405. See Comments.
  • A193103 (program): G.f.: exp( Sum_{n>=1} 2*sigma(n*4^n)*x^n/n ).
  • A193108 (program): The tetrahedral numbers A000292 mod 10.
  • A193127 (program): Numbers of spanning trees of the antiprism graphs.
  • A193129 (program): Number of spanning trees of the n-barbell graph.
  • A193130 (program): Numbers of spanning trees of the cocktail party graphs.
  • A193131 (program): Numbers of spanning trees of the complete tripartite graphs K_{n,n,n}.
  • A193132 (program): a(n) = 3n*4^(2n-1).
  • A193133 (program): Numbers of spanning trees of the crown graphs.
  • A193138 (program): Number of square satins of order n.
  • A193139 (program): Number of symmetric satins of order n.
  • A193140 (program): Number of isonemal satins of exact period n.
  • A193144 (program): Primes of the form n^2 + n + 1, where n is semiprime.
  • A193146 (program): Expansion of 1/(1 - x - x^2 + x^3 - x^4 + x^6).
  • A193147 (program): G.f.: 1/(1 - x - 2*x^3 - x^5).
  • A193160 (program): E.g.f. A(x) satisfies: A(x/(1-x)) = x*A’(x).
  • A193161 (program): E.g.f. A(x) satisfies: A(x/(1-x))/(1-x) = d/dx x*A(x).
  • A193162 (program): G.f. A(x) satisfies: A’(x) = 1 + A(x*exp(x)).
  • A193166 (program): Numbers that are not the product of consecutive primes.
  • A193169 (program): Number of odd divisors of lambda(n).
  • A193181 (program): a(n) = lcm(f(1),f(2),…,f(n)) with f(x) = x^2+1.
  • A193198 (program): G.f.: A(x) = Sum_{n>=0} x^n/(1 - 3^n*x)^n.
  • A193199 (program): G.f.: A(x) = Sum_{n>=0} x^n/(1 - 4^n*x)^n.
  • A193214 (program): Primes in A007066.
  • A193215 (program): Number of Dyck paths of semilength n having the property that the heights of the first and the last peaks coincide.
  • A193218 (program): Number of vertices in truncated tetrahedron with faces that are centered polygons.
  • A193220 (program): Denominators of the fourth row of Akiyama-Tanigawa algorithm leading to Bernoulli numbers A164555(n)/A027642(n).
  • A193228 (program): Truncated octahedron with faces of centered polygons.
  • A193229 (program): A double factorial triangle.
  • A193231 (program): Blue code of n: in binary coding of a polynomial over GF(2), substitute x+1 for x.
  • A193238 (program): Number of prime digits in decimal representation of n.
  • A193242 (program): a(n) = (C(n, floor(n/2)) + 2)^n for n >= 0.
  • A193248 (program): Truncated dodecahedron, and truncated icosahedron with faces of centered polygons.
  • A193249 (program): Snub dodecahedron with faces of centered polygons.
  • A193250 (program): Small rhombicuboctahedron with faces of centered polygons.
  • A193251 (program): Small rhombicosidodecahedron with faces of centered polygons.
  • A193252 (program): Great rhombicuboctahedron with faces of centered polygons.
  • A193253 (program): Great rhombicosidodecahedron with faces of centered polygons.
  • A193254 (program): Sum of odd divisors of lambda(n).
  • A193259 (program): G.f.: x = Sum_{n>=1} x^n * ((1+x)^n - x^n) / (1+x)^a(n).
  • A193260 (program): G.f.: x+x^2 = Sum_{n>=1} x^n * ((1+x+x^2)^n - x^(2*n)) / (1+x+x^2)^a(n).
  • A193267 (program): The number 1 alternating with the numbers A006953/A002445 (which are integers).
  • A193274 (program): a(n) = binomial(Bell(n), 2) where B(n) = Bell numbers A000110(n).
  • A193282 (program): a(n) = (n!/floor(n/2)!)^2.
  • A193291 (program): Number of even divisors of Fibonacci(n).
  • A193295 (program): Number of prime divisors (with multiplicity) of n^2 - 1.
  • A193298 (program): Gica-Panaitopol recursion: a(1) = 1; a(n+1) = 2*a(n) if a(n) <= n; otherwise a(n+1) = a(n) - 1.
  • A193303 (program): Squarefree numbers multiplied by powers of three.
  • A193304 (program): Squarefree numbers multiplied by powers of 5.
  • A193315 (program): Write 2n=j+q (j,q positive noncomposite numbers); j*q maximal; then a(n)=j*q.
  • A193330 (program): Number of prime factors of n^2 + 1, counted with multiplicity.
  • A193331 (program): Triangle read by rows: T(n,k) = floor((k-1)*n^2/(2*k)) is an upper bound on the number of edges in the (n-k)-Turán graph.
  • A193334 (program): Number of even divisors of sigma(n).
  • A193335 (program): Number of odd divisors of sigma(n).
  • A193336 (program): Sum of even divisors of sigma(n).
  • A193337 (program): Sum of odd divisors of sigma(n).
  • A193339 (program): Indices of record values in A001783.
  • A193347 (program): Number of even divisors of tau(n).
  • A193348 (program): Number of odd divisors of tau(n).
  • A193349 (program): Sum of odd divisors of tau(n).
  • A193350 (program): Sum of even divisors of tau(n).
  • A193356 (program): If n is even then 0, otherwise n.
  • A193358 (program): a(0)=1; a(1)=2 and for n>1: a(n)=a(n-a(n-2))+2.
  • A193361 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-3)*a(n-2) + 1.
  • A193365 (program): a(n) = A220371(n)/(4*A220371(n-1))
  • A193374 (program): E.g.f.: A(x) = exp( Sum_{n>=1} x^(n*(n+1)/2) / (n*(n+1)/2) ).
  • A193375 (program): E.g.f.: A(x) = exp( Sum_{n>=1} x^(n*(n+1)/2) ).
  • A193376 (program): T(n,k) = number of ways to place any number of 2 X 1 tiles of k distinguishable colors into an n X 1 grid; array read by descending antidiagonals, with n, k >= 1.
  • A193382 (program): G.f. is the real part of the function C(x) that satisfies C(x) = 1 + x/C(I*x).
  • A193383 (program): G.f. is the imaginary part of the function C(x) that satisfies: C(x) = 1 + x/C(I*x).
  • A193386 (program): Number of even divisors of phi(n).
  • A193388 (program): Sum of even divisors of phi(n).
  • A193390 (program): The hyper-Wiener index of a benzenoid consisting of a straight-line chain of n hexagons (s=2; see the Gutman et al. reference).
  • A193391 (program): Wiener index of a benzenoid consisting of a spiral chain of n hexagons (s=1; see the Gutman et al. reference).
  • A193393 (program): Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).
  • A193394 (program): Hyper-Wiener index of a benzenoid consisting of a zig-zag chain of n hexagons (s=13; see the Gutman et al. reference).
  • A193395 (program): Wiener index of a benzenoid consisting of a double-step zig-zag chain of n hexagons (n >= 2, s = 2123; see the Gutman et al. reference).
  • A193397 (program): Wiener index of a benzenoid consisting of a double-step spiral chain of n hexagons (n>=2, s=21; see the Gutman et al. reference).
  • A193399 (program): Wiener index of a benzenoid consisting of a chain of n hexagons characterized by the encoding s = 1133 (see the Gutman et al. reference, Sec. 5).
  • A193410 (program): Expansion of (1-3*x)/(1-6*x+18*x^2).
  • A193414 (program): Numbers m such that written in base 2 the structure of digits represents a valley.
  • A193415 (program): Numbers from A193414 written in base 2.
  • A193416 (program): Minimum surface area of polycubes with volume n.
  • A193418 (program): Expansion of x*(x^2+x-1)/(3*x^6-4*x^5+x^4-3*x^2+4*x-1).
  • A193421 (program): E.g.f.: Sum_{n>=0} x^n * exp(n^2*x).
  • A193422 (program): Smallest number m such that A193358(m) = n.
  • A193426 (program): Expansion of (a(q^2) + a(q^3) - 2*a(q^6)) / 6 in powers of q where a() is a cubic AGM function.
  • A193427 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(8*k).
  • A193432 (program): Number of divisors of n^2 + 1.
  • A193433 (program): Sum of the divisors of n^2+1.
  • A193434 (program): 6*n/5 = (n written backwards), n > 0.
  • A193436 (program): exp( Sum_{n>=1} x^n/n^3 ) = Sum_{n>=0} a(n)*x^n/n!^3.
  • A193437 (program): E.g.f.: exp( Sum_{n>=0} x^(3*n+1)/(3*n+1) ).
  • A193438 (program): E.g.f.: exp( Sum_{n>=0} x^(4*n+1)/(4*n+1) ).
  • A193446 (program): a(n) = n! * Sum_{k=1..n-1} H(k)*H(n-k) for n>=2, where H(n) is the n-th harmonic number.
  • A193448 (program): a(n) = 4*(5*n^2 - 5*n + 1).
  • A193449 (program): Products of the Jacobsthal numbers and the integers: a(n) = n * A001045(n+1).
  • A193450 (program): Triangle of a binomial convolution sum related to Jacobsthal numbers.
  • A193451 (program): Triangle of a binomial convolution sum related to Jacobsthal numbers.
  • A193453 (program): Number of odd divisors of phi(n).
  • A193454 (program): Sum of odd divisors of phi(n).
  • A193461 (program): Numbers n such that phi(n) divides 2*(n-1).
  • A193462 (program): Sum of the distinct prime divisors of n^2+1.
  • A193463 (program): Row sums of triangle A076732.
  • A193464 (program): Row sums of triangle A076731.
  • A193465 (program): Row sums of triangle A061312.
  • A193467 (program): E.g.f.: Sum_{n>=0} x^n * exp(n*(n+1)/2*x).
  • A193469 (program): a(n) = A193467(n)/n for n>=1.
  • A193475 (program): a(n) = 4*16^n - 2*4^n.
  • A193476 (program): The denominators of the Bernoulli secant numbers at odd indices.
  • A193477 (program): Denominator(n!/floor(n/2)!^4).
  • A193494 (program): Worst case of an unbalanced recursive algorithm over all n-node binary trees.
  • A193496 (program): a(n) = 1 iff digit n+1 of Pi is >= digit n, otherwise a(n) = 0. We consider 3 to be digit 1 of Pi.
  • A193497 (program): a(n) = 1, if digit n+1 of e is greater than or equal to digit n of e, else 0.
  • A193505 (program): Decimal expansion of bean curve area.
  • A193508 (program): a(n) = n if n is not a power of 2 and a(2^n) = a(n).
  • A193509 (program): Number of odd divisors of Omega(n).
  • A193510 (program): Number of even divisors of Omega(n).
  • A193511 (program): a(n) = Sum of even divisors of Omega(n), a(1) = 0.
  • A193512 (program): a(n) = Sum of odd divisors of Omega(n), a(1) = 0.
  • A193514 (program): Expansion of phi(-q)^2 * phi(-q^9) / phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
  • A193515 (program): T(n,k) = number of ways to place any number of 3X1 tiles of k distinguishable colors into an nX1 grid.
  • A193519 (program): a(n) = (2/3)*Sum_{i=1..n-1} A000129(i)*3^(n-i).
  • A193523 (program): Number of odd divisors of Sopf(n).
  • A193525 (program): Number of even divisors of sopf(n).
  • A193526 (program): Sum of even divisors of sopf(n).
  • A193529 (program): Sum of odd divisors of sopf(n).
  • A193530 (program): Expansion of (1 - 2*x - 2*x^2 + 3*x^3 + x^5)/((1-x)*(1-2*x-x^2)*(1-2*x^2-x^4)).
  • A193532 (program): G.f.: x = Sum_{n>=1} x^n * ((1+x)^(n+1) - x^(n+1)) / (1+x)^a(n).
  • A193534 (program): Decimal expansion of (1/3) * (Pi/sqrt(3) - log(2)).
  • A193535 (program): Decimal expansion of log(2)/3.
  • A193538 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2*n)-sigma(n))^2/2 * x^n/n ).
  • A193539 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2*n)-sigma(n))^3 * x^n/n ).
  • A193552 (program): Prime numbers ending in James Bond number ‘‘007’’
  • A193553 (program): Sum of divisors of 4*n.
  • A193554 (program): Triangle read by rows: first column: top entry is 1, then powers of 2; rest of triangle is Pascal’s triangle A007318.
  • A193558 (program): Differences between consecutive primes of the form k^2+1.
  • A193561 (program): Augmentation of the triangle A004736. See Comments.
  • A193562 (program): Number of divisors of n^4+1.
  • A193563 (program): a(0) = 0, a(n) = n^2 * (a(n-1) + 1).
  • A193564 (program): In A014675, replace the n-th occurrence of 1 with n-1 and also replace the n-th occurrence of 2 with n-1.
  • A193575 (program): T(n)^3 - n^3 where T(n) is a triangular number.
  • A193576 (program): T(n)^3+n^3 where T(n) is a triangular number.
  • A193577 (program): 5*7^n
  • A193578 (program): (13^n+1)/2.
  • A193579 (program): a(n) = 2*4^n + 7.
  • A193581 (program): Sort-and-subtract: a(n) = n - A004185(n).
  • A193583 (program): Number of fixed points under iteration of sum of squares of digits in base b.
  • A193588 (program): A Fibonacci triangle: T(n,k) = Fib(k+2) for 0 <= k <= n.
  • A193592 (program): Triangle read by rows having n-th row 1, n, n-1, n-2,…, 2, 1 for n>=0.
  • A193596 (program): Triangle given by p(n,k) = ceiling(C(n,k)/2).
  • A193599 (program): Indices n such that Padovan(n) > R^n/(2*R+3) where R is the only real root of the polynomial x^3-x-1.
  • A193600 (program): Indices n such that Padovan(n) < r^n/(2*r+3) where r is the real root of the polynomial x^3-x-1.
  • A193605 (program): Triangle: (row n) = partial sums of partial sums of row n of Pascal’s triangle.
  • A193608 (program): The consecutive squares of numbers multiplied by their next consecutive integer.
  • A193616 (program): Integers often used as card values in Planning Poker decks.
  • A193618 (program): G.f. A(x) satisfies: A(x)^2 + A(-x)^2 = 2 and A(x)^-2 - A(-x)^-2 = -8*x.
  • A193619 (program): G.f. A(x) satisfies: A(x)^-2 + A(-x)^-2 = 2 and A(x)^2 - A(-x)^2 = -8*x.
  • A193627 (program): Indices n such that Perrin(n) < r^n where r is the real root of the polynomial x^3-x-1.
  • A193632 (program): Triangle: T(n,k)=C(4n-1,2k), 0<=k<=n.
  • A193633 (program): Triangle: T(n,k)=C(4n,2k), 0<=k<=n.
  • A193634 (program): Triangle: T(n,k)=C(4n+1,2k), 0<=k<=n.
  • A193635 (program): Triangle: T(n,k)=C(3n-k,k), 0<=k<=n.
  • A193636 (program): Triangle: T(n,k) = C(3n-2k,k), 0 <= k <= n.
  • A193637 (program): a(n) = a(n-1)^2 - n^(n+1).
  • A193640 (program): Indices n such that Perrin(n) > r^n where r is the real root of the polynomial x^3-x-1.
  • A193641 (program): Number of arrays of -1..1 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.
  • A193642 (program): Number of arrays of -2..2 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero
  • A193643 (program): Number of arrays of -3..3 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero
  • A193644 (program): Number of arrays of -4..4 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.
  • A193645 (program): Number of arrays of -5..5 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero.
  • A193646 (program): Number of arrays of -6..6 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero
  • A193647 (program): Number of arrays of -7..7 integers x(1..n) with every x(i) in a subsequence of length 1 or 2 with sum zero
  • A193649 (program): Q-residue of the (n+1)st Fibonacci polynomial, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)
  • A193651 (program): a(n) = ((2*n + 1)!! + 1)/2.
  • A193652 (program): A020988 and A007583 interleaved.
  • A193653 (program): Q-residue of the Delannoy triangle A008288, where Q is the triangular array (t(i,j)) given by t(i,j)=1.
  • A193654 (program): Q-residue of the triangle p(n,k)=floor((n+1)/(n+k+2)/2), 0<=k<=n, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)
  • A193655 (program): Q-residue of the triangle p(n,k)=floor(1/2+(n+1)/(n+k+2)/2), 0<=k<=n, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)
  • A193656 (program): Q-residue of the triangle p(n,k)=(2^(n - k))*5^k, 0<=k<=n, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)
  • A193657 (program): First difference of A002627.
  • A193658 (program): Q-residue of the triangle A051162, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)
  • A193659 (program): Q-residue of the triangle A094727, where Q=Pascal’s triangle. (See Comments.)
  • A193660 (program): Q-residue of the triangle A038207 of coefficients of (x+2)^n, where Q is the triangle given by t(i,j)=1 for 0<=i<=j. (See Comments.)
  • A193661 (program): Q-residue of the triangle A193673, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)
  • A193662 (program): Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for 0<=i<=j. (See Comments.)
  • A193663 (program): Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q is the triangle given by t(n,k)=k+1 for 0<=k<=n. (See Comments.)
  • A193664 (program): Q-residue of A049310 (triangle of coefficients of Fibonacci polynomials), where Q=Pascal’s triangle. (See Comments.)
  • A193665 (program): Q-residue of A075392, where Q=A075392. (See Comments.)
  • A193667 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=(x+1^n and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
  • A193668 (program): a(n) = Sum_{i=0..n-1} (n+i)*a(n-1-i) for n>1, a(0)=1, a(1)=1.
  • A193669 (program): G.f.: (1-x^4)/(1-x+x^8)
  • A193673 (program): Triangle given by p(n,k)=(coefficient of x^(n-k) in (1/2) ((x+3)^n+(x+1)^n)), 0<=k<=n.
  • A193676 (program): Number of nonnegative zeros of minimal polynomials of 2*cos(Pi/n), n>=1.
  • A193677 (program): Number of negative zeros of minimal polynomials of 2*cos(Pi/n), n>=1.
  • A193678 (program): Discriminant of Chebyshev C-polynomials.
  • A193680 (program): Period 6 sequence 0,1,2,0,2,1.
  • A193682 (program): Period 8: repeat [0, 1, 2, 3, 0, 3, 2, 1].
  • A193683 (program): Alternating row sums of Sheffer triangle A143495 (3-restricted Stirling2 numbers).
  • A193684 (program): Alternating row sums of Sheffer triangle A143496 (4-restricted Stirling2 numbers).
  • A193686 (program): Lucas numbers (mod 100).
  • A193688 (program): Number of steps to reach 1 in Collatz (3x+1) problem starting with 2^n - 1.
  • A193690 (program): Expansion of (1 - x^2)^2 * (1 - x^4) / ((1 - x)^2 * (1 - x^6)) in powers of x.
  • A193695 (program): Number of arrays of -1..1 integers x(1..n) with every x(i) in a subsequence of length 1, 2 or 3 with sum zero
  • A193715 (program): Positions of triangular numbers (A000217) in the union of squares and triangular numbers (A005214).
  • A193722 (program): Triangular array: the fusion of (x+1)^n and (x+2)^n; see Comments for the definition of fusion.
  • A193723 (program): Mirror of the fusion triangle A193722.
  • A193724 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=(x+1)^n.
  • A193725 (program): Mirror of the triangle A193724.
  • A193726 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=(x+2)^n.
  • A193727 (program): Mirror of the triangle A193726.
  • A193728 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=(2x+1)^n.
  • A193729 (program): Mirror of the triangle A193728.
  • A193730 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(2x+1)^n and q(n,x)=(2x+1)^n.
  • A193731 (program): Mirror of the triangle A193730.
  • A193732 (program): Connell-like sequence.
  • A193734 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(2x+1)^n and q(n,x)=(x+2)^n.
  • A193735 (program): Mirror of the triangle A193734.
  • A193736 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(n+1)-st Fibonacci polynomial and q(n,x)=(x+1)^n.
  • A193737 (program): Mirror of the triangle A193736.
  • A193738 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193739 (program): Mirror of the triangle A193738.
  • A193744 (program): Partial sum of Perrin numbers.
  • A193758 (program): Denominator of H(n)/H(n-1), where H(n) is the n-th harmonic number = Sum_{k=1..n} 1/k.
  • A193760 (program): Replace 3^i with n^i in ternary representation of n.
  • A193763 (program): Number of signed permutations of length n avoiding (-2, 1) and (2, -1).
  • A193766 (program): The number of dominoes in a largest saturated domino covering of the 3 by n board.
  • A193767 (program): The number of dominoes in a largest saturated domino covering of the 4 by n board.
  • A193768 (program): The domination number of the 4 X n board.
  • A193770 (program): Table T(m,n) = (5^m + 3^n)/2, m,n = 0,1,2,…, read by antidiagonals.
  • A193771 (program): Expansion of 1 / (1 - x - x^3 + x^6) in powers of x.
  • A193773 (program): Number of ways to write n as 2*x*y - x - y with 1 <= x <= y.
  • A193777 (program): Number of signed permutations of size 2n invariant under D and D’bar and avoiding (-2, 1) and (2, -1).
  • A193778 (program): Number of signed permutations of length 2n invariant under D and D’bar.
  • A193787 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+1)^n and q(n,x)=1+x^n.
  • A193790 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(2x+1)^n and q(n,x)=1+x^n.
  • A193791 (program): Mirror of the triangle A193790.
  • A193794 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(3x+1)^n and q(n,x)=1+x^n.
  • A193795 (program): Mirror of the triangle A193794.
  • A193800 (program): Least m > 0 such that (n+m)^2 - m^2 (= n^2 + 2*m*n) is a square.
  • A193807 (program): Smallest positive integer k such that n*k^2 + 1 is a prime.
  • A193815 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x) = x^n + x^(n-1) + … + x+1 and q(n,x)=(x+1)^n.
  • A193816 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x) = x^n + x^(n-1) + … + x+1 and q(n,x) = (x+2)^n.
  • A193817 (program): Mirror of the triangle A193816.
  • A193818 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x) = x^n + x^(n-1) + … + x+1 and q(n,x)=(2x+1)^n.
  • A193819 (program): Mirror of the triangle A193818.
  • A193820 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+1)^n and q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193821 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193822 (program): Mirror of the triangle A193821.
  • A193823 (program): Triangular array: the fusion of polynomial sequences P and Q given by p(n,x)=(2x+1)^n and q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193824 (program): Mirror of the triangle A193823.
  • A193828 (program): Even generalized pentagonal numbers.
  • A193832 (program): Irregular triangle read by rows in which row n lists 2n-1 copies of 2n-1 and n copies of 2n, for n >= 1.
  • A193838 (program): Size k of smallest square of k X k lattice points from which n points with distinct mutual distances can be chosen.
  • A193842 (program): Triangular array: the fission of the polynomial sequence ((x+1)^n: n >= 0) by the polynomial sequence ((x+2)^n: n >= 0). (Fission is defined at Comments.)
  • A193843 (program): Mirror image of the triangle A193842.
  • A193844 (program): Triangular array: the fission of ((x+1)^n) by ((x+1)^n); i.e., the self-fission of Pascal’s triangle.
  • A193845 (program): Mirror of the triangle A193844.
  • A193846 (program): Triangular array: the fission of ((x+2)^n) by ((x+1)^n).
  • A193847 (program): Mirror of the triangle A193846.
  • A193848 (program): Triangular array: (1/2)*A193846.
  • A193849 (program): Triangular array: (1/2)*A193847.
  • A193850 (program): Triangular array: the fission of ((x+2)^n) by (q(n,x)) given by q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193851 (program): Mirror of the triangle A193850.
  • A193852 (program): Triangular array: (1/2)*A193850.
  • A193853 (program): Triangular array: (1/2)*A193851.
  • A193856 (program): Triangular array: the fission of (p(n,x)) by ((2x+1)^n, where p(n,x)=(x+1)^n.
  • A193857 (program): Mirror of the triangle A193856.
  • A193858 (program): Triangular array: the fission of ((x+1)^n) by ((2x+1)^n.
  • A193859 (program): Mirror of the triangle A193858.
  • A193860 (program): Triangular array: the fission of ((2x+1)^n) by (q(n,x)), where q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193861 (program): Mirror of the triangle A193860.
  • A193862 (program): Mirror of the triangle A115068.
  • A193866 (program): Even pentagonal numbers divided by 2.
  • A193867 (program): Odd central polygonal numbers.
  • A193868 (program): Even central polygonal numbers.
  • A193871 (program): Square array T(n,k) = k^n - k + 1 read by antidiagonals.
  • A193872 (program): Even dodecagonal numbers: 4*n*(5*n - 2).
  • A193879 (program): Different leap years in the Gregorian and the revised Julian calendars
  • A193884 (program): G.f.: (1-x^2)/(1-x+x^4)
  • A193885 (program): a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) - a(n-4), n>=4; a(0) = 1, a(1) = 1, a(2) = 2, a(3) = 3.
  • A193887 (program): Decimal expansion of Pi * sqrt(2)/8.
  • A193891 (program): Triangular array: the self-fusion of (p(n,x)), where p(n,x)=x^n+2x^(n-1)+3x^(n-2)+…+nx+(n+1).
  • A193892 (program): Mirror of the triangle A193891.
  • A193895 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{(k+1)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{(k+1)*x^k : 0<=k<=n}.
  • A193896 (program): Mirror of the triangle A193895.
  • A193897 (program): Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{(k+1)*x^k : 0<=k<=n}.
  • A193898 (program): Mirror of the triangle A193897.
  • A193899 (program): Triangular array: the self-fusion of (p(n,x)), where p(n,x)=x*p(n-1,x)+2^n, p(0,x)=1.
  • A193900 (program): Mirror of the triangle A193899.
  • A193902 (program): Triangular array: the self-fusion of (p(n,x)), where p(n,x)=2x*p(n-1,x)+1, p(0,x)=1.
  • A193903 (program): Mirror of the triangle A193902.
  • A193904 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+2^n with p(0,x)=1, and q(n,x)=2x*q(n-1,x)+1 with q(0,x)=1.
  • A193905 (program): Mirror of the triangle A193904.
  • A193910 (program): Leap centuries in the revised Julian calendar.
  • A193911 (program): Sums of the diagonals of the matrix formed by listing the h-Stohr sequences in increasing order.
  • A193912 (program): Partial sums of A193911.
  • A193913 (program): Diagonal element T(n,n) of the infinite array with T(n,1) = T(1,n) = Fibonacci(n) and recursively T(n,k) = T(n-1,k-1) + T(n,k-1) + T(n-1,k).
  • A193915 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=2x*q(n-1,x)+1 with q(0,x)=1.
  • A193916 (program): Mirror of the triangle A193915.
  • A193919 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=(x+1)^n.
  • A193920 (program): Mirror of the triangle A193919.
  • A193921 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=x^n+x^(n-1)+…+x+1.
  • A193922 (program): Mirror of the triangle A193921.
  • A193923 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=(x+1)^n and q(n,x)=Sum_{k=0..n}F(k+1)*x^(n-k), where F=A000045 (Fibonacci numbers).
  • A193924 (program): Mirror of the triangle A193923.
  • A193929 (program): Number of prime factors of n^4 + 1, counted with multiplicity.
  • A193930 (program): E.g.f.: exp(x+x^2+x^3+x^4).
  • A193931 (program): E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5).
  • A193932 (program): E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6).
  • A193933 (program): E.g.f. A(x) = exp(x+x^2+x^3+x^4+x^5+x^6+x^7).
  • A193941 (program): G.f.: (1+x^3)/(1-x-x^6).
  • A193942 (program): G.f.: (1+x^4)/(1-x-x^8).
  • A193951 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
  • A193952 (program): Mirror of the triangle A193951.
  • A193953 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=x*q[n-1,x}+n+1, n>=0.
  • A193954 (program): Mirror of the triangle A193953.
  • A193955 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=sum{((k+1)^2)*x^(n-k) : 0<=k<=n}.
  • A193956 (program): Mirror of the triangle A193955.
  • A193957 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers), and q(n,x)=sum{(k+1)(n+1)*x^(n-k) : 0<=k<=n}.
  • A193958 (program): Mirror of the triangle A193955.
  • A193959 (program): Triangular array: the fusion of (p(n,x)) by (q(n,x)), where p(n,x)=sum{((k+1)^2)*x^(n-k) : 0<=k<=n} and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) .
  • A193960 (program): Mirror of the triangle A193959.
  • A193961 (program): Triangular array: the self-fusion of (p(n,x)), where p(n,x)=sum{((k+1)^2)*x^(n-k) : 0<=k<=n}.
  • A193962 (program): Mirror of the triangle A193961.
  • A193971 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=(x+1)^n.
  • A193972 (program): Mirror of the triangle A193971.
  • A193973 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=x*p(n-1,x)+1 with p(0,x)=1.
  • A193974 (program): Mirror of the triangle A193973.
  • A193975 (program): Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n+1, where p(0,x)=1.
  • A193976 (program): Mirror of the triangle A193975.
  • A193977 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p(0,x)=1, and q(n,x)=sum{(k+1)*x^k ; 0<=k<=n}.
  • A193978 (program): Mirror of the triangle A193977.
  • A193979 (program): Triangular array: the self-fission of (p(n,x)), where p(n,x)=x*p(n-1,x)+n, with p(0,x)=1.
  • A193980 (program): Mirror of the triangle A193979.
  • A193989 (program): Numbers n such that sigma_3(n) > sigma_3(k) for all k < n.
  • A193990 (program): Number of distinct prime factors <= n of binomial(2*n,n).
  • A193997 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=(x+1^n.
  • A193998 (program): Mirror of the triangle A193997.
  • A193999 (program): Mirror of the triangle A094585.
  • A194005 (program): Triangle of the coefficients of an (n+1)-th order differential equation associated with A103631.
  • A194007 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers) and q(n,x)=x*q(n-1,x)+n+1, with q(0,x)=1.
  • A194008 (program): Mirror of the triangle A194007.
  • A194009 (program): Triangular array: the fission of (p(n,x)) by (q(n,x)), where p(n,x)=x*p(n-1,x)+n+1 with p[0,x)=1, and q(n,x)=sum{F(k+1)*x^(n-k) : 0<=k<=n}, where F=A000045 (Fibonacci numbers).
  • A194010 (program): Mirror of the triangle A194009.
  • A194011 (program): Natural interspersion of A002061; a rectangular array, by antidiagonals.
  • A194012 (program): Inverse permutation of A194011; every positive integer occurs exactly once.
  • A194019 (program): E.g.f. = exp(-x*(x+4)/2)/(1-x)^3.
  • A194028 (program): Beatty sequence for sqrt(12).
  • A194029 (program): Natural fractal sequence of the Fibonacci sequence (1, 2, 3, 5, 8, …).
  • A194032 (program): Natural interspersion of the squares (1,4,9,16,25,…), a rectangular array, by antidiagonals.
  • A194038 (program): Natural interspersion of A034856, a rectangular array, by antidiagonals.
  • A194039 (program): Sum of nonprime divisors of n^2 + 1.
  • A194040 (program): Inverse permutation to A194038; contains every positive integer exactly once.
  • A194045 (program): Numbers whose binary expansion is a preorder traversal of a binary tree
  • A194046 (program): Natural interspersion of A052905, a rectangular array, by antidiagonals.
  • A194047 (program): Inverse permutation to A194046; contains every positive integer exactly once.
  • A194050 (program): Natural fractal sequence of A014739.
  • A194053 (program): Natural fractal sequence of A054347.
  • A194055 (program): Natural fractal sequence of A000071 (Fibonacci numbers minus 1; a rectangular array, by antidiagonals.
  • A194061 (program): Natural interspersion of A002620; a rectangular array, by antidiagonals.
  • A194063 (program): Natural fractal sequence of A006578.
  • A194066 (program): Natural fractal sequence of A087483; a rectangular array, by antidiagonals.
  • A194067 (program): Natural interspersion of A087483; a rectangular array, by antidiagonals.
  • A194069 (program): 1+floor((2/3)*n^2).
  • A194070 (program): Natural fractal sequence of A194069.
  • A194073 (program): a(n) = 1 + floor((3/4)*n^2).
  • A194074 (program): Natural fractal sequence of A194073.
  • A194081 (program): Smallest m such that A005375(m) = n.
  • A194082 (program): Sum{floor(sqrt(3)*k/2) : 1<=k<=n}
  • A194087 (program): G.f.: eta(q)*eta(q^4)*eta(q^16)*eta(q^64)*eta(q^256)*eta(q^1024)*…, where eta(q) = Product_{m=1..oo} (1 - q^m).
  • A194102 (program): a(n) = Sum_{j=1..n} floor(j*sqrt(2)); n-th partial sum of Beatty sequence for sqrt(2), A001951.
  • A194103 (program): Natural fractal sequence of A194102.
  • A194106 (program): Sum{floor(j*sqrt(3) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(3).
  • A194107 (program): Natural fractal sequence of A194106.
  • A194110 (program): Sum{floor(j*sqrt(5) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(5).
  • A194111 (program): Sum{floor(j*sqrt(7) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(7).
  • A194112 (program): a(n) = Sum_{j=1..n} floor(j*sqrt(8)); n-th partial sum of Beatty sequence for sqrt(8).
  • A194113 (program): a(n) = Sum_{j=1..n} floor(j*sqrt(10)); n-th partial sum of Beatty sequence for sqrt(10).
  • A194114 (program): Sum{floor(j*sqrt(11) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(11).
  • A194115 (program): Sum{floor(j*sqrt(12) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(12).
  • A194116 (program): a(n) = Sum_{j=1..n} floor(j*sqrt(13)); n-th partial sum of Beatty sequence for sqrt(13).
  • A194117 (program): Sum{floor(j*((1+sqrt(3))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for sqrt(13).
  • A194118 (program): Triangular array: T(n,k)=C(n+2,k)+C(n+2,k+2), 0<=k<=n.
  • A194119 (program): Triangular array: T(n,k)=C(n+3,k)+C(n+3,k+3), 0<=k<=n.
  • A194120 (program): Triangular array: T(n,k)=C(n+4,k)+C(n+4,k+4), 0<=k<=n.
  • A194121 (program): Triangular array: T(n,k)=C(n+2,k)+C(n+2,k+1)+C(n+2,k+2), 0<=k<=n.
  • A194122 (program): Triangular array: T(n,k) = C(n+4,k) + C(n+4,k+1) + C(n+4,k+2) + C(n+4,k+3) + C(n+4,k+4), 0 <= k <= n.
  • A194123 (program): Triangular array: T(n,k)=|C(n+2,k)-C(n+2,k+2)|, 0<=k<=n.
  • A194124 (program): a(n) = Sum_{k=0..floor(n/2)} (C(n+2,k) - C(n+2,k+2)).
  • A194126 (program): -1+A088207.
  • A194127 (program): Listed by antidiagonals, array A(k,n) = digital root of n-th nonzero centered k-gonal number.
  • A194129 (program): Number of digits in n^100.
  • A194130 (program): a(n) = n!/gcd(n,3).
  • A194137 (program): a(n) = Sum_{j=1..n} floor(j*sqrt(6)); n-th partial sum of Beatty sequence for sqrt(6).
  • A194138 (program): a(n) = Sum_{j=1..n} floor(j*(1+sqrt(2))), n-th partial sum of Beatty sequence for 1+sqrt(2).
  • A194139 (program): a(n) = Sum_{j=1..n} floor(j*(2+sqrt(2))); n-th partial sum of Beatty sequence for 2+sqrt(2).
  • A194140 (program): a(n) = Sum_{j=1..n} floor(j*(1+sqrt(3))); n-th partial sum of Beatty sequence for 1+sqrt(3).
  • A194141 (program): Sum{floor(j*(2+sqrt(3)) : 1<=j<=n}; n-th partial sum of Beatty sequence for 2+sqrt(3).
  • A194142 (program): a(n) = Sum_{j=1..n} floor(j*(3-sqrt(3)); n-th partial sum of Beatty sequence for 3-sqrt(3).
  • A194143 (program): Sum{floor(j*(3+sqrt(3))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for (3+sqrt(3))/2.
  • A194144 (program): Sum{floor(j*(-1+sqrt(5)) : 1<=j<=n}; n-th partial sum of Beatty sequence for -1+sqrt(5).
  • A194145 (program): Beatty sequence for -1+sqrt(6), a(n) = floor(n*(-1+sqrt(6))); complement of A194146.
  • A194146 (program): Beatty sequence for (4+sqrt(6))/2; complement of A194145.
  • A194147 (program): Sum{floor(j*(-1+sqrt(6)) : 1<=j<=n}; n-th partial sum of Beatty sequence for -1+sqrt(6).
  • A194148 (program): Sum_{j=1..n} floor(j*(1/2 + sqrt(2))); n-th partial sum of Beatty sequence for 1/2 + sqrt(2).
  • A194149 (program): Sum{floor(j*(5-sqrt(3))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for (5-sqrt(3))/2.
  • A194150 (program): Sum{floor(j*(3+sqrt(5)) : 1<=j<=n}; n-th partial sum of Beatty sequence for (3+sqrt(5).
  • A194151 (program): Beatty sequence for (1/2)*sqrt(5); complement of A194152.
  • A194152 (program): Beatty sequence for 5+2*sqrt(5); complement of A194151.
  • A194153 (program): Sum{floor(j*(sqrt(5))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for (sqrt(5))/2.
  • A194157 (program): Product of first n nonzero even-indexed Fibonacci numbers F(2), F(4), F(6), …, F(2*n).
  • A194158 (program): Product of first n nonzero odd-indexed Fibonacci numbers F(1), …, F(2*n-1).
  • A194187 (program): Difference of n-th prime and (bitwise XOR of n and n-th prime).
  • A194189 (program): Number of primes between the n-th triangular number and the n-th square.
  • A194195 (program): First inverse function (numbers of rows) for pairing function A060734
  • A194220 (program): [sum{(k/4) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.
  • A194221 (program): Partial sums of A194220.
  • A194222 (program): a(n) = floor(Sum_{k=1..n} frac(k/5)), where frac() = fractional part.
  • A194223 (program): a(n) = [sum{(k/6) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.
  • A194224 (program): Partial sums of A194223.
  • A194225 (program): [sum{(k/7) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.
  • A194226 (program): Partial sums of A194225.
  • A194227 (program): [sum{(2k/7) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.
  • A194228 (program): Partial sums of A194227.
  • A194229 (program): Partial sums of A057357.
  • A194235 (program): a(n) = [Sum_{k=1..n} (k/8)], where [ ]=floor, ( )=fractional part.
  • A194236 (program): Partial sums of A194235.
  • A194237 (program): a(n) = [Sum_{k=1..n} (3k/8)], where [ ]=floor, ( )=fractional part.
  • A194238 (program): Partial sums of A194237.
  • A194258 (program): Second inverse function (numbers of columns) for pairing function A060734.
  • A194268 (program): 8*n^2 + 7*n + 1.
  • A194272 (program): Array T(n,k) with 6 columns read by rows in which row n lists 3*n-2, 3*n-1, 3*n, 3*n, 3*n, 3*n.
  • A194273 (program): Concentric triangular numbers (see Comments lines for definition).
  • A194274 (program): Concentric square numbers (see Comments lines for definition).
  • A194275 (program): Concentric pentagonal numbers of the second kind: a(n) = floor(5*n*(n+1)/6).
  • A194276 (program): Number of distinct polygonal shapes after n-th stage in the D-toothpick structure of A194270.
  • A194283 (program): Numbers n such that at stage n of A194270 appears for first time a new distinct polygonal shape in the structure.
  • A194349 (program): E.g.f.: -log( sqrt(1-x^2) - x ).
  • A194350 (program): Numbers covering A000027: a(n)=(1, 1, 2, 5) * A011557(n)).
  • A194363 (program): Lucas entry points: smallest m >= 0 such that the n-th prime divides Lucas(m), or -1 if there is no such m.
  • A194364 (program): The number of n-permutations having precisely two cycles whose lengths are relatively prime.
  • A194367 (program): Smallest k such that prime(n) divides k*prime(n+1)+1.
  • A194374 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(5) and < > denotes fractional part.
  • A194375 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(5) and < > denotes fractional part.
  • A194376 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(6) and < > denotes fractional part.
  • A194377 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(6) and < > denotes fractional part.
  • A194385 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(10) and < > denotes fractional part.
  • A194386 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(10) and < > denotes fractional part.
  • A194388 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(11) and < > denotes fractional part.
  • A194390 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=sqrt(12) and < > denotes fractional part.
  • A194391 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) > 0, where r=sqrt(12) and < > denotes fractional part.
  • A194402 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) = 0, where r=(1+sqrt(5))/2 and < > denotes fractional part.
  • A194403 (program): (A194402)/2.
  • A194408 (program): Numbers m such that Sum_{k=1..m} (<1/2 + k*r> - <k*r>) < 0, where r=Pi and < > denotes fractional part.
  • A194431 (program): a(n) = 8*n^2 - 6*n - 1.
  • A194432 (program): D-toothpick sequence starting with a cross formed by 4 toothpicks.
  • A194433 (program): Number of toothpicks and D-toothpicks added at n-th stage to the structure of A194432.
  • A194439 (program): Number of regions in the set of partitions of n that contain only one part.
  • A194450 (program): Vertex number of a rectangular spiral which contains exactly between its edges the successive shells of the partitions of the positive integers.
  • A194451 (program): Partition numbers of positive integers and positive integers interleaved.
  • A194453 (program): E.g.f. satisfies: A(x) = exp(x) - sqrt(1 - A(x)^2).
  • A194454 (program): a(n) = 12*n^2 + 2*n + 1.
  • A194455 (program): a(n) = 2^n + 3n + 1.
  • A194458 (program): Total number of entries in rows 0,1,…,n of Pascal’s triangle not divisible by 5.
  • A194459 (program): Number of entries in the n-th row of Pascal’s triangle not divisible by 5.
  • A194460 (program): a(n) is the number of basic ideals in the standard Borel subalgebra of the untwisted affine Lie algebra sl_n.
  • A194475 (program): Number of ways to arrange 3 indistinguishable points on an n X n X n triangular grid so that no three points are in the same row or diagonal.
  • A194486 (program): Number of ways to arrange 2 nonattacking knights on the lower triangle of an n X n board
  • A194508 (program): First coordinate of the (2,3)-Lagrange pair for n.
  • A194509 (program): Second coordinate of (2,3)-Lagrange pair for n.
  • A194510 (program): First coordinate of (2,5)-Lagrange pair for n.
  • A194511 (program): Second coordinate of (2,5)-Lagrange pair for n.
  • A194513 (program): Second coordinate of (2,7)-Lagrange pair for n.
  • A194514 (program): First coordinate of (3,4)-Lagrange pair for n.
  • A194515 (program): Second coordinate of (3,4)-Lagrange pair for n.
  • A194516 (program): First coordinate of (3,5)-Lagrange pair for n.
  • A194517 (program): Second coordinate of (3,5)-Lagrange pair for n.
  • A194518 (program): First coordinate of (3,7)-Lagrange pair for n.
  • A194519 (program): Second coordinate of (3,7)-Lagrange pair for n.
  • A194522 (program): First coordinate of (4,5)-Lagrange pair for n.
  • A194525 (program): Second coordinate of (4,7)-Lagrange pair for n.
  • A194531 (program): Numerator of row 4 in A051714(n) or row 3 in A176672(n).
  • A194532 (program): Jordan function ratio J_6(n)/J_2(n).
  • A194533 (program): Jordan function ratio J_8(n)/J_2(n).
  • A194553 (program): Centered cube numbers: (n+1)^25 + n^25.
  • A194560 (program): G.f.: Sum_{n>=1} G_n(x)^n where G_n(x) = x + x*G_n(x)^n.
  • A194561 (program): Centered cube numbers: (n+1)^27 + n^27.
  • A194579 (program): Numbers whose sum of the their nonprime divisors is prime.
  • A194582 (program): Triangle T(n,k), read by rows, given by (0, 3, -7/3, -2/21, 3/7, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A194584 (program): Differences of A035336.
  • A194586 (program): Triangle read by rows, T(n,k) the coefficients of the polynomials Sum_{k=0..n} binomial(n,k)*A056040(k)*(k mod 2)*q^k.
  • A194588 (program): a(n) = A189912(n-1)-a(n-1) for n>0, a(0) = 1; extended Riordan numbers.
  • A194589 (program): a(n) = A194588(n) - A005043(n); complementary Riordan numbers.
  • A194590 (program): a(n) = (-1)^n*(A056040(n+1)*A152271(n)-2^n)/2.
  • A194593 (program): Semiprimes s such that phi(s)/2 is prime.
  • A194597 (program): Digital roots of the nonzero hexagonal numbers.
  • A194599 (program): Units’ digits of the nonzero hexagonal numbers.
  • A194602 (program): Integer partitions interpreted as binary numbers.
  • A194641 (program): Digital roots of the nonzero heptagonal numbers.
  • A194642 (program): Units’ digits of the nonzero heptagonal numbers.
  • A194644 (program): Number of ways to place 2n nonattacking kings on a 4 X 2n cylindrical chessboard.
  • A194650 (program): Number of ways to place 2 nonattacking kings on an n X n cylindrical chessboard.
  • A194688 (program): First differences of A036554 (numbers whose binary representation ends in an odd number of zeros).
  • A194689 (program): a(n) = Sum_{k=0..n} binomial(n,k)*w(k)*w(n-k) where w() = A000296().
  • A194698 (program): a(n) = floor((n - 1)/12) - floor((n^2 - 1)/(24*n)).
  • A194699 (program): a(n) = floor((p - 1)/12) - floor((p^2 - 1)/(24*p)), where p = prime(n).
  • A194702 (program): Triangle read by rows: T(k,m) = number of occurrences of k in the last section of the set of partitions of (2 + m).
  • A194713 (program): 13 times hexagonal numbers: 13*n*(2*n-1).
  • A194715 (program): 15 times triangular numbers.
  • A194716 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting four doublets into the initially empty word.
  • A194717 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting five doublets into the initially empty word.
  • A194718 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting six doublets into the initially empty word.
  • A194719 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting seven doublets into the initially empty word.
  • A194720 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting eight doublets into the initially empty word.
  • A194721 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting nine doublets into the initially empty word.
  • A194722 (program): Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting ten doublets into the initially empty word.
  • A194723 (program): Number of ternary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194724 (program): Number of quaternary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194725 (program): Number of 5-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194726 (program): Number of 6-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194727 (program): Number of 7-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194728 (program): Number of 8-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194729 (program): Number of 9-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194730 (program): Number of 10-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
  • A194731 (program): Digital roots of the nonzero octagonal numbers.
  • A194732 (program): Units’ digits of the nonzero octagonal numbers.
  • A194733 (program): Number of k < n such that {k*r} > {n*r}, where { } = fractional part, r = (1+sqrt(5))/2 (the golden ratio).
  • A194734 (program): Number of k such that {-k*r} > {-n*r}, where { } = fractional part, r = (1+sqrt(5))/2 (the golden ratio).
  • A194735 (program): Number of positive integers k <= n such that {k*sqrt(2)} > {n*sqrt(2)}, where { } = fractional part.
  • A194736 (program): Number of k such that {-k*sqrt(2)} < {-n*sqrt(2)}, where { } = fractional part.
  • A194737 (program): Number of k such that {-k*sqrt(2)} > {-n*sqrt(2)}, where { } = fractional part.
  • A194738 (program): Number of k such that {k*sqrt(3)} < {n*sqrt(3)}, where { } = fractional part.
  • A194739 (program): Number of k such that {k*sqrt(3)} > {n*sqrt(3)}, where { } = fractional part.
  • A194740 (program): Number of k such that {-k*sqrt(3)} < {-n*sqrt(3)}, where { } = fractional part.
  • A194741 (program): Number of k such that {-k*sqrt(3)} > {-n*sqrt(3)}, where { } = fractional part.
  • A194742 (program): Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part.
  • A194743 (program): Number of k such that {k*sqrt(5)} > {n*sqrt(5)}, where { } = fractional part.
  • A194744 (program): Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part.
  • A194745 (program): Number of k such that {-k*sqrt(5)} > {-n*sqrt(5)}, where { } = fractional part.
  • A194746 (program): Number of k such that {k*sqrt(6)} < {n*sqrt(6)}, where { } = fractional part.
  • A194747 (program): Number of k such that {k*sqrt(6)} > {n*sqrt(6)}, where { } = fractional part.
  • A194748 (program): Number of k such that {-k*sqrt(6)} < {-n*sqrt(6)}, where { } = fractional part.
  • A194749 (program): Number of k such that {-k*sqrt(6)} > {-n*sqrt(6)}, where { } = fractional part.
  • A194750 (program): Number of k such that {k*e} < {n*e}, where { } = fractional part.
  • A194751 (program): Number of k such that {k*e} > {n*e}, where { } = fractional part.
  • A194752 (program): Number of k such that {-k*e} < {-n*e}, where { } = fractional part.
  • A194753 (program): Number of k such that {-k*e} > {-n*e}, where { } = fractional part.
  • A194754 (program): Number of integers k in 1..n such that {k*Pi} < {n*Pi}, where { } = fractional part.
  • A194755 (program): Number of integers k in 1..n such that {k*Pi} > {n*Pi}, where { } = fractional part.
  • A194756 (program): Number of k such that {-k*Pi} < {-n*Pi}, where { } = fractional part.
  • A194757 (program): Number of k such that {-k*Pi} > {-n*Pi}, where { } = fractional part.
  • A194767 (program): Denominator of the fourth increasing diagonal of the autosequence of second kind from (-1)^n / (n+1).
  • A194770 (program): E.g.f. 2*sqrt(3)/3*arctan(sqrt(3)*x/(x+2)).
  • A194772 (program): Number of lower triangles of an (n+2) X (n+2) 0..2 array with new values introduced in row major order 0..2 and no element unequal to more than one horizontal or vertical neighbor.
  • A194799 (program): Triangle read by rows: T(n,k) = number of partitions of n that are formed by k sections, k >= 1.
  • A194805 (program): Number of parts that are visible in one of the three views of the section model of partitions version “tree” with n sections.
  • A194807 (program): Decimal expansion of 1/(e-2).
  • A194808 (program): Twin primes modulo 5.
  • A194811 (program): Number of grid points that are covered after n-th stage of A139250 version “Tree”, starting with a(0) = 1 and assuming the toothpicks have length 4, 3, and 2.
  • A194813 (program): Number of integers k in [1,n] such that {n*r + k*r} < {n*r - k*r}, where { } = fractional part and r = (1+sqrt(5))/2 (the golden ratio).
  • A194814 (program): Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=(1+sqrt(5))/2 (the golden ratio).
  • A194815 (program): Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(2).
  • A194816 (program): Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(2).
  • A194817 (program): Number of integers k in [1,n] such that {n*r+k*r} < {n*r-k*r}, where { } = fractional part and r=sqrt(3).
  • A194818 (program): Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=sqrt(3).
  • A194825 (program): Digital roots of the nonzero 9-gonal (nonagonal) numbers.
  • A194826 (program): Units’ digits of the nonzero 9-gonal (nonagonal) numbers.
  • A194827 (program): 2-adic valuation of the number of n X n Alternating Sign Matrices (A005130(n)).
  • A194847 (program): Write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives i values.
  • A194848 (program): Write n = C(i,3)+C(j,2)+C(k,1) with i>j>k>=0; sequence gives j values.
  • A194880 (program): The numerators of the inverse Akiyama-Tanigawa algorithm from A001045(n).
  • A194881 (program): A number of sum-free sets related to fractional parts of multiples of a rational number in the range 1/3 to 2/3.
  • A194882 (program): Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; sequence gives i values.
  • A194883 (program): Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; sequence gives j values.
  • A194884 (program): Write n = C(i,4)+C(j,3)+C(k,2)+C(l,1) with i>j>k>l>=0; sequence gives k values.
  • A194886 (program): Units’ digits of the nonzero decagonal numbers.
  • A194887 (program): Numbers that are the sum of two powers of 12.
  • A194894 (program): The number of the ordered triples (A,B,C) satisfying the system of the modular relations {A*B - B*A = C, B*C - C*B = A, C*A - A*C = B}, where A,B,C are distinct 2 X 2 matrices over Z(n).
  • A194899 (program): Triangular array (and fractal sequence): row n is the permutation of (1,2,…,n) obtained from the increasing ordering of fractional parts {r}, {2r}, …, {nr}, where r=sqrt(12).
  • A194900 (program): Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194899; an interspersion.
  • A194901 (program): Inverse permutation of A194900; every positive integer occurs exactly once.
  • A194902 (program): Triangular array (and fractal sequence): row n is the permutation of (1,2,…,n) obtained from the increasing ordering of fractional parts {r}, {2r}, …, {nr}, where r=-sqrt(12).
  • A194903 (program): Rectangular array, by antidiagonals: row n gives the positions of n in the fractal sequence A194902; an interspersion.
  • A194904 (program): Inverse permutation of A194903; every positive integer occurs exactly once.
  • A194914 (program): Fractalization of (1+[n/sqrt(8)]), where [ ]=floor.
  • A194916 (program): Inverse permutation of A194915; every positive integer occurs exactly once.
  • A194920 (program): a(n) = n - floor(n/sqrt(2)).
  • A194924 (program): The number of set partitions of {1,2,…,n} into exactly two subsets A,B such that the greatest common divisor of |A| and |B| = 1.
  • A194932 (program): Number of lower triangles of a 3 X 3 0..n array with no element differing from any of its horizontal or vertical neighbors by more than one.
  • A194939 (program): Table T read by rows, where T(n, k) is the sum of the largest k primes up to and including prime(n), for 1 <= k <= n.
  • A194959 (program): Fractalization of (1 + floor(n/2)).
  • A194960 (program): a(n) = floor((n+2)/3) + ((n-1) mod 3).
  • A194964 (program): a(n) = 1 + floor(n/sqrt(5)).
  • A194979 (program): a(n) = 1 + floor(n/sqrt(3)).
  • A194986 (program): a(n) = 1 + floor(n/sqrt(6)).
  • A194990 (program): a(n) = 1+ floor(n/sqrt(8)).
  • A194991 (program): Primes whose squares are odious.
  • A194992 (program): Number of lower triangles of an n X n 0..2 array with each element differing from all of its horizontal and vertical neighbors by one.
  • A194999 (program): Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its horizontal and vertical neighbors by one.
  • A195009 (program): Triangle read by rows, T(n,k) = k^n*A056040(n), n>=0, 0<=k<=n.
  • A195010 (program): a(n) = (1/n) * [x^n] 1/(1 - n^2*x)^(1/n), where [x^n] F(x) denotes the coefficient of x^n in F(x).
  • A195013 (program): Multiples of 2 and of 3 interleaved: a(2n-1) = 2n, a(2n) = 3n.
  • A195014 (program): Vertex number of a square spiral whose edges have length A195013.
  • A195015 (program): Main axis of the square spiral whose edges have length A195013 and whose vertices are the numbers A195014.
  • A195016 (program): (n*(5*n+7)-(-1)^n+1)/2.
  • A195017 (program): If n = Product_{k >= 1} (p_k)^(c_k) where p_k is k-th prime and c_k >= 0 then a(n) = Sum_{k >= 1} c_k*((-1)^(k-1)).
  • A195018 (program): a(n) = n*(10*n-3).
  • A195019 (program): Multiples of 3 and of 4 interleaved: a(2*n-1) = 3*n, a(2*n) = 4*n.
  • A195020 (program): Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [3, 4, 5]. The edges of the spiral have length A195019.
  • A195021 (program): a(n) = n*(14*n - 11).
  • A195023 (program): a(n) = 14*n^2 - 4*n.
  • A195024 (program): a(n) = n*(14*n - 1).
  • A195025 (program): a(n) = n*(14*n + 3).
  • A195026 (program): a(n) = 7*n*(2*n + 1).
  • A195027 (program): a(n) = 2*n*(7*n + 5).
  • A195028 (program): a(n) = n*(14*n + 13).
  • A195029 (program): a(n) = n*(14*n + 13) + 3.
  • A195030 (program): a(n) = (n-2)*(14*n-39) for n > 2, otherwise a(n) = n.
  • A195031 (program): Multiples of 5 and of 12 interleaved: a(2n-1) = 5n, a(2n) = 12n.
  • A195032 (program): Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [5, 12, 13]. The edges of the spiral have length A195031.
  • A195033 (program): Multiples of 21 and of 20 interleaved: a(2n-1) = 21n, a(2n) = 20n.
  • A195034 (program): Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [21, 20, 29]. The edges of the spiral have length A195033.
  • A195035 (program): Multiples of 15 and of 8 interleaved: a(2n-1) = 15n, a(2n) = 8n.
  • A195036 (program): Vertex number of a square spiral in which the length of the first two edges are the legs of the primitive Pythagorean triple [15, 8, 17]. The edges of the spiral have length A195035.
  • A195037 (program): 17 times triangular numbers.
  • A195038 (program): 41 times triangular numbers.
  • A195039 (program): 23 times triangular numbers.
  • A195041 (program): Concentric heptagonal numbers.
  • A195042 (program): Concentric 9-gonal numbers.
  • A195043 (program): Concentric 11-gonal numbers.
  • A195045 (program): Concentric 13-gonal numbers.
  • A195046 (program): Concentric 15-gonal numbers.
  • A195047 (program): Concentric 17-gonal numbers.
  • A195048 (program): Concentric 19-gonal numbers.
  • A195049 (program): Concentric 21-gonal numbers.
  • A195050 (program): Square array T(n,k) read by antidiagonals in which column k lists the number of divisors of n that are divisible by k.
  • A195051 (program): Number of divisors of 24*n - 1.
  • A195052 (program): Number of divisors of 24*n - 1 divided by 2.
  • A195053 (program): Parity of the spt function, A092269.
  • A195055 (program): Decimal expansion of Pi^2/3.
  • A195056 (program): Decimal expansion of Pi^2/7.
  • A195057 (program): Decimal expansion of Pi^2/11.
  • A195058 (program): Concentric 23-gonal numbers.
  • A195059 (program): Decimal expansion of Pi^2/13.
  • A195062 (program): Period 7: repeat [1, 0, 1, 0, 1, 0, 1].
  • A195067 (program): G.f. satisfies: A(x) = Sum{n>=0} x^n * A(2*n*x).
  • A195072 (program): a(n) = n - floor(n/sqrt(3)).
  • A195076 (program): Fractalization of (1+[n/3]), where [ ]=floor.
  • A195078 (program): Inverse permutation of A195077; every positive integer occurs exactly once.
  • A195082 (program): Fractalization of (1+[2n/3]), where [ ] = floor.
  • A195084 (program): a(2n-1) = 2-n, a(2n) = 2+n.
  • A195085 (program): Positive integers n for which there exist exactly two integers k in {1,2,3,…,n-1} such that k*n is square.
  • A195086 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 2.
  • A195087 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 3.
  • A195088 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 4.
  • A195089 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 5.
  • A195090 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 6.
  • A195091 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 7.
  • A195092 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 8.
  • A195093 (program): Numbers k such that (number of prime factors of k counted with multiplicity) less (number of distinct prime factors of k) = 9.
  • A195094 (program): G.f.: Sum_{n>=1} -moebius(2*n)*x^n/(1-x^n)^3.
  • A195095 (program): G.f.: Sum_{n>=1} -moebius(2*n)*x^n/(1 - 2*x^n).
  • A195096 (program): Inverse permutation of A195083; every positive integer occurs exactly once.
  • A195116 (program): a(n) = (2+3^n)*(3+2^n).
  • A195117 (program): Primes of the form 2*n^3 + 4*n^2 + 4*n + 1.
  • A195119 (program): a(n) = 2*n - floor(n*sqrt(2)).
  • A195120 (program): a(n) = 2*n - floor(n*sqrt(3)).
  • A195121 (program): a(n) = 2*n - floor(n/r), where r = (1 + sqrt(5))/2 (the golden ratio).
  • A195122 (program): a(n) = 2*n - floor(n*r/2), where r=(1+sqrt(5))/2.
  • A195123 (program): a(n) = 2*n - floor(n*r/3), where r = (1 + sqrt(5))/2.
  • A195124 (program): 2n-floor(n*e/2).
  • A195125 (program): a(n) = 2*n - floor(n*r), where r=Pi-3.
  • A195126 (program): a(n) = 2*n - floor(n*r/4), where r = (1 + sqrt(5))/2.
  • A195127 (program): a(n) = 2*n - floor(n*r/5), where r = (1 + sqrt(5))/2.
  • A195128 (program): a(n) = 2*n - floor(n*sqrt(1/2)).
  • A195129 (program): a(n) = 2*n - floor(n*sqrt(1/3)).
  • A195131 (program): Numbers k such that 666k-1 is prime.
  • A195140 (program): Multiples of 5 and odd numbers interleaved.
  • A195142 (program): Concentric 10-gonal numbers.
  • A195143 (program): a(n) = n-th concentric 12-gonal number.
  • A195145 (program): Concentric 14-gonal numbers.
  • A195146 (program): Concentric 16-gonal numbers.
  • A195147 (program): Concentric 18-gonal numbers.
  • A195148 (program): Concentric 20-gonal numbers.
  • A195149 (program): Concentric 22-gonal numbers.
  • A195150 (program): Number of divisors d of n such that d-1 does not divide n.
  • A195151 (program): Square array read by antidiagonals upwards: T(n,k) = n*((k-2)*(-1)^n+k+2)/4, n >= 0, k >= 0.
  • A195155 (program): Number of divisors d of n such that d-1 also divides n or d-1 = 0.
  • A195156 (program): a(n) = (16^n-1)/3.
  • A195158 (program): Concentric 24-gonal numbers.
  • A195159 (program): Multiples of 7 and odd numbers interleaved.
  • A195160 (program): Generalized 11-gonal (or hendecagonal) numbers: m*(9*m - 7)/2 with m = 0, 1, -1, 2, -2, 3, -3, …
  • A195161 (program): Multiples of 8 and odd numbers interleaved.
  • A195162 (program): Generalized 12-gonal numbers: k*(5*k-4) for k = 0, +-1, +-2, …
  • A195163 (program): 1000-gonal numbers: a(n) = n*(499*n - 498).
  • A195167 (program): a(n) = 3*n - floor(n*r/2), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195168 (program): a(n) = 3*n - floor(n*r/3), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195169 (program): a(n) = 3*n - floor(2*n*r/3), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195170 (program): a(n) = 4*n - floor(n*r), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195171 (program): a(n) = 5*n - floor(n*r), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195172 (program): a(n) = 4*n - floor(2*n*r), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195173 (program): a(n) = 5*n - floor(2n*r), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195174 (program): a(n) = 5*n - floor(3*n*r), where r=(1+sqrt(5))/2 (the golden ratio.)
  • A195175 (program): a(n) = 8*n - floor(4*n*r), where r=(1+sqrt(5))/2 (the golden ratio.)
  • A195176 (program): a(n) = 3*n - floor(n*sqrt(2)).
  • A195177 (program): a(n) = 3*n - floor(2*n*sqrt(2)).
  • A195178 (program): a(n) = 4*n - floor(2*n*sqrt(2)).
  • A195179 (program): a(n) = 5*n - floor(2*n*sqrt(2)).
  • A195180 (program): a(n) = 5*n - floor(3*n*sqrt(2)).
  • A195181 (program): a(n) = 6*n - floor(3*n*sqrt(3)).
  • A195182 (program): a(n) = 6*n - floor(2*n*e).
  • A195198 (program): Characteristic function of squares or three times squares.
  • A195212 (program): Numbers n for which the exponent of the largest prime factor of n is even.
  • A195233 (program): Number of lower triangles of a 3 X 3 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.
  • A195234 (program): Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.
  • A195241 (program): Expansion of (1-x+19*x^3-3*x^4)/(1-x)^3.
  • A195242 (program): Expansion of Sum_{n>=0} n^n*x^n/(1 - n*x)^n.
  • A195254 (program): O.g.f.: Sum_{n>=0} 2*(n+2)^(n-1)*x^n/(1+n*x)^n.
  • A195255 (program): O.g.f.: Sum_{n>=0} 3*(n+3)^(n-1)*x^n/(1+n*x)^n.
  • A195256 (program): O.g.f.: Sum_{n>=0} 4*(n+4)^(n-1)*x^n/(1+n*x)^n.
  • A195257 (program): O.g.f.: Sum_{n>=0} 5*(n+5)^(n-1)*x^n/(1+n*x)^n.
  • A195279 (program): Number of lower triangles of a 3 X 3 integer array with each element differing from all of its vertical and horizontal neighbors by n or less and triangles differing by a constant counted only once.
  • A195284 (program): Decimal expansion of shortest length of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(3,4,5); i.e., decimal expansion of 2*sqrt(10)/3.
  • A195286 (program): Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(5,12,13).
  • A195288 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(5,12,13).
  • A195290 (program): Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(7,24,25).
  • A195291 (program): Years in the Gregorian calendar which are not (proleptic) leap years.
  • A195293 (program): Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(8,15,17).
  • A195298 (program): Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(28,45,53).
  • A195299 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(28,45,53).
  • A195309 (program): Row sums of an irregular triangle read by rows in which row n lists the next A026741(n+1) natural numbers A000027.
  • A195311 (program): Row sums of A195310.
  • A195312 (program): Multiples of 9 and odd numbers interleaved.
  • A195313 (program): Generalized 13-gonal numbers: m*(11*m-9)/2 with m = 0, 1, -1, 2, -2, 3, -3, …
  • A195314 (program): Centered 28-gonal numbers.
  • A195315 (program): Centered 32-gonal numbers.
  • A195316 (program): Centered 36-gonal numbers.
  • A195317 (program): Centered 40-gonal numbers.
  • A195318 (program): Centered 44-gonal numbers.
  • A195319 (program): Three times second hexagonal numbers: 3*n*(2*n+1).
  • A195320 (program): 7 times hexagonal numbers: 7*n*(2*n-1).
  • A195321 (program): a(n) = 18*n^2.
  • A195322 (program): a(n) = 20*n^2.
  • A195323 (program): a(n) = 22*n^2.
  • A195326 (program): Numerators of fractions leading to e - 1/e (A174548).
  • A195338 (program): a(n) = A091137(n) / A016116(n).
  • A195339 (program): Expansion of 1/(1-4*x+2*x^3+x^4).
  • A195341 (program): Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(1,2,sqrt(5)).
  • A195342 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(1,2,sqrt(5)).
  • A195346 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(1,3,sqrt(10)).
  • A195350 (program): Expansion of (1 - 3*x - x^2)/(1 - 4*x + 2*x^3 + x^4).
  • A195352 (program): Smallest prime p such that 2*n+1 = 2*p + q for some odd prime q.
  • A195364 (program): Number of partitions of n plus number of divisors of n.
  • A195367 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(2),sqrt(3),sqrt(5)).
  • A195371 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(2),sqrt(3)).
  • A195384 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(2,sqrt(5),3).
  • A195397 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(sqrt(3),sqrt(5),sqrt(8)).
  • A195400 (program): Decimal expansion of shortest length, (B), of segment from side BC through incenter to side BA in right triangle ABC with sidelengths (a,b,c)=(sqrt(7),3,4).
  • A195403 (program): Decimal expansion of shortest length, (A), of segment from side AB through incenter to side AC in right triangle ABC with sidelengths (a,b,c)=(1,sqrt(r),r), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195409 (program): Decimal expansion of shortest length, (C), of segment from side CA through incenter to side CB in right triangle ABC with sidelengths (a,b,c)=(r-1,r,sqrt(3)), where r=(1+sqrt(5))/2 (the golden ratio).
  • A195422 (program): Permanents of certain n X 2 cyclic (1,-1) matrices.
  • A195437 (program): Triangle formed by: 1 even, 2 odd, 3 even, 4 odd… starting with 2.
  • A195458 (program): a(n) = floor(sqrt(n) * a(n-1)), starting with 1.
  • A195459 (program): a(n) = phi(3*n)/2.
  • A195460 (program): 2^(2*n+1) - 3*2^n - 1.
  • A195462 (program): 1!*2!*3!*…*n!*H(n); H(n) the n-th harmonic number.
  • A195463 (program): a(n) = 4^(n+1) + 7.
  • A195464 (program): a(n) = 2^(4*n + 3) + 2*4^n + 3.
  • A195470 (program): Number of numbers k with 0 <= k < n such that 2^k + 1 is multiple of n.
  • A195499 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(3).
  • A195503 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to sqrt(3).
  • A195507 (program): Smallest integer m greater than n such that m (mod k) == n (mod k) for k = 1..n-1.
  • A195508 (program): Number of iterations in a Draim factorization of 2n+1.
  • A195509 (program): E.g.f.: (exp(x*exp(x)) + exp(x/exp(x)))/2.
  • A195527 (program): Integers n that are k-gonal for precisely 3 distinct values of k, where k >= 3.
  • A195528 (program): Integers n that are k-gonal for precisely 4 distinct values of k, where k >= 3.
  • A195531 (program): Hypotenuses of Pythagorean triples in A195499 and A195503.
  • A195538 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to sqrt(8).
  • A195539 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to sqrt(8).
  • A195540 (program): Hypotenuses of primitive Pythagorean triples in A195538 and A195539.
  • A195547 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 1/2.
  • A195548 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to 1/2.
  • A195549 (program): Hypotenuses of primitive Pythagorean triples in A195547 and A195548.
  • A195550 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3/2.
  • A195552 (program): Hypotenuses of primitive Pythagorean triples in A195550 and A195551.
  • A195553 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5/2.
  • A195555 (program): Hypotenuses of primitive Pythagorean triples in A195553 and A195554.
  • A195558 (program): Hypotenuses of primitive Pythagorean triples in A195556 and A195557.
  • A195573 (program): Hypotenuses of primitive Pythagorean triples in A195571 and A195572.
  • A195584 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2*n^2)-sigma(n^2)) * x^n/n ).
  • A195585 (program): sigma(2*n^2) - sigma(n^2).
  • A195586 (program): G.f.: exp( Sum_{n>=1} A163659(n^2)*x^n/n ), where x*exp(Sum_{n>=1} A163659(n)*x^n/n) = S(x) is the g.f. of Stern’s diatomic series (A002487).
  • A195587 (program): a(n) = A163659(n^2), where A163659 is the logarithmic derivative of Stern’s diatomic series (A002487).
  • A195589 (program): G.f.: x/exp( Sum_{n>=1} a(n)*x^n/n ) = Sum_{n>=1} moebius(n)*x^n.
  • A195590 (program): Number of ways to place 2n nonattacking kings on a vertical cylinder 4 X 2n.
  • A195591 (program): Number of ways to place 3n nonattacking kings on a vertical cylinder 6 X 2n.
  • A195603 (program): Numerator of floor(Pi*10^n)/10^n.
  • A195604 (program): Numerator of floor(e*10^n)/10^n, where e = exp(1) = A001113.
  • A195605 (program): a(n) = (4*n*(n+2)+(-1)^n+1)/2 + 1.
  • A195607 (program): Numerator of floor(Phi*10^n)/10^n, where phi = (sqrt(5) + 1)/2 = A001622 is the Golden Ratio.
  • A195608 (program): Numbers n such that Sum_{i=1..n} A(i) = A(n)*A(n+1)/4, where A(n) = A001969(n).
  • A195609 (program): Numbers n such that Sum_{i=1..n} A(i) = A(n)*A(n+1)/4, where A(n) = A000069(n).
  • A195613 (program): Numbers n with property that n, 2n-1 and 2n+1 are composite.
  • A195614 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 2.
  • A195615 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to 2.
  • A195616 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3.
  • A195617 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to 3.
  • A195619 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 4.
  • A195620 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to 4.
  • A195621 (program): Decimal expansion of arccsc(4).
  • A195622 (program): Denominators a(n) of Pythagorean approximations b(n)/a(n) to 5.
  • A195623 (program): Numerators b(n) of Pythagorean approximations b(n)/a(n) to 5.
  • A195629 (program): Sequence with chaotic first differences: a(1)=2; a(n)=prime((prime(n) mod 10)+pi(a(n-1))).
  • A195679 (program): Order of n-th homotopy group of the topological group O(oo), with -1 if the homotopy group is Z.
  • A195686 (program): a(n) = C(2*n,n) / gcd(n,C(2*n,n)).
  • A195692 (program): Decimal expansion of arccos(1/phi), where phi = (1+sqrt(5))/2 (the golden ratio).
  • A195693 (program): Decimal expansion of arctan(1/phi), where phi = (1+sqrt(5))/2 (the golden ratio).
  • A195727 (program): Decimal expansion of arccot(4).
  • A195734 (program): G.f.: exp( Sum_{n>=1} (2*sigma(n^2) - sigma(n)^2) * x^n/n ).
  • A195735 (program): 2*sigma(n^2) - sigma(n)^2.
  • A195744 (program): a(n) = 15*2^(n+1) + 1.
  • A195758 (program): Lesser prime factor of n-th Blum number.
  • A195759 (program): Greater prime factor of n-th Blum number.
  • A195772 (program): Decimal expansion of arccsc(5).
  • A195774 (program): Decimal expansion of arccot(6).
  • A195776 (program): Decimal expansion of arccsc(6).
  • A195782 (program): Decimal expansion of arccot(8).
  • A195784 (program): Decimal expansion of arccsc(8).
  • A195786 (program): Decimal expansion of arccot(9).
  • A195788 (program): Decimal expansion of arccsc(9).
  • A195790 (program): Decimal expansion of arccot(10).
  • A195792 (program): Decimal expansion of arccsc(10).
  • A195817 (program): Multiples of 10 and odd numbers interleaved.
  • A195818 (program): Generalized 14-gonal numbers: m*(6*m-5), m = 0,+1,-1,+2,-2,+3,-3,…
  • A195819 (program): Multiples of 29.
  • A195824 (program): a(n) = 24*n^2.
  • A195848 (program): Expansion of 1 / f(-x^1, -x^5) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A195850 (program): Column 6 of array A195825. Also column 1 of triangle A195840. Also 1 together with the row sums of triangle A195840.
  • A195852 (program): Column 8 of array A195825. Also column 1 of triangle A195842. Also 1 together with the row sums of triangle A195842.
  • A195855 (program): a(n) = T(9,n), array T given by A048505.
  • A195856 (program): a(n) = T(10,n), array T given by A048505.
  • A195857 (program): a(n) = T(9, n), array T given by A047858.
  • A195858 (program): a(n) = T(10, n), array T given by A047858.
  • A195859 (program): n^8-n
  • A195861 (program): Expansion of (psi(x) / phi(x))^5 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A195878 (program): y-values in the solution to 7*x^2-6 = y^2.
  • A195896 (program): Numbers of the form 2*p-1 or 3*p-1 where p is 1 or a prime.
  • A195904 (program): Base-2 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,0,0,0,0.
  • A195905 (program): Primes of the form 10 * n^2 + 7.
  • A195908 (program): Powers of 7 which have no zero in their decimal expansion.
  • A195913 (program): The denominator in a fraction expansion of log(2)-Pi/8.
  • A195917 (program): Numbers k such that both k+1 and 7k+1 are squares.
  • A195938 (program): a(n) = n/2 if n mod 4 = 2, 0 otherwise.
  • A195946 (program): Powers of 11 which have no zero in their decimal expansion.
  • A195948 (program): Powers of 5 which have no zero in their decimal expansion.
  • A195956 (program): Number of n X 2 0..4 arrays with each element equal to the number its horizontal and vertical neighbors unequal to itself.
  • A195971 (program): Number of n X 1 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4.
  • A195986 (program): Exponent of the largest power of 2 that divides 5^n - 3^n.
  • A195989 (program): Quotient of denominators of (BernoulliB(2n)/n) and BernoulliB(2n).
  • A195993 (program): Numbers n such that 90n + 73 is prime.
  • A196000 (program): Numbers k such that 90*k + 19 is prime.
  • A196007 (program): Numbers n such that 90n + 83 is prime.
  • A196024 (program): Odious Fibonacci numbers.
  • A196032 (program): Numbers having at least one zero in base 4 representation.
  • A196047 (program): Path length of the rooted tree with Matula-Goebel number n.
  • A196050 (program): Number of edges in the rooted tree with Matula-Goebel number n.
  • A196052 (program): Sum of the degrees of the nodes at level 1 in the rooted tree with Matula-Goebel number n.
  • A196068 (program): Visitation length of the rooted tree with Matula-Goebel number n.
  • A196072 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,2,1,4 for x=0,1,2,3,4.
  • A196080 (program): Numerators of the sum of the n-th partial sums of the expansions of e and 1/e.
  • A196081 (program): Dungeons and Dragons Ability Modifier Sequence.
  • A196082 (program): Greatest residue of x^n (mod n), x=0..n-1.
  • A196096 (program): Occurrences of ‘11’ in base 3 expansion of n.
  • A196126 (program): Let A = {(x,y): x, y positive natural numbers and y <= x <= y^2}. a(n) is the cardinality of the subset {(x,y) in A such that x <= n}.
  • A196127 (program): Union of p-1, 2p-1 and 3p-1 where p is a prime (without repetition).
  • A196140 (program): Number of nX2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4
  • A196147 (program): Bits obtained using Pi and e’s digits after the decimal: if, the corresponding digits’ parities (cf. even vs. odd) are the same, output is 0; otherwise, output is 1.
  • A196153 (program): Primes of the form 2*n^3 + 5*n^2 + 3*n + 1.
  • A196168 (program): In binary representation of n: replace each 0 with 1, and each 1 with 10.
  • A196196 (program): G.f.: A(x) = Sum_{n>=0} x^n*(A(n*x) + A(-n*x))/2.
  • A196199 (program): Count up from -n to n for n = 0, 1, 2, … .
  • A196202 (program): a(n) = 2^(prime(n)-1) mod prime(n)^2.
  • A196204 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,3,4,1 for x=0,1,2,3,4.
  • A196221 (program): Binomial(n+10, 10)*9^n
  • A196226 (program): m such that A054024(m) (sum of divisors of m reduced modulo m) is 3 + m/2.
  • A196227 (program): Number of 2 X 2 integer matrices with elements from {1,…,n} whose determinant is 1.
  • A196258 (program): a(n) = 11^n*n!.
  • A196265 (program): Number of standard puzzles of shape 2 X n with support CK (see reference for precise definition).
  • A196274 (program): Half of the gaps A067970 between odd nonprimes A014076.
  • A196276 (program): Numbers m such that A196274(m) = 1.
  • A196277 (program): Numbers m such that A196274(m) > 1.
  • A196279 (program): Let r= (7n) mod 10 and x=floor(7n/10) be the last digit and leading part of 7n. Then a(n) = (x-2r)/7.
  • A196280 (program): Binomial(n+9, 9)*8^n
  • A196288 (program): n^8 + n.
  • A196289 (program): n^9 - n.
  • A196290 (program): n^9 + n.
  • A196291 (program): n^10 - n.
  • A196292 (program): n^10+n
  • A196305 (program): a(n) = 15*2^n - 1.
  • A196316 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,0,2,4 for x=0,1,2,3,4.
  • A196347 (program): Triangle T(n, k) read by rows, T(n, k) = n!*binomial(n, k).
  • A196361 (program): Decimal expansion of the absolute minimum of cos(t) + cos(2t) + cos(3t).
  • A196375 (program): a(1)=2; a(n)=smallest prime greater than the half-sum of all previous terms.
  • A196382 (program): Number of sequences of n coin flips, that win on the last flip, if the sequence of flips ends with (1,1,0) or (1,0,1).
  • A196389 (program): Triangle T(n,k), read by rows, given by (0,1,-1,0,0,0,0,0,0,0,…) DELTA (1,0,0,1,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A196390 (program): Positive integers a for which there is a (-6)-Pythagorean triple (a,b,c) satisfying a<=b.
  • A196410 (program): a(n) = n*2^(n-5).
  • A196411 (program): n! - n^4
  • A196412 (program): n! - n^5.
  • A196413 (program): n! - n^6.
  • A196414 (program): n! - n^7.
  • A196421 (program): a(n) = prime(n)*T(n), where T = A000217.
  • A196423 (program): Number of n X 1 0..4 arrays with each element equal to the number its horizontal and vertical neighbors less than itself.
  • A196437 (program): a(n) = the number of numbers k <= n such that GCQ_A(n, k) = LCQ_A(n, k) = 0 (see definition in comments).
  • A196438 (program): a(n) is the number of integers k <= n such that GCQ_A(n, k) >= 2 (see definition in comments).
  • A196445 (program): Numbers k >= 2 such that A055035(k) is an odd integer.
  • A196460 (program): E.g.f.: A(x) = Sum_{n>=0} (1+2^n)^n * exp((1+2^n)*x) * x^n/n!.
  • A196468 (program): a(1)=11; a(n) = floor((2 + sqrt(8))*a(n-1)) for n > 1.
  • A196472 (program): a(1)=1; a(n) = floor((3 + sqrt(21))*a(n-1)/2) for n > 1.
  • A196499 (program): Numbers k such that the greatest residue of the congruence x^k (mod k) equals k-1 for x in [0..k-1].
  • A196506 (program): a(n) = 1*3*5 + 3*5*7 + 5*7*9 + … (n terms).
  • A196507 (program): a(n) = n*(3*n^2 + 6*n + 1).
  • A196508 (program): a(n) = 2^n*(n^2 - n + 4)-4.
  • A196512 (program): Expansion of (1-9x)/(1-28x).
  • A196513 (program): a(n) = 1*4*7 + 4*7*10 + 7*10*13 + … (n terms).
  • A196514 (program): Partial sums of A100381.
  • A196524 (program): a(n) = phi(n)*tau(n^2).
  • A196525 (program): Decimal expansion of log(1+sqrt(2))/sqrt(2).
  • A196529 (program): Half of greatest common divisor of products of first n prime numbers and first n composite numbers.
  • A196530 (program): Decimal expansion of log(2+sqrt(3))/sqrt(3).
  • A196532 (program): a(n) = (n+1)!*(H(n)+H(n+1)), where H(n) = Sum_{k=1..n} 1/k is the n-th harmonic number.
  • A196533 (program): Decimal expansion of 15*e.
  • A196537 (program): Number of nX1 0..4 arrays with each element equal to the number its horizontal and vertical neighbors less than or equal to itself
  • A196554 (program): Decimal expansion of Sum_{i>=0} 1/((8*i+1)*(8*i+5)).
  • A196563 (program): Number of even digits in decimal representation of n.
  • A196564 (program): Number of odd digits in decimal representation of n.
  • A196592 (program): Maximum number of floors with n elevators and 3 stops.
  • A196593 (program): Number of fixed tree-like convex polyominoes.
  • A196594 (program): Maximum number of floors with 4 elevators and s stops.
  • A196630 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4.
  • A196655 (program): 33*2^(n+1) + 7.
  • A196657 (program): 63*2^(n+1) + 1.
  • A196660 (program): Smallest k>0 such that k*n+(n-1) is prime.
  • A196661 (program): Expansion of (1-2x)/(1-7x).
  • A196662 (program): Expansion of (1-3x)/(1-10x).
  • A196663 (program): Expansion of (1-4x)/(1-13x).
  • A196664 (program): Expansion of (1-5x)/(1-16x).
  • A196665 (program): Expansion of (1-6x)/(1-19x).
  • A196666 (program): Expansion of (1-7x)/(1-22x).
  • A196676 (program): Expansion of (1-8x)/(1-25x).
  • A196678 (program): a(n) = 5*binomial(4*n+5,n)/(4*n+5).
  • A196686 (program): Number of odd digits of Pi minus number of even digits.
  • A196690 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,1,3,0,4 for x=0,1,2,3,4.
  • A196700 (program): Number of n X 1 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,0,4,2 for x=0,1,2,3,4.
  • A196731 (program): Expansion of (1-x)/(1-12*x).
  • A196738 (program): n! - n^8
  • A196739 (program): n! - n^10
  • A196747 (program): Numbers n such that 3 does not divide swing(n) = A056040(n).
  • A196751 (program): Decimal expansion of 8*Pi^4/729.
  • A196787 (program): a(n) = 3*a(n-1) - 2*a(n-2) - a(n-4) + a(n-5) with initial terms 1, 1, 1, 3, 6.
  • A196789 (program): Binomial coefficients C(2*n+10,10).
  • A196790 (program): Binomial coefficients C(2*n-9,10).
  • A196791 (program): T(9, n), array T given by A047848.
  • A196792 (program): a(n)=T(10,n), array T given by A047848.
  • A196793 (program): a(n) = T(n,n), array T given by A047848.
  • A196794 (program): a(n) = Sum_{k=0..n} binomial(n,k)*2^k*(k+1)^(n-k).
  • A196795 (program): a(n) = Sum_{k=0..n} binomial(n,k)*3^k*(k+1)^(n-k).
  • A196834 (program): Row sums of Sheffer triangle A193685 (5-restricted Stirling2 numbers).
  • A196835 (program): Alternating row sums of Sheffer triangle A193685 (5-restricted Stirling2 numbers).
  • A196836 (program): (1^n + 2^n +3^n + 4^n)/2.
  • A196858 (program): Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,4,2,0,1 for x=0,1,2,3,4.
  • A196870 (program): a(n+1) = A001610(n)*a(n).
  • A196872 (program): A007018(n) repeated A007018(n) times.
  • A196875 (program): a(n) = a(n-4) + a(n-3) + a(n-2) + a(n-1) + (n-5).
  • A196876 (program): a(n) = a(n-no-1)+….+a(n-1)+(n-no-2) where no is the ‘no+1’th order of the series and ‘n’ is the element number, here no=6.
  • A196906 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,1,2,0,4 for x=0,1,2,3,4.
  • A196917 (program): Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,4,0 for x=0,1,2,3,4.
  • A196932 (program): Decimal expansion of sinh(1)*cosh(1).
  • A196990 (program): Numbers that are not the sum of two powers of 3.
  • A197032 (program): Decimal expansion of the x-intercept of the shortest segment from the positive x axis through (2,1) to the line y=x.
  • A197034 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (3,1) to the line y=x.
  • A197036 (program): Decimal expansion of the Modified Bessel Function I of order 0 at 1.
  • A197039 (program): Numbers such that sum of the cube of decimal digits is a perfect square.
  • A197049 (program): Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical zero neighbors.
  • A197056 (program): Number of nX3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to 2
  • A197070 (program): Decimal expansion of the Dirichlet eta-function at 3.
  • A197092 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,4,0,0,1 for x=0,1,2,3,4.
  • A197110 (program): Decimal expansion of Pi^4/120.
  • A197113 (program): Nonprime numbers n such that the greatest residue of the congruence x^n (mod n) equals n-1 where x = 0..n-1.
  • A197130 (program): Sum of reflection (or absolute) lengths of all elements in the Coxeter group of type B_n
  • A197131 (program): Sum of the reflection (absolute) lengths of all elements in the Coxeter group of type D_n
  • A197136 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (4,1) to the line y=x.
  • A197138 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (3,2) to the line y=x.
  • A197140 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (1,1) to the line y=2x.
  • A197142 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (2,1) to the line y=2x.
  • A197144 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (3,1) to the line y=2x.
  • A197146 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (4,1) to the line y=2x.
  • A197148 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (1,1) to the line y=3x.
  • A197150 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (2,1) to the line y=3x.
  • A197152 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (3,1) to the line y=x/2.
  • A197154 (program): Decimal expansion of the x-intercept of the shortest segment from the x axis through (4,1) to the line y=x/2.
  • A197168 (program): Number of 2 X 2 integer matrices with elements from {1,…,n} whose determinant is 2.
  • A197181 (program): Numbers that are a divisor of the product of the factorials of their digits in decimal representation.
  • A197183 (program): Number of partitions of n^2 into distinct factorials.
  • A197189 (program): a(n) = 3*a(n-1) + 5*a(n-2), with a(0)=1, a(1)=2.
  • A197190 (program): a(0) = 2, a(n) = Lucas(phi(n^2)) for n > 0.
  • A197192 (program): Binomial(n+9, 9)*7^n
  • A197193 (program): Binomial(n+10, 10)*7^n
  • A197194 (program): a(n) = binomial(n+9, 9)*9^n.
  • A197211 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,2,1,0 for x=0,1,2,3,4.
  • A197219 (program): a(0) = 2, a(n) = Lucas(phi(n)) for n > 0.
  • A197244 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,0,1,1,1 for x=0,1,2,3,4.
  • A197271 (program): a(n) = 10/((3*n+1)*(3*n+2))*binomial(4*n,n).
  • A197272 (program): a(n) = 6/((4*n+1)*(4*n+2))*binomial(5*n,n).
  • A197292 (program): Decimal expansion of least x>0 having sin(6x)=(sin 3x)^2.
  • A197320 (program): a(n) = cosh(n*arccosh(2^n)).
  • A197321 (program): Binomial(n+10, 10)*8^n
  • A197322 (program): Floor((2*n+1/n)^n)
  • A197323 (program): Floor((3*n+1/n)^n)
  • A197324 (program): Floor((4n+1/n)^n)
  • A197325 (program): Floor((5n+1/n)^n)
  • A197344 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,1,1,0 for x=0,1,2,3,4.
  • A197351 (program): a(0)=0, a(1)=1, a(2n)=17*a(n), a(2n+1)=a(2n)+1.
  • A197352 (program): a(0)=0, a(1)=1, a(2n)=18*a(n), a(2n+1)=a(2n)+1.
  • A197353 (program): a(0)=0, a(1)=1, a(2n)=19*a(n), a(2n+1)=a(2n)+1.
  • A197354 (program): a(n) = Sum_{k>=0} A030308(n,k)*(2k+1).
  • A197355 (program): Special values of Hermite polynomials.
  • A197366 (program): Number of Abelian groups of order 2n which are isomorphic with at least one Galois Field GF(k).
  • A197376 (program): Decimal expansion of least x>0 having sin(x)=(sin x/2)^2.
  • A197410 (program): Product of cumulative sums of divisors of n.
  • A197424 (program): Number of subsets of {1, 2, …, 4*n + 2} which do not contain two numbers whose difference is 4.
  • A197432 (program): a(n) = Sum_{k>=0} A030308(n,k)*C(k) where C(k) is the k-th Catalan number (A000108).
  • A197433 (program): Sum of distinct Catalan numbers: a(n) = Sum_{k>=0} A030308(n,k)*C(k+1) where C(n) is the n-th Catalan number (A000108). (C(0) and C(1) not treated as distinct.)
  • A197469 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,0,0,0 for x=0,1,2,3,4.
  • A197497 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,1,1,0 for x=0,1,2,3,4.
  • A197504 (program): Odd numbers m >= 3 for which phi(2*m)/2 = phi(m)/2 is odd, where phi = A000010 (Euler’s totient), and the number 1 is included.
  • A197562 (program): Partial sums of A073177 (product of n-th digit of Pi and n-th digit of e).
  • A197563 (program): Partial sums of A073212 (n-th digit of Pi plus n-th digit of e).
  • A197566 (program): Sum of the n-th digit of Pi and the n-th digit of the Golden Ratio.
  • A197567 (program): Partial sums of A197566 (sum of n-th digit of Pi and n-th digit of the Golden Ratio).
  • A197568 (program): Product of n-th digit of Pi and n-th digit of the Golden Ratio.
  • A197569 (program): Partial sums of A197568 (product of n-th digit of Pi and n-th digit of the Golden Ratio).
  • A197588 (program): Decimal expansion of the maximum of (cos(x))^2+(sin(3x))^2.
  • A197595 (program): Floor((6n+1/n)^n)
  • A197596 (program): Floor((7n+1/n)^n)
  • A197597 (program): Floor((8n+1/n)^n)
  • A197598 (program): Floor((9n+1/n)^n)
  • A197599 (program): Floor((10n+1/n)^n)
  • A197600 (program): Floor((11n+1/n)^n)
  • A197601 (program): G.f.: exp( Sum_{n>=1} [Sum_{k=0..2*n} C(2*n,k)^2 *x^k] *x^n/n ).
  • A197602 (program): Floor((n+1/n)^3).
  • A197603 (program): Floor((n+1/n)^4).
  • A197604 (program): Floor((n+1/n)^5).
  • A197605 (program): Floor( ( n + 1/n )^6 ).
  • A197617 (program): Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,3,1,1,1 for x=0,1,2,3,4.
  • A197638 (program): GA1 numbers: composite m with G(m) >= G(m/p) for all prime factors p of m, where G(k) = sigma(k)/(k*log(log(k))) and sigma(k) = sum of divisors of k.
  • A197649 (program): a(n) = Sum_{k=0..n} k*Fibonacci(2*k).
  • A197652 (program): Numbers that are congruent to 0 or 1 mod 10.
  • A197657 (program): Row sums of A194595.
  • A197658 (program): Smallest k such that i^k = i mod n for each i in [0..n-1], or 0 if no such k exists.
  • A197680 (program): Numbers whose exponents in their prime power factorization are squares.
  • A197682 (program): Decimal expansion of Pi/(2 + 2*Pi).
  • A197683 (program): Decimal expansion of Pi/(2+4*Pi).
  • A197686 (program): Decimal expansion of Pi/(2 + Pi).
  • A197687 (program): Decimal expansion of 3*Pi/(6 + 2*Pi).
  • A197688 (program): Decimal expansion of 2*Pi/(4+Pi).
  • A197689 (program): Decimal expansion of 3*Pi/(6 + Pi).
  • A197690 (program): Decimal expansion of Pi/(4 + 2*Pi).
  • A197691 (program): Decimal expansion of Pi/(4 + 4*Pi).
  • A197694 (program): Decimal expansion of Pi/(4 + Pi).
  • A197695 (program): Decimal expansion of Pi/(6 + 2*Pi).
  • A197696 (program): Decimal expansion of Pi/(6 + 4*Pi).
  • A197699 (program): Decimal expansion of Pi/(6 + Pi).
  • A197700 (program): Decimal expansion of Pi/(1 + 2*Pi).
  • A197701 (program): Decimal expansion of Pi/(1 + 4*Pi).
  • A197708 (program): Floor((n+1/n)^7)
  • A197709 (program): Floor((n+1/n)^8)
  • A197710 (program): Floor((n+1/n)^9)
  • A197711 (program): Floor((n+1/n)^10)
  • A197712 (program): a(n) = floor((n+1/2)^n).
  • A197713 (program): Floor((n+1/3)^n)
  • A197714 (program): Floor((n+1/4)^n).
  • A197715 (program): Floor((n+1/5)^n)
  • A197716 (program): Ceiling((2n+1/n)^n).
  • A197717 (program): Ceiling((3n+1/n)^n).
  • A197723 (program): Decimal expansion of (3/2)*Pi.
  • A197726 (program): Decimal expansion of Pi/(1 + Pi).
  • A197727 (program): Decimal expansion of 2*Pi/(2+Pi).
  • A197728 (program): Decimal expansion of 3*Pi/(2 + 2*Pi).
  • A197729 (program): Decimal expansion of 3*Pi/(2 + Pi).
  • A197730 (program): Decimal expansion of 3*Pi/(4+Pi).
  • A197731 (program): Decimal expansion of 2*Pi/(1 + 4*Pi).
  • A197732 (program): Decimal expansion of 2*Pi/(1 + 2*Pi).
  • A197733 (program): Decimal expansion of 2*Pi/(1+Pi).
  • A197735 (program): Decimal expansion of 3*Pi/(1 + Pi).
  • A197736 (program): Decimal expansion of 4*Pi/(1 + Pi).
  • A197762 (program): Decimal expansion of sqrt(1/phi), where phi = (1 + sqrt(5))/2 is the golden ratio.
  • A197764 (program): Ceiling((4n+1/n)^n).
  • A197765 (program): a(n) = ceiling((5n+1/n)^n).
  • A197766 (program): Ceiling((6n+1/n)^n).
  • A197767 (program): Ceiling((7*n+1/n)^n)
  • A197768 (program): Ceiling((8*n+1/n)^n)
  • A197769 (program): Ceiling((9*n+1/n)^n)
  • A197770 (program): Ceiling((10*n+1/n)^n).
  • A197771 (program): Ceiling((11*n+1/n)^n)
  • A197773 (program): Ceiling((n+1/n)^3)
  • A197818 (program): Walsh matrix antidiagonals converted to decimal.
  • A197837 (program): Decimal expansion of least x>0 satisfying (cos(x))^2+(sin(3*Pi*x))^2=1.
  • A197863 (program): Smallest powerful number that is a multiple of n.
  • A197870 (program): Expansion of false theta series variation of Ramanujan theta function psi(x).
  • A197878 (program): a(n) = floor(2*(1 + sqrt(2))*n).
  • A197879 (program): Parity of floor(n*sqrt(8)).
  • A197880 (program): Squarefree part of ((2n-1)!)^(2n-3).
  • A197881 (program): Number of times n occurs in A197863.
  • A197903 (program): Ceiling((n+1/n)^4).
  • A197904 (program): a(n) = ceiling((n+1/n)^5).
  • A197905 (program): Ceiling((n+1/n)^6).
  • A197906 (program): a(n) = ceiling((n+1/n)^7).
  • A197907 (program): Ceiling((n+1/n)^8).
  • A197908 (program): Ceiling((n+1/n)^9).
  • A197909 (program): Ceiling((n+1/n)^10).
  • A197910 (program): Ceiling((n+1/2)^n).
  • A197911 (program): Representable by A001045 (Jacobsthal sequence). Complement of A003158.
  • A197916 (program): Related to the periodic sequence A171654.
  • A197927 (program): The number of isolated nodes in all labeled directed graphs (with self loops allowed) on n nodes.
  • A197943 (program): Greatest residue of x^(n-1) (mod n), x=0..n-1.
  • A197953 (program): a(n) = 1 + Sum_{d|n, d>1} d * a(n/d).
  • A197972 (program): a(n) = ceiling((n+1/3)^n).
  • A197973 (program): Ceiling((n+1/4)^n)
  • A197974 (program): Ceiling((n+1/5)^n)
  • A197975 (program): Round((2*n+1/n)^n)
  • A197976 (program): Round((3*n+1/n)^n)
  • A197977 (program): Round((4*n+1/n)^n)
  • A197978 (program): a(n) = round((5*n+1/n)^n).
  • A197979 (program): Round((6*n+1/n)^n)
  • A197980 (program): Round((7*n+1/n)^n)
  • A197981 (program): Round((8*n+1/n)^n)
  • A197982 (program): Round((9*n+1/n)^n)
  • A197983 (program): Round((10*n+1/n)^n)
  • A197984 (program): Round((11*n+1/n)^n)
  • A197985 (program): Round((n+1/n)^2)
  • A197986 (program): Round((n+1/n)^3).
  • A197987 (program): a(n) = prime(n)^(n+1).
  • A197988 (program): Number of isomorphism classes of nanocones with 3 pentagons and a symmetric boundary of length n.
  • A197989 (program): Number of binary arrangements of total n 1’s, without adjacent 1’s on n X n array connected n-s
  • A198014 (program): Number of isomorphism classes of nanocones with 3 pentagons and a nearsymmetric boundary of length n
  • A198017 (program): a(n) = n*(7*n + 11)/2 + 1.
  • A198059 (program): a(n) = Sum_{k=1..n} binomial(2*k, n-k)^2 * n/k.
  • A198063 (program): Triangle read by rows (n >= 0, 0 <= k <= n, m = 3); T(n,k) = Sum{j=0..m} Sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).
  • A198064 (program): Triangle read by rows (n >= 0, 0 <= k <= n, m = 4); T(n,k) = Sum{j=0..m} Sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).
  • A198065 (program): Triangle read by rows (n >= 0, 0 <= k <= n, m = 5); T(n,k) = Sum{j=0..m} Sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).
  • A198069 (program): Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=2^(n-1) T(n,k) = gcd(k,2^(n-1)).
  • A198070 (program): Round((n+1/n)^5).
  • A198071 (program): Round((n+1/n)^6).
  • A198072 (program): Round((n+1/n)^7).
  • A198073 (program): Round((n+1/n)^8).
  • A198074 (program): Round((n+1/n)^9).
  • A198075 (program): Round((n+1/n)^10).
  • A198076 (program): Round((n+1/2)^n).
  • A198077 (program): Round((n+1/3)^n).
  • A198078 (program): a(n) = round((n+1/4)^n).
  • A198079 (program): Round((n+1/5)^n).
  • A198080 (program): a(n) = (3^(3*n + 3)- 26*n - 27)/169.
  • A198081 (program): a(n) = ceiling(n*sqrt(3)).
  • A198082 (program): Ceiling(n*Sqrt(5)).
  • A198083 (program): Ceiling(n*Sqrt(6)).
  • A198084 (program): Ceiling(n*sqrt(7)).
  • A198148 (program): a(n) = n*(n+2)*(9 - 7*(-1)^n)/16.
  • A198191 (program): Start with sequence 1,2,3, after this a(n) is smallest number > a(n-1) coprime to sum of previous elements.
  • A198192 (program): Replace 2^k in the binary representation of n with n-k (i.e. if n = 2^a + 2^b + 2^c + … then a(n) = (n-a) + (n-b) + (n-c) + …).
  • A198193 (program): Replace 2^k in the binary representation of n with n+(k-L) where L = floor(log(n)/log(2)).
  • A198194 (program): Greatest number k such that p(k) <= n, p(k) being the number of unrestricted partitions of k.
  • A198204 (program): Series reversion of (1 - t*x)*log(1 + x) with respect to x.
  • A198205 (program): Number of 2nX2 0..3 arrays with values 0..3 introduced in row major order and each element unequal to exactly two horizontal and vertical neighbors
  • A198256 (program): Row sums of A197653.
  • A198261 (program): Triangular array read by rows T(n,k) is the number of simple labeled graphs on n nodes with exactly k isolated nodes, 0<=k<=n.
  • A198263 (program): a(n) = ceiling(n*sqrt(8)).
  • A198264 (program): Round(n*sqrt(10)).
  • A198265 (program): Ceiling(n*sqrt(10)).
  • A198266 (program): a(n) = ceiling(n*sqrt(11)).
  • A198267 (program): Round(n*sqrt(11)).
  • A198268 (program): Round(n*sqrt(12)).
  • A198269 (program): Ceiling(n*sqrt(12)).
  • A198270 (program): Ceiling(n*sqrt(13)).
  • A198271 (program): Round(n*sqrt(13)).
  • A198272 (program): a(n) = round(n*sqrt(17)).
  • A198274 (program): a(n) = 13*2^n-1.
  • A198275 (program): 17*2^n - 1.
  • A198276 (program): 19*2^n-1.
  • A198279 (program): Number of 2n X 4 0..2 arrays with values 0..2 introduced in row major order and each element equal to exactly two horizontal and vertical neighbors.
  • A198286 (program): a(n) = Sum_{d|n} (A053143(d) or smallest square divisible by d).
  • A198287 (program): Number of 2n X 2 0..3 arrays with values 0..3 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor.
  • A198292 (program): Irregular triangle with row n being A045917(n) copies of n.
  • A198295 (program): Riordan array (1, x*(1+x)/(1-x^3)).
  • A198300 (program): Square array M(k,g), read by antidiagonals, of the Moore lower bound on the order of a (k,g)-cage.
  • A198301 (program): G.f.: exp( Sum_{n>=1} (x^n/n) * Sum_{d|n} d*sigma(n/d,d) ).
  • A198302 (program): a(n) = Sum_{d|n} d * sigma(n/d, d).
  • A198306 (program): Moore lower bound on the order of a (6,g)-cage.
  • A198307 (program): Moore lower bound on the order of a (7,g)-cage.
  • A198308 (program): Moore lower bound on the order of an (8,g)-cage.
  • A198309 (program): Moore lower bound on the order of a (9,g)-cage.
  • A198310 (program): Moore lower bound on the order of a (10,g)-cage.
  • A198321 (program): Triangle T(n,k), read by rows, given by (0,1,0,0,0,0,0,0,0,0,0,…) DELTA (1,1,-1,1,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A198326 (program): Sum of lengths of all directed paths in the rooted tree having Matula-Goebel number n.
  • A198327 (program): Semiprimes k such that k-2 is also a semiprime.
  • A198382 (program): Numbers n such that 90n + 37 is prime.
  • A198383 (program): a(n) = Sum_{k=1..n} 2^(n mod k).
  • A198386 (program): Third of a triple of squares in arithmetic progression.
  • A198390 (program): Square root of third term of a triple of squares in arithmetic progression.
  • A198392 (program): a(n) = (6*n*(3*n+7)+(2*n+13)*(-1)^n+3)/16 + 1.
  • A198395 (program): a(n) = ceiling(n*sqrt(17)).
  • A198396 (program): a(n) = 6^n-6*n.
  • A198397 (program): 7^n - 7*n.
  • A198398 (program): 8^n - 8*n.
  • A198399 (program): 9^n - 9*n.
  • A198400 (program): 10^n-10*n.
  • A198401 (program): 8^n+n^8.
  • A198402 (program): a(n) = 5^n * n^5.
  • A198403 (program): a(n) = 6^n * n^6.
  • A198404 (program): 8^n*n^8.
  • A198410 (program): ((3^(n-1) + 1)^3 -1)/3^n.
  • A198412 (program): a(n) = (3^(6*n) - 2^(6*n))/35.
  • A198437 (program): Third term of a triple of squares in arithmetic progression, which is not a multiple of another triple in (A198384,A198385,A198386).
  • A198441 (program): Square root of third term of a triple of squares in arithmetic progression that is not a multiple of another triple in (A198384, A198385, A198386).
  • A198442 (program): Number of sequences of n coin flips that win on the last flip, if the sequence of flips ends with (1,1,0) or (1,0,0).
  • A198447 (program): Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element unequal to exactly two horizontal and vertical neighbors.
  • A198474 (program): Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an odd number of horizontal and vertical neighbors.
  • A198478 (program): a(n) = 9^n * n^9.
  • A198479 (program): a(n) = 10^n * n^10.
  • A198480 (program): a(n) = 2*7^n - 1.
  • A198486 (program): Numbers with the property that all pairs of consecutive digits differ by 9.
  • A198516 (program): Largest lifetime of any configuration starting from n cells which are bishop-connected for the cell automaton defined in A198514.
  • A198517 (program): Period 5: repeat [1,0,1,0,0].
  • A198586 (program): a(n) = (4^A001651(n+1) - 1)/3: numbers (4^k-1)/3 for k > 1, not multiples of 3.
  • A198589 (program): Odd numbers producing 6 odd numbers in the Collatz iteration.
  • A198590 (program): Odd numbers producing 7 odd numbers in the Collatz iteration.
  • A198591 (program): Odd numbers producing 8 odd numbers in the Collatz iteration.
  • A198592 (program): Odd numbers producing 9 odd numbers in the Collatz iteration.
  • A198593 (program): Odd numbers producing 10 odd numbers in the Collatz iteration.
  • A198620 (program): Number of n X 1 0..5 arrays with values 0..5 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.
  • A198628 (program): Alternating sums of powers for 1,2,3,4 and 5.
  • A198629 (program): Alternating sums of powers of 1,2,…,6, divided by 3.
  • A198630 (program): Alternating sums of powers of 1,2,…,7.
  • A198631 (program): Numerators of the rational sequence with e.g.f. 1/(1+exp(-x)).
  • A198633 (program): Total number of round trips, each of length 2*n on the graph P_3 (o-o-o).
  • A198635 (program): Total number of round trips, each of length 2*n on the graph P_5 (o-o-o-o-o).
  • A198636 (program): One half of total number of round trips, each of length 2n, on the graph P_6 (o-o-o-o-o-o).
  • A198638 (program): Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.
  • A198643 (program): a(n) = 5*3^n-1.
  • A198644 (program): 8*3^n-1.
  • A198645 (program): a(n) = 10*3^n - 1.
  • A198646 (program): a(n) = 11*3^n-1.
  • A198647 (program): 3*7^n-1
  • A198648 (program): Number of n X 1 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.
  • A198662 (program): Number of n X 1 0..4 arrays with values 0..4 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.
  • A198680 (program): Multiples of 3 whose sum of base-3 digits are also multiples of 3.
  • A198681 (program): Nonnegative multiples of 3 whose sum of base-3 digits are of the form 3k+1.
  • A198682 (program): Nonnegative multiples of 3 whose sum of base-3 digits are of the form 3*k+2.
  • A198686 (program): 4*7^n-1.
  • A198687 (program): 5*7^n-1.
  • A198688 (program): 6*7^n-1.
  • A198689 (program): 8*7^n-1.
  • A198690 (program): 9*7^n-1.
  • A198691 (program): 10*7^n-1.
  • A198692 (program): a(n) = 11*7^n-1.
  • A198693 (program): a(n) = 3*4^n-1.
  • A198694 (program): 7*4^n-1.
  • A198695 (program): 11*4^n-1
  • A198698 (program): 3*10^n-1.
  • A198699 (program): 7*10^n-1
  • A198700 (program): 11*10^n-1.
  • A198710 (program): Number of n X 3 0..3 arrays with values 0..3 introduced in row major order and no element equal to any horizontal or vertical neighbor.
  • A198759 (program): The number of pairs of braces to note the properly nested set with n elements.
  • A198762 (program): 3*5^n-1= 2*A057651(n).
  • A198763 (program): 4*5^n-1.
  • A198764 (program): 6*5^n-1.
  • A198765 (program): 7*5^n-1.
  • A198766 (program): (7*5^n-1)/2.
  • A198767 (program): 8*5^n-1.
  • A198768 (program): a(n) = 9*5^n-1.
  • A198769 (program): (9*5^n-1)/4.
  • A198770 (program): 11*5^n-1.
  • A198771 (program): (11*5^n-1)/2.
  • A198772 (program): Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y.
  • A198773 (program): Numbers having exactly two representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.
  • A198786 (program): G.f. satisfies: A(x) = 1 + 2*x*sqrt(A(x)/A(-x)).
  • A198787 (program): Triangle read by rows: T(n,k) is the number of edges in the (n,k)-Turán graph.
  • A198788 (program): Array T(k,n) read by descending antidiagonals: Last survivor positions in Josephus problem for n numbers and a count of k, n >= 1, k >= 1.
  • A198789 (program): Array T(n,k) read by antidiagonals: Last survivor positions in Josephus problem for n numbers and a count of k, n >= 1, k >= 1.
  • A198792 (program): Triangle T(n,k), read by rows, given by (0,1,1,0,0,0,0,0,0,0,…) DELTA (1,0,0,1,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A198793 (program): Triangle T(n,k), read by rows, given by (1,0,0,1,0,0,0,0,0,0,0,…) DELTA (0,1,1,0,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A198794 (program): a(n) = 5*6^n - 1.
  • A198795 (program): 7*6^n-1.
  • A198796 (program): 3*6^n-1.
  • A198797 (program): 4*6^n-1.
  • A198798 (program): Least odd number a(n) > -3 such that a(n) = p(n) - j*(j+1), where p(n) is the n-th prime.
  • A198833 (program): The number of inequivalent ways to color the vertices of a regular octahedron using at most n colors.
  • A198834 (program): Number of sequences of n coin flips that win on the last flip, if the sequence of flips ends with (0,1,1) or (1,1,1).
  • A198845 (program): 8*6^n-1.
  • A198846 (program): 9*6^n-1.
  • A198847 (program): a(n) = 10*6^n - 1.
  • A198848 (program): 11*6^n-1.
  • A198849 (program): a(n) = (11*6^n - 1)/5.
  • A198850 (program): 2*8^n-1
  • A198851 (program): a(n) = 3*8^n-1.
  • A198852 (program): a(n) = 4*8^n - 1.
  • A198853 (program): a(n) = 5*8^n - 1.
  • A198854 (program): 6*8^n-1.
  • A198855 (program): a(n) = 7*8^n - 1.
  • A198856 (program): a(n) = 9*8^n - 1.
  • A198857 (program): a(n) = 10*8^n - 1.
  • A198858 (program): a(n) = 11*8^n-1.
  • A198859 (program): 2*9^n-1.
  • A198862 (program): Sum of the n-th antidiagonal in the triangle A192011.
  • A198864 (program): a(0) = 1; a(n) = n + product_{i=0..n-1} a(i), n >= 1.
  • A198888 (program): G.f. satisfies: A(x) = (1 + x*A(x))*(1 + x^3*A(x)^4).
  • A198897 (program): Rank of elliptic curve y^2 = x^3 + A179107(n).
  • A198900 (program): Number of n X 2 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.
  • A198947 (program): x values in the solution to 11*x^2 - 10 = y^2.
  • A198949 (program): y-values in the solution to 11*x^2-10 = y^2.
  • A198951 (program): G.f. satisfies: A(x) = (1 + x*A(x))*(1 + x^3*A(x)^3).
  • A198953 (program): G.f. satisfies: A(x) = (1 + x*A(x))*(1 + x*A(x)^3).
  • A198954 (program): Expansion of the rotational partition function for a heteronuclear diatomic molecule.
  • A198955 (program): q-expansion of modular form t_{3B}.
  • A198956 (program): q-expansion of modular form psi_0^4/t_{3B}.
  • A198957 (program): G.f. satisfies: A(x) = (1 + x*A(x))*(1 + x^2*A(x)^4).
  • A198960 (program): 3*9^n-1.
  • A198961 (program): 4*9^n-1.
  • A198962 (program): 5*9^n-1.
  • A198963 (program): 6*9^n-1.
  • A198964 (program): (7*9^n-1)/2.
  • A198965 (program): 7*9^n-1.
  • A198966 (program): a(n) = 8*9^n-1.
  • A198967 (program): 10*9^n-1.
  • A198968 (program): 11*9^n-1.
  • A198969 (program): (11*9^n-1)/2.
  • A198970 (program): a(n) = 4*10^n-1.
  • A198971 (program): a(n) = 5*10^n - 1.
  • A198972 (program): (7*10^n-1)/3.
  • A198973 (program): 8*10^n-1.
  • A198974 (program): 2*11^n-1.
  • A198976 (program): Number of n X 2 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.
  • A199010 (program): Arises in enumeration of Ehrhart polynomials for triangles.
  • A199011 (program): Triangle T(n,k), read by rows, given by (1,1,-1,1,0,0,0,0,0,0,0,…) DELTA (0,1,0,0,0,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A199015 (program): G.f.: 1/(1-x) * Product_{n>=1} (1 - x^(2*n))^2/(1 - x^(2*n-1))^2.
  • A199018 (program): (3*11^n-1)/2.
  • A199019 (program): 3*11^n-1.
  • A199020 (program): 4*11^n-1.
  • A199021 (program): (5*11^n-1)/2.
  • A199022 (program): 5*11^n-1.
  • A199023 (program): (6*11^n - 1) / 5.
  • A199024 (program): 6*11^n-1.
  • A199025 (program): (7*11^n-1)/2.
  • A199026 (program): 7*11^n-1.
  • A199027 (program): 8*11^n-1.
  • A199028 (program): (9*11^n-1)/2.
  • A199029 (program): 9*11^n-1.
  • A199030 (program): 10*11^n-1.
  • A199031 (program): 2*12^n-1.
  • A199032 (program): 3*12^n-1.
  • A199033 (program): Number of ways to place n non-attacking bishops on a 2 X 2n board.
  • A199042 (program): Expansion of e.g.f. exp(arctan(1+2*x) - Pi/4).
  • A199084 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) gcd(k,n).
  • A199085 (program): Number of distinct values taken by 3rd derivative of x^x^…^x (with n x’s and parentheses inserted in all possible ways) at x=1.
  • A199106 (program): 4*12^n-1.
  • A199107 (program): 5*12^n-1.
  • A199108 (program): 4*3^n+1.
  • A199109 (program): a(n) = (7*3^n + 1)/2.
  • A199110 (program): a(n) = 7*3^n+1.
  • A199111 (program): a(n) = 8*3^n+1.
  • A199112 (program): 10*3^n+1.
  • A199113 (program): (11*3^n+1)/2.
  • A199114 (program): 11*3^n+1.
  • A199115 (program): a(n) = 5*4^n+1.
  • A199116 (program): 6*4^n+1.
  • A199142 (program): Number of n X 1 0..3 arrays with values 0..3 introduced in row major order and each element equal to one or two horizontal and vertical neighbors.
  • A199206 (program): a(n) = (1+(A034939(n))^2)/5^n.
  • A199207 (program): 7*4^n+1.
  • A199208 (program): 9*4^n+1.
  • A199209 (program): 10*4^n+1.
  • A199210 (program): a(n) = (11*4^n+1)/3.
  • A199211 (program): 11*4^n+1.
  • A199212 (program): a(n) = 2*5^n+1.
  • A199213 (program): (3*5^n+1)/2.
  • A199214 (program): 3*5^n+1.
  • A199215 (program): 4*5^n+1.
  • A199216 (program): 6*5^n+1.
  • A199238 (program): n mod (number of ones in binary representation of n).
  • A199247 (program): G.f. satisfies: A(x) = (1 + x*A(x))*(1 + x^2*A(x)^3 + x^3*A(x)^4).
  • A199264 (program): Period 18: repeat (9,8,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,8).
  • A199299 (program): a(n) = (2*n + 1)*6^n.
  • A199300 (program): a(n) = (2*n + 1)*7^n.
  • A199301 (program): (2n+1)*8^n.
  • A199307 (program): Primes of the form 4n^3 + 1.
  • A199308 (program): (7*5^n+1)/4.
  • A199309 (program): (7*5^n+1)/2.
  • A199310 (program): 7*5^n+1.
  • A199311 (program): 8*5^n+1.
  • A199312 (program): (9*5^n+1)/2.
  • A199313 (program): 9*5^n+1.
  • A199314 (program): (11*5^n+1)/4.
  • A199315 (program): (11*5^n+1)/2.
  • A199316 (program): 11*5^n+1.
  • A199317 (program): 2*6^n+1.
  • A199318 (program): 3*6^n+1.
  • A199319 (program): 4*6^n+1.
  • A199320 (program): 5*6^n+1.
  • A199321 (program): 7*6^n+1.
  • A199322 (program): Number of twin prime numbers of the form n*(n+1) + 2*k-3 and n*(n+1) + 2*k-1 with k = 1 to n+1.
  • A199323 (program): Number of primes of the form n*(n+1)+2*k-3 with k from 1 to n+1.
  • A199324 (program): Triangle T(n,k), read by rows, given by (-1,1,-1,0,0,0,0,0,0,0,…) DELTA (1,0,0,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A199331 (program): Number of ordered ways of writing n as the sum of two semiprimes.
  • A199332 (program): Triangle read by rows, where even numbered rows contain the nonsquares (cf. A000037) and odd rows contain replicated squares.
  • A199334 (program): Triangle T(n,k) = Fibonacci(n+k), related to A000045 (Fibonacci numbers).
  • A199335 (program): Triangle T(n,k), read by rows, given by (0,1,0,2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,…) DELTA (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,…), where DELTA is the operator defined in A084938.
  • A199336 (program): x-values in the solution to 15*x^2 - 14 = y^2.
  • A199338 (program): y-values in the solution to 15*x^2 - 14 = y^2.
  • A199339 (program): a(n) = number of primes with an even digit sum among the first n primes minus the number with an odd digit sum.
  • A199344 (program): Least integer > n having a digital sum larger than that of n.
  • A199364 (program): Numbers k such that 4k^3 + 3 is prime.
  • A199365 (program): Primes of the form 4n^3 + 3.
  • A199366 (program): Numbers n such that 4n^3-1 is prime.
  • A199367 (program): Primes of the form 4*n^3 - 1.
  • A199368 (program): Numbers k such that 4k^3 - 3 is prime.
  • A199369 (program): Primes of the form 4*n^3 - 3.
  • A199394 (program): The number of ways to color the vertices of all (11) simple unlabeled graphs on 4 nodes using at most n colors.
  • A199398 (program): XOR of the first n odd numbers.
  • A199400 (program): Triangle T(n,k), read by rows, given by (2,0,3,0,4,0,5,0,6,0,7,0,8,0,9,…) DELTA (2,1,3,2,4,3,5,4,6,5,7,6,8,7,9,…) where DELTA is the operator defined in A084938.
  • A199402 (program): Binary XOR of 2^k - (-1)^k as k varies from 1 to n.
  • A199403 (program): Binary XOR of (2^k - (-1)^k)/3 as k varies from 1 to n.
  • A199404 (program): x-values in the solution to 13*x^2 - 12 = y^2.
  • A199405 (program): y-values in the solution to 13*x^2 - 12 = y^2.
  • A199408 (program): Triangle T(n,k) = n + k - gcd(n,k) read by rows, 1 <= n, 1 <= k <= n.
  • A199411 (program): 8*6^n+1.
  • A199412 (program): a(n) = (9*6^n+1)/5.
  • A199413 (program): 9*6^n+1.
  • A199414 (program): 10*6^n+1.
  • A199415 (program): 11*6^n+1.
  • A199416 (program): 2*7^n+1.
  • A199417 (program): (3*7^n+1)/2.
  • A199418 (program): 3*7^n+1.
  • A199419 (program): 4*7^n+1.
  • A199420 (program): a(n) = (5*7^n+1)/3.
  • A199421 (program): (5*7^n+1)/2.
  • A199422 (program): 5*7^n+1.
  • A199423 (program): Greatest prime factor of n and 2*n+1
  • A199427 (program): Numbers n such that 4n+1 and 8n+3 are prime.
  • A199474 (program): Leftmost column in the monotonic justified array of all positive generalized Fibonacci sequences (A160271).
  • A199475 (program): G.f. satisfies: A(x) = Sum_{n>=0} x^n * (1 - A(x)^(2*n+2))/(1 - A(x)^2).
  • A199478 (program): Irregular triangle read by rows: T(n,i) = 2^(i-1)*(binomial(n-i+1,i)+binomial(n-i,i)), n >= 1, 0 <= i <= (n+1)/2.
  • A199479 (program): Triangle T(n,k), read by rows, given by (1,0,0,0,0,0,0,0,0,0,…) DELTA (1,1,1,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A199483 (program): 6*7^n+1.
  • A199484 (program): (8*7^n+1)/3.
  • A199485 (program): 8*7^n+1.
  • A199486 (program): (9*7^n+1)/2.
  • A199487 (program): 9*7^n+1.
  • A199488 (program): 10*7^n+1.
  • A199489 (program): (11*7^n+1)/6.
  • A199490 (program): (11*7^n+1)/3.
  • A199491 (program): (11*7^n+1)/2.
  • A199492 (program): 11*7^n+1.
  • A199493 (program): 2*8^n+1.
  • A199494 (program): a(n) = 3*8^n + 1.
  • A199495 (program): Number of permutations of [n] starting and ending with an odd number.
  • A199502 (program): From Janet helicoidal classification of the periodic table.
  • A199512 (program): Triangle T(n,k) = Fibonacci(n+k+1), related to A000045 (Fibonacci numbers).
  • A199531 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive zero elements.
  • A199536 (program): The first column in Clark Kimberling’s even first column Stolarsky array (beginning column count at 1).
  • A199537 (program): The second column in Clark Kimberling’s even first column Stolarsky array (beginning column count at 1).
  • A199552 (program): 4*8^n+1.
  • A199553 (program): 5*8^n+1.
  • A199554 (program): 6*8^n+1.
  • A199555 (program): 7*8^n+1.
  • A199556 (program): 9*8^n+1.
  • A199557 (program): 10*8^n+1.
  • A199558 (program): 11*8^n+1.
  • A199559 (program): 2*9^n+1.
  • A199560 (program): (3*9^n+1)/2.
  • A199561 (program): a(n) = 3*9^n+1.
  • A199562 (program): 4*9^n+1.
  • A199563 (program): 5*9^n+1.
  • A199564 (program): 6*9^n+1.
  • A199565 (program): (7*9^n+1)/4.
  • A199566 (program): (7*9^n+1)/2.
  • A199567 (program): 7*9^n+1.
  • A199572 (program): Number of round trips of length n on the cycle graph C_2 from any of the two vertices.
  • A199573 (program): Number of round trips of length n from any of the four vertices of the cycle graph C_4.
  • A199575 (program): a(n) = floor(Fibonacci(n)^(1/4)).
  • A199578 (program): Row sums of coefficient triangle of the monic associated Laguerre polynomials of order 1.
  • A199589 (program): Decimal expansion of the greatest root of 6x^3 - 6x - 2 = 0.
  • A199590 (program): Decimal expansion (unsigned) of the greatest root of 6x^3 + 18x^2 + 12x + 2 = 0.
  • A199593 (program): Numbers n such that 3n-2, 3n-1 and 3n are all composite.
  • A199594 (program): Number of sequences of n coin flips that win on the last flip, if the sequence of flips ends with (0,0,1,1) or (1,1,1,1).
  • A199595 (program): Numbers n such that 3n+6, 3n+7 and 3n+8 are all composite.
  • A199596 (program): a(n) = floor(phi(2*n+1)/phi(2*n+2)).
  • A199626 (program): G.f.: (1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4)) for g=0.
  • A199656 (program): Triangular array read by rows, T(n,k) is the number of functions from {1,2,…,n} into {1,2,…,n} with maximum value of k.
  • A199659 (program): Expansion of q^(1/4) * (eta(q) / eta(q^3))^3 in powers of q.
  • A199673 (program): Number of ways to form k labeled groups, each with a distinct leader, using n people. Triangle T(n,k) = n!*k^(n-k)/(n-k)! for 1 <= k <= n.
  • A199677 (program): 8*9^n+1.
  • A199678 (program): 10*9^n+1.
  • A199679 (program): (11*9^n+1)/4.
  • A199680 (program): (11*9^n+1)/2.
  • A199681 (program): 11*9^n+1.
  • A199682 (program): 2*10^n+1.
  • A199683 (program): 3*10^n+1.
  • A199684 (program): a(n) = 4*10^n+1.
  • A199685 (program): a(n) = 5*10^n+1.
  • A199686 (program): 6*10^n+1.
  • A199687 (program): 7*10^n+1.
  • A199688 (program): (8*10^n+1)/3.
  • A199689 (program): a(n) = 8*10^n+1.
  • A199690 (program): (11*10^n+1)/3.
  • A199691 (program): 11*10^n+1.
  • A199705 (program): Number of -n..n arrays x(0..2) of 3 elements with zero sum and no two neighbors equal.
  • A199706 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two neighbors equal.
  • A199710 (program): Expansion of (1+x-14*x^2+13*x^3)/(1-28*x^2+169*x^4).
  • A199715 (program): A puzzle - explanation is not known.
  • A199716 (program): Numbers n such that 6n-5 and 6n-1 are both composite.
  • A199717 (program): Numbers k such that 6*k-1 is composite, but 6*k-5 is prime.
  • A199718 (program): Numbers n such that 6*n-5 is composite, but 6*n-1 is prime.
  • A199744 (program): G.f.: 1/(1 + x + 2*x^2 + 2*x^3 + x^4).
  • A199747 (program): a(n) = binomial(n*(3*n+1)/2, n).
  • A199748 (program): a(n) = binomial(n*(3*n-1)/2, n).
  • A199750 (program): 2*11^n+1.
  • A199751 (program): (3*11^n+1)/2.
  • A199752 (program): 3*11^n+1
  • A199753 (program): 4*11^n+1.
  • A199754 (program): (5*11^n+1)/2.
  • A199755 (program): 5*11^n+1.
  • A199756 (program): 6*11^n+1.
  • A199757 (program): (7*11^n+1)/2.
  • A199758 (program): 7*11^n+1
  • A199759 (program): 8*11^n+1.
  • A199760 (program): (9*11^n+1)/10.
  • A199761 (program): (9*11^n+1)/5.
  • A199762 (program): (9*11^n+1)/2.
  • A199763 (program): a(n) = 9*11^n+1.
  • A199764 (program): 10*11^n+1.
  • A199769 (program): Number of brackets in distinct sets with fewest possible elements
  • A199771 (program): Row sums of the triangle in A199332.
  • A199799 (program): Totatives of 111111.
  • A199802 (program): G.f.: 1/(1-2*x+2*x^2-x^3+x^4).
  • A199803 (program): G.f.: 1/(1 + x - x^2 - x^3 + x^4).
  • A199804 (program): G.f.: 1/(1+x+x^3).
  • A199805 (program): G.f.: 1/(1 + x + 5*x^2 - x^3 + x^4).
  • A199806 (program): Alternating LCM-sum: a(n) = Sum_{k=1..n} (-1)^(k-1)*lcm(k,n).
  • A199813 (program): G.f.: exp( Sum_{n>=1} A000984(n)*A000172(n) * x^n/n ), which involves central binomial coefficients (A000984) and Franel numbers (A000172).
  • A199816 (program): G.f.: exp( Sum_{n>=1} A000984(n)*A000172(n)/4 * x^n/n ), which involves central binomial coefficients (A000984) and Franel numbers (A000172).
  • A199825 (program): Number of -1..1 arrays x(0..n+1) of n+2 elements with zero sum and no two neighbors summing to zero
  • A199833 (program): Number of -n..n arrays of 4 elements with zero sum and no two neighbors summing to zero.
  • A199848 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no element more than one greater than the previous.
  • A199853 (program): Expansion of (1-3*x+x^3)/(1-2*x-x^2+x^3).
  • A199855 (program): Inverse permutation of A210521.
  • A199859 (program): Numbers k such that 6k-5 is a composite number of the form (6x-5)*(6y-5) when x or y is not equal to 1 except for k=1.
  • A199860 (program): Numbers k such that 6k-5 is a composite number of the form (6x-1) * (6y-1).
  • A199874 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2)*(1 + x^2*A(x)^2).
  • A199876 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3)*(1 + x^2*A(x)^3).
  • A199877 (program): G.f. satisfies: A(x) = (1 + x*A(x)^4)*(1 + x^2*A(x)^4).
  • A199881 (program): Triangle T(n,k), read by rows, given by (1,-1,0,0,0,0,0,0,0,0,0,…) DELTA (1,0,-1,1,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A199899 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.
  • A199900 (program): Number of -n..n arrays x(0..4) of 5 elements with zero sum, and adjacent elements not both strictly positive and not both strictly negative.
  • A199910 (program): Number of -n..n arrays x(0..2) of 3 elements with zero sum, and adjacent elements not equal modulo three (with -1 modulo 3 = 2).
  • A199918 (program): Expansion of false theta series variation of Euler’s pentagonal number series in powers of x.
  • A199922 (program): Table read by rows, T(0,0) = 1 and for n>0, 0<=k<=3^(n-1) T(n,k) = gcd(k,3^(n-1)).
  • A199923 (program): a(n) = Sum_{k=0..3^(n-1)} gcd(k,3^(n-1)) for n > 0 and a(0) = 1.
  • A199925 (program): Number of sequences of n coin flips that win on the last flip, if the sequence of flips ends with (0,0,1,1).
  • A199926 (program): Number of sequences of n coin flips that win on the last flip, if the sequence of flips ends with (1,1,1,1).
  • A199927 (program): Trisection 0 of A199802.
  • A199928 (program): Trisection 1 of A199802.
  • A199929 (program): Trisection 2 of A199802.
  • A199930 (program): Trisection 0 of A199803.
  • A199931 (program): Trisection 1 of A199803.
  • A199933 (program): Trisection 0 of A199744.
  • A199935 (program): Size (b^3_n) of unit sphere in a certain graph (see Hazama article for precise definition).
  • A199944 (program): Number of -n..n arrays x(0..2) of 3 elements with zeroth through 2nd differences all nonzero.
  • A199968 (program): a(n) = the smallest non-divisor h of n (1<h<n), or 0 if no such h exists.
  • A199969 (program): a(n) = the greatest non-divisor h of n (1 < h < n), or 0 if no such h exists.
  • A199970 (program): a(n) = the smallest number m with the smallest non-divisor n such that 1<n<m, or 0 if no such m exists.
  • A199972 (program): a(n) = the sum of GCQ_B(n, k) for 1 <= k <= n (see definition in comments).
  • A199975 (program): Multiplicative digital root of n-th prime.
  • A199976 (program): Multiplicative digital root of n-th nonprime number.
  • A199979 (program): Nonprime numbers whose multiplicative digital root is 1.
  • A199981 (program): Composite numbers whose multiplicative digital root is 2.
  • A199984 (program): Composite numbers whose multiplicative digital root is 4.
  • A199985 (program): Numbers with digital product = 5.
  • A199986 (program): Numbers with digital product = 2.
  • A199991 (program): Nonprime numbers whose multiplicative persistence is 1.

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