List of integer sequences with links to LODA programs.

  • A200039 (program): Number of -n..n arrays x(0..2) of 3 elements with sum zero and with zeroth through 2nd differences all nonzero.
  • A200050 (program): a(2) = 1, then (p-1)*(p-4)/2, with p = prime(n), n > 2.
  • A200058 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and elements alternately strictly increasing and strictly decreasing.
  • A200067 (program): Maximum sum of all products of absolute differences and distances between element pairs among the integer partitions of n.
  • A200142 (program): Number of near-matchings on the complete graph over 2n+1 vertices.
  • A200155 (program): Number of 0..n arrays x(0..3) of 4 elements with zero 3rd differences.
  • A200166 (program): Number of -n..n arrays x(0..2) of 3 elements with nonzero sum and with zero through 2 differences all nonzero.
  • A200182 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive declines, no adjacent equal elements, and no element more than one greater than the previous (random base sawtooth pattern).
  • A200193 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.
  • A200213 (program): Ordered factorizations of n with 2 distinct parts, both > 1.
  • A200244 (program): a(n)=1 iff binary weight of n-th prime is even.
  • A200245 (program): Partial sums of A200244.
  • A200246 (program): a(n)=1 iff binary weight of n-th prime is odd.
  • A200247 (program): Partial sums of A200246.
  • A200249 (program): Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 6.
  • A200252 (program): Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).
  • A200258 (program): a(n) = Fibonacci(8n+7) mod Fibonacci(8n+1).
  • A200261 (program): a(n) = 1 iff n-th prime has an even digit sum.
  • A200262 (program): Partial sums of A200261.
  • A200263 (program): a(n) = 1 iff n-th prime has an odd digit sum.
  • A200264 (program): Partial sums of A200263.
  • A200311 (program): Number of comparisons needed for optimal merging of 2 elements with n elements.
  • A200408 (program): -4 + 5*Fibonacci(n+1)^2.
  • A200431 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two or three adjacent elements summing to zero.
  • A200439 (program): Decimal expansion of constant arising in clubbed binomial approximation for the lightbulb process.
  • A200441 (program): Expansion of 1/(1-33*x+x^2).
  • A200442 (program): Expansion of 1/(1-31*x+x^2).
  • A200455 (program): Number of -n..n arrays x(0..2) of 3 elements with zero sum and nonzero first and second differences
  • A200535 (program): G.f. satisfies: A(x) = exp( Sum_ n>=1 [Sum_ k=0..2n C(2n,k)^2 * x^k] / A(x)^n * x^n/n ).
  • A200648 (program): Length of Stolarsky representation of n.
  • A200672 (program): Partial sums of A173862.
  • A200675 (program): Powers of 2 repeated 4 times.
  • A200676 (program): Expansion of -(3x^2-5x+1)/(x^3-3x^2+5x-1).
  • A200678 (program): Partial sums of A200675.
  • A200746 (program): Completely multiplicative function with a(prime(k)) = prime(k)*prime(k-1), a(2) = 2.
  • A200748 (program): Smallest number requiring n terms to be expressed as a sum of factorials.
  • A200752 (program): Expansion of (-x^2 + 3x - 1)/(x^3 - x^2 + 3x - 1).
  • A200810 (program): Iterate k -> d(k) until an odd prime is reached.
  • A200815 (program): Number of iterations of k -> d(k) until n reaches an odd prime.
  • A200860 (program): Multiples of 682.
  • A200864 (program): Expansion of 1/((1+x)(1-3x)(1-5x)).
  • A200872 (program): Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors.
  • A200887 (program): Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors.
  • A200905 (program): a(n) = 3*phi(n), where phi (A000010) is the Euler totient function.
  • A200919 (program): Number of crossings on periodic braids with n strands such that all strands meet.
  • A200975 (program): Numbers on the diagonals in Ulam’s spiral.
  • A200979 (program): Number of ways to arrange n books on 4 consecutive bookshelves, leaving no shelf empty.
  • A200993 (program): Triangular numbers, T(m), that are two-thirds of another triangular number; T(m) such that 3T(m) = 2T(k) for some k.
  • A200994 (program): Triangular numbers, T(m), that are three-halves of another triangular number; T(m) such that 2T(m) = 3T(k) for some k.
  • A200998 (program): Triangular numbers, T(m), that are three-quarters of another triangular number: T(m) such that 4T(m)=3T(k) for some k.
  • A200999 (program): Triangular numbers, T(m), that are four-thirds of another triangular number; T(m) such that 3T(m) = 4T(k) for some k.
  • A201003 (program): Triangular numbers, T(m), that are four-fifths of another triangular number: T(m) such that 5T(m) = 4T(k) for some k.
  • A201004 (program): Triangular numbers, T(m), that are five-quarters of another triangular number; T(m) such that 4T(m) = 5T(k) for some k.
  • A201008 (program): Triangular numbers, T(m), that are five-sixths of another triangular number: T(m) such that 6T(m)=5T(k) for some k.
  • A201058 (program): Numerator of binomial(2n,n)/(2n).
  • A201059 (program): Denominator of binomial(2n,n)/(2n).
  • A201106 (program): a(n) = binomial(n^2,3)/(2*n).
  • A201157 (program): y-values in the solution to 5*x^2 - 20 = y^2.
  • A201208 (program): One 1, two 2’s, three 1’s, four 2’s, five 1’s, …
  • A201219 (program): a(1) = 0; for n>1, a(n) = 1 if n is a power of 2, otherwise a(n) = 2.
  • A201227 (program): a(n) = (A201225(n))^3 - (A201226(n))^2.
  • A201236 (program): Number of ways to place 2 non-attacking wazirs on an n X n toroidal board.
  • A201243 (program): Number of ways to place 2 non-attacking ferses on an n X n board.
  • A201279 (program): a(n) = 6n^2 + 10n + 5.
  • A201347 (program): Number of n X 2 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
  • A201371 (program): Number of n X 4 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
  • A201455 (program): a(n) = 3a(n-1) + 4a(n-2) for n>1, a(0)=2, a(1)=3.
  • A201471 (program): Maximal diameter of a connected n-gamma_t-vertex-critical graph.
  • A201472 (program): The Griesmer lower bound q_4(5,n) on the length of a linear code over GF(4) of dimension 5 and minimal distance n.
  • A201498 (program): a(n) = (prime(n) - 1)*(prime(n+1) - 1)/2 + 3.
  • A201500 (program): Number of n X 3 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
  • A201553 (program): Number of arrays of 6 integers in -n..n with sum zero.
  • A201629 (program): a(n) = n if n is even and otherwise its nearest multiple of 4.
  • A201630 (program): a(n) = a(n-1)+2*a(n-2) with n>1, a(0)=2, a(1)=7.
  • A201686 (program): a(n) = binomial(n, [n/2]) - 2.
  • A201722 (program): Number of n X 1 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself.
  • A201776 (program): Decimal expansion of 1/(e+1).
  • A201812 (program): Number of arrays of 4 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
  • A201813 (program): Number of arrays of 5 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
  • A201824 (program): G.f.: Sum_ n>=0 log( 1/sqrt(1-2^n*x) )^n / n!.
  • A201864 (program): ((F(n-1)+F(n-2))-1)/2 if F(n) is odd, otherwise ((F(n-1)+F(n-2))-2)/2, where F(n)=A000045(n) is the n-th Fibonacci number.
  • A201874 (program): Number of zero-sum -n..n arrays of 3 elements with first and second differences also in -n..n.
  • A201920 (program): a(n) = 2^n mod 125.
  • A201975 (program): Number of n X 2 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
  • A202018 (program): a(n) = n^2 + n + 41.
  • A202022 (program): Characteristic functions of repdigit numbers in decimal representation.
  • A202023 (program): Triangle T(n,k), read by rows, given by (1, 0, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202048 (program): Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202049 (program): Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202050 (program): Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202051 (program): Number of (n+2) X 9 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202068 (program): Denominator of mass of oriented maximal Wicks forms of genus n.
  • A202094 (program): Number of (n+2)X4 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202096 (program): Number of (n+2)X6 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202103 (program): Number of points matched in largest non-crossing matching of n=w+b points in the plane (w white, b black).
  • A202104 (program): Numbers n such that 90*n + 41 is prime.
  • A202107 (program): n^4*(n+1)^4/8.
  • A202109 (program): n^3(n+1)^3(n+2)^3/72.
  • A202141 (program): a(n) = 13n^2 - 16n + 5.
  • A202155 (program): x-values in the solution to x^2 - 13*y^2 = -1.
  • A202156 (program): y-values in the solution to x^2 - 13*y^2 = -1.
  • A202169 (program): Size of maximal independent set in graph S_3(n).
  • A202171 (program): The covering numbers rho_3(n).
  • A202174 (program): In base 10 lunar arithmetic, a(n) is the smallest number than has exactly n different square roots (or -1 if no such number exists).
  • A202194 (program): Number of (n+2)X(n+2) binary arrays avoiding patterns 001 and 101 in rows and columns
  • A202195 (program): Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202196 (program): Number of (n+2) X 4 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202197 (program): Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202198 (program): Number of (n+2) X 6 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202199 (program): Number of (n+2) X 7 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202200 (program): Number of (n+2) X 8 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202201 (program): Number of (n+2) X 9 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202206 (program): a(n) = 3a(n-1)+3a(n-2) with a(0)=1 and a(1)=2.
  • A202207 (program): a(n) = 3*a(n-1) - a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=5.
  • A202238 (program): Characteristic function of positive integers not prime and not a power of 2.
  • A202253 (program): Number of zero-sum -n..n arrays of 3 elements with adjacent element differences also in -n..n.
  • A202254 (program): Number of zero-sum -n..n arrays of 4 elements with adjacent element differences also in -n..n.
  • A202278 (program): Right-truncatable Fibonacci numbers: every prefix is Fibonacci number.
  • A202299 (program): y-values in the solution to x^2 - 18*y^2 = 1.
  • A202301 (program): Next prime after the partial sum of the first n primes.
  • A202304 (program): a(n) = floor(sqrt(3*n)).
  • A202305 (program): Floor(sqrt(5*n)).
  • A202306 (program): Floor(sqrt(7*n)).
  • A202307 (program): Floor(sqrt(11*n)).
  • A202308 (program): Floor(sqrt(13*n)).
  • A202330 (program): Number of (n+1) X 4 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202331 (program): Number of (n+1) X 5 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202337 (program): Range of A062723.
  • A202391 (program): Indices of the smallest of four consecutive triangular numbers summing up to a square.
  • A202440 (program): Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.
  • A202451 (program): Upper triangular Fibonacci matrix, by SW antidiagonals.
  • A202452 (program): Lower triangular Fibonacci matrix, by SW antidiagonals.
  • A202455 (program): Number of (n+2) X 4 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.
  • A202462 (program): a(n) = Sum_ j=1..n Sum_ i=1..n F(i,j), where F is the Fibonacci fusion array of A202453.
  • A202563 (program): Numbers which are both decagonal and pentagonal.
  • A202564 (program): Indices of pentagonal numbers which are also decagonal.
  • A202565 (program): Indices of decagonal numbers which are also pentagonal.
  • A202606 (program): Ceiling(((10^n - 1)^2/9 + 10^n)/18).
  • A202654 (program): Number of ways to place 3 nonattacking semi-queens on an n X n board.
  • A202750 (program): Triangle T(n,k) = binomial(n,k)^4 read by rows, 0<=k<=n.
  • A202803 (program): a(n) = n(5n+1).
  • A202804 (program): a(n) = n(6n+4).
  • A202827 (program): E.g.f.: exp(4*x/(1-x)) / sqrt(1-x^2).
  • A202865 (program): Number of 3 X 3 0..n arrays with row and column sums one greater than the previous row and column.
  • A202946 (program): a(n+1) = 6A060544(n)a(n).
  • A202950 (program): a(n) = Sum_ k=0..n (2n-k)!2^(k-n)/k!.
  • A202963 (program): Number of arrays of 3 integers in -n..n with sum zero and adjacent elements differing in absolute value
  • A202964 (program): Number of arrays of 4 integers in -n..n with sum zero and adjacent elements differing in absolute value.
  • A202990 (program): E.g.f: Sum_ n>=0 3^n * 2^(n^2) * exp(-22^nx) * x^n/n!.
  • A203016 (program): Numbers congruent to 1, 2, 3, 4 mod 6, multiplied by 3.
  • A203134 (program): Decagonal hexagonal numbers
  • A203135 (program): Indices of hexagonal numbers that are also decagonal
  • A203136 (program): Indices of decagonal numbers that are also hexagonal.
  • A203150 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,1,2,1,2,1,2,1,2,…)=A000034.
  • A203157 (program): (n-1)-st elementary symmetric function of the first n triangular numbers.
  • A203230 (program): (n-1)-st elementary symmetric function of the first n terms of A010684.
  • A203232 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (2,3,2,3,2,3,…).
  • A203234 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,2,1,1,1,2,…).
  • A203241 (program): Second elementary symmetric function of the first n terms of (1,2,4,8,…).
  • A203243 (program): Second elementary symmetric function of the first n terms of (1,3,9,27,81,…).
  • A203244 (program): Second elementary symmetric function of the first n terms of (1,4,16,64,256,…).
  • A203246 (program): Second elementary symmetric function of the first n terms of (1,1,2,2,3,3,4,4,…).
  • A203286 (program): Number of arrays of 2n nondecreasing integers in -3..3 with sum zero and equal numbers greater than zero and less than zero.
  • A203292 (program): Number of arrays of 4 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.
  • A203298 (program): Second elementary symmetric function of the first n terms of (1,2,2,3,3,4,4,5,5…).
  • A203299 (program): Second elementary symmetric function of the first n terms of (2,2,3,3,4,4,5,5…).
  • A203302 (program): Cumulative sums of A201206.
  • A203307 (program): v(n+1)/(2*v(n)), where v=A203305.
  • A203310 (program): a(n) = A203309(n+1)/A203309(n).
  • A203423 (program): w(n+1)/(2*w(n)), where w=A203422.
  • A203425 (program): a(n) = w(n+1)/(4*w(n)), where w = A203424.
  • A203429 (program): w(n+1)/(3*w(n)), where w=A203428.
  • A203469 (program): v(n)/A000178(n); v=A093883 and A000178=(superfactorials).
  • A203473 (program): v(n+1)/v(n), where v=A203472.
  • A203536 (program): Number of nX2 0..2 arrays with every element neighboring horizontally or vertically both a 0 and a 1
  • A203551 (program): a(n) = n*(5n^2 + 3n + 4) / 6.
  • A203552 (program): a(n) = n(5n^2 - 3*n + 4) / 6.
  • A203571 (program): Period length 10: [0, 1, 2, 3, 4, 0, 4, 3, 2, 1] repeated.
  • A203572 (program): Period length 12: 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1 repeated.
  • A203574 (program): Bisection of A099924 (Lucas convolution); one half of the terms with odd arguments.
  • A203579 (program): Exponential (or binomial) convolution of A000032 (Lucas) with itself, divided by 2.
  • A203580 (program): a(n) = Sum d(i)2^i: i=0,1,…,m , where Sum d(i)7^i: i=0,1,…,m =n, d(i)∈ 0,1,…,6
  • A203623 (program): Partial sums of A061395.
  • A203639 (program): Multiplicative with a(p^e) = e*p^(e-1).
  • A203648 (program): a(n) = (1/4) * period of repeating sequence S(j) mod 2n , where S(j) is the sum of the first j squares.
  • A203777 (program): Aliquot sequence starting at 220.
  • A203789 (program): Number of (n+1)X2 0..3 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203819 (program): Number of (n+1)X2 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203820 (program): Number of (n+1)X3 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203821 (program): Number of (n+1)X4 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203872 (program): Number of (n+1)X3 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order
  • A203873 (program): Number of (n+1)X4 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order
  • A203880 (program): Number of (n+1)X2 0..6 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203927 (program): Number of (n+1)X2 0..5 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203967 (program): The number of positive integers <= n that have a prime number of divisors.
  • A203979 (program): Number of (n+1)X4 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order
  • A203994 (program): Symmetric matrix based on f(i,j) = (i+j)*min i,j , by antidiagonals.
  • A204002 (program): Symmetric matrix based on f(i,j)=min 2i+j,i+2j , by antidiagonals.
  • A204006 (program): Symmetric matrix based on f(i,j)=min 2i+j-2,i+2j-2 , by antidiagonals.
  • A204008 (program): Symmetric matrix based on f(i,j) = max 3i+j-3,i+3j-3 , by antidiagonals.
  • A204016 (program): Symmetric matrix based on f(i,j) = max j mod i, i mod j), by antidiagonals.
  • A204018 (program): Symmetric matrix based on f(i,j)=1+max j mod i, i mod j), by antidiagonals.
  • A204022 (program): Symmetric matrix based on f(i,j) = max(2i-1, 2j-1), by antidiagonals.
  • A204026 (program): Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.
  • A204028 (program): Symmetric matrix based on f(i,j)=min(3i-2,3j-2), by antidiagonals.
  • A204078 (program): Number of nX2 0..3 arrays with every element neighboring horizontally or vertically both a 0 and a 1.
  • A204089 (program): The number of 1 by n Haunted Mirror Maze puzzles with a unique solution ending with a mirror, where mirror orientation is fixed.
  • A204091 (program): The number of 1 X n Haunted Mirror Maze puzzles with a unique solution ending with a mirror.
  • A204093 (program): Numbers whose set of base-10 digits is 0,6 .
  • A204094 (program): Numbers whose set of base 10 digits is 0,7 .
  • A204095 (program): Numbers whose base 10 digits are a subset of 0, 8 .
  • A204125 (program): Symmetric matrix based on f(i,j)=(i if i=j and 1 otherwise), by antidiagonals.
  • A204127 (program): Symmetric matrix based on f(i,j)=(F(i+1) if i=j and 1 otherwise), where F=A000045 (Fibonacci numbers), by antidiagonals.
  • A204129 (program): Symmetric matrix based on f(i,j)=(L(i) if i=j and 1 otherwise), where L=A000032 (Lucas numbers), by antidiagonals.
  • A204131 (program): Symmetric matrix based on f(i,j)=(2i-1 if i=j and 1 otherwise), by antidiagonals.
  • A204133 (program): Symmetric matrix based on f(i,j)=(2^(i-1) if i=j and 1 otherwise), by antidiagonals.
  • A204160 (program): Symmetric matrix based on f(i,j)=(3i-2 if i=j and = 0 otherwise), by antidiagonals.
  • A204162 (program): Symmetric matrix based on f(i,j) = (floor((i+1)/2) if i=j and = 1 otherwise), by antidiagonals.
  • A204164 (program): Symmetric matrix based on f(i,j)=floor[(i+j)/2], by antidiagonals.
  • A204166 (program): Symmetric matrix based on f(i,j)=ceiling[(i+j)/2], by antidiagonals.
  • A204171 (program): Symmetric matrix based on f(i,j)=(1 if max(i,j) is odd, and 0 otherwise), by antidiagonals.
  • A204175 (program): Symmetric matrix based on f(i,j)=(1 if max(i,j) is even, and 0 otherwise), by antidiagonals.
  • A204177 (program): Symmetric matrix based on f(i,j)=(1 if i=1 or j=1 or i=j, and 0 otherwise), by antidiagonals.
  • A204185 (program): Number of quadrilaterals in a triangular matchstick arrangement of side n.
  • A204188 (program): Decimal expansion of sqrt(5)/4.
  • A204189 (program): Benoît Perichon’s 26 primes in arithmetic progression.
  • A204200 (program): INVERT transform of [1, 0, 1, 3, 9, 27, 81, …].
  • A204217 (program): G.f.: Sum_ n>=1 n * x^(n*(n+1)/2) / (1 - x^n).
  • A204221 (program): Integers of the form (n^2 - 1) / 15.
  • A204253 (program): Symmetric matrix given by f(i,j)=1+[(i+j) mod 3].
  • A204255 (program): Symmetric matrix given by f(i,j)=1+[(i+j) mod 4].
  • A204257 (program): Matrix given by f(i,j)=1+[(i+2j) mod 3], by antidiagonals.
  • A204259 (program): Matrix given by f(i,j) = 1 + [(2i+j) mod 3], by antidiagonals.
  • A204263 (program): Symmetric matrix: f(i,j)=(i+j mod 3), by antidiagonals.
  • A204267 (program): Symmetric matrix: f(i,j)=(i+j+1 mod 3), by antidiagonals.
  • A204269 (program): Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j)/4], by (constant) antidiagonals.
  • A204292 (program): Binomial(n, d(n)), where d(n) = A000005(n) is the number of divisors of n.
  • A204330 (program): a(n) is the number of k satisfying 1 <= k <= n and such that floor(sqrt(k)) divides k.
  • A204399 (program): Numbers k such that floor(2^k / 3^n) = 1.
  • A204418 (program): Periodic sequence 1,0,1,…, arranged in a triangle.
  • A204421 (program): Symmetric matrix: f(i,j)=(i+j+2 mod 3), by antidiagonals.
  • A204423 (program): Infinite matrix: f(i,j)=(2i+j mod 3), by antidiagonals.
  • A204425 (program): Infinite matrix: f(i,j)=(2i+j+1 mod 3), by antidiagonals.
  • A204427 (program): Infinite matrix: f(i,j)=(2i+j+2 mod 3), read by antidiagonals.
  • A204429 (program): Symmetric matrix: f(i,j)=(2i+j mod 3), by antidiagonals.
  • A204431 (program): Symmetric matrix: f(i,j)=(2i+j+1 mod 3), by antidiagonals.
  • A204433 (program): Symmetric matrix: f(i,j)=(2i+j+2 mod 3), by antidiagonals.
  • A204435 (program): Symmetric matrix: f(i,j)=((i+j)^2 mod 3), read by (constant) antidiagonals.
  • A204437 (program): Symmetric matrix: f(i,j)=((i+j+1)^2 mod 3), by (constant) antidiagonals.
  • A204439 (program): Symmetric matrix: f(i,j)=((i+j+2)^2 mod 3), by (constant) antidiagonals.
  • A204441 (program): Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j-1)/4], by (constant) antidiagonals.
  • A204443 (program): Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j)/4], by (constant) antidiagonals.
  • A204445 (program): Symmetric matrix: f(i,j)=floor[(i+j+4)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
  • A204447 (program): Symmetric matrix: f(i,j)=floor[(i+j+5)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.
  • A204453 (program): Period length 14: [0, 1, 2, 3, 4, 5, 6, 0, 6, 5, 4, 3, 2, 1] repeated.
  • A204454 (program): Odd numbers not divisible by 11.
  • A204455 (program): Squarefree product of all odd primes dividing n, and 1 if n is a power of 2: A099985/2.
  • A204457 (program): Odd numbers not divisible by 13.
  • A204458 (program): Odd numbers not divisible by 17.
  • A204467 (program): Number of 3-element subsets that can be chosen from 1,2,…,6n+3 having element sum 9n+6.
  • A204468 (program): Number of 4-element subsets that can be chosen from 1,2,…,4n having element sum 8n+2.
  • A204502 (program): Numbers such that floor[a(n)^2 / 9] is a square.
  • A204503 (program): Squares n^2 such that floor(n^2/9) is again a square.
  • A204539 (program): a(n) = number of integers N=4k whose “basin” sequence (cf. comment) ends in n^2.
  • A204542 (program): Numbers that are congruent to 1, 4, 11, 14 mod 15.
  • A204544 (program): Fractional part of (3/2)^n without the decimal point.
  • A204545 (program): Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
  • A204547 (program): Symmetric matrix: f(i,j)=floor[(i+j+4)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.
  • A204549 (program): Symmetric matrix: f(i,j)=floor[(i+j+5)/4]-floor[(i+j+3)/4], by (constant) antidiagonals.
  • A204551 (program): Symmetric matrix: f(i,j)=floor[(2i+2j+1)/4]-floor[(i+j)/4], by (constant) antidiagonals.
  • A204553 (program): Symmetric matrix: f(i,j)=floor[(2i+2j+2)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
  • A204556 (program): Left edge of the triangle A045975.
  • A204557 (program): Right edge of the triangle A045975.
  • A204558 (program): Row sums of the triangle A045975.
  • A204560 (program): Symmetric matrix: f(i,j)=floor[(2i+2j+4)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.
  • A204562 (program): Symmetric matrix: f(i,j) = floor((2i+2j+6)/4)-floor((i+j+3)/4), by (constant) antidiagonals.
  • A204595 (program): a(n) = maximal i such that there is a quasigroup q of order n such that q, q^2, …, q^i are quasigroups of order n.
  • A204623 (program): Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order
  • A204644 (program): Number of (n+1) X 2 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.
  • A204671 (program): a(n) = n^n (mod 6).
  • A204674 (program): a(n) = 4n^3 + 5n^2 + 2*n + 1.
  • A204675 (program): a(n) = 16n^2 + 2n + 1.
  • A204688 (program): a(n) = n^n (mod 3).
  • A204689 (program): a(n) = n^n (mod 4).
  • A204690 (program): n^n (mod 5).
  • A204693 (program): a(n) = n^n (mod 7).
  • A204694 (program): a(n) = n^n (mod 8).
  • A204695 (program): a(n) = n^n (mod 9).
  • A204696 (program): G.f.: (32x^7/(1-2x) + 16x^5 + 24x^6)/(1-2*x^2).
  • A204697 (program): Final nonzero digit of n^n in base 3.
  • A204707 (program): Number of (n+1) X 3 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
  • A204708 (program): Number of (n+1) X 4 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
  • A204766 (program): a(n) = 167*(n-1)-a(n-1) with n>1, a(1)=13.
  • A204769 (program): a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.
  • A204815 (program): Final nonzero digit of n^n in base 5.
  • A204816 (program): Final nonzero digit of n^n in base 6.
  • A204817 (program): Final nonzero digit of n^n in base 7.
  • A204818 (program): Final nonzero digit of n^n in base 8.
  • A204819 (program): Final nonzero digit of n^n in base 9.
  • A204877 (program): Continued fraction expansion of 3*tanh(1/3).
  • A204879 (program): Numbers that can be written as sum of perfect numbers.
  • A204896 (program): p(n)-q(n), where (p(n), q(n)) is the least pair of primes (ordered as in A204890) for which n divides p(n)-q(n).
  • A204897 (program): a(n) = (p(n)-q(n))/n, where (p(n), q(n)) is the least pair of primes for which n divides p(n)-q(n).
  • A204904 (program): p(n)-q(n), where (p(n), q(n)) is the least pair of odd primes for which n divides p(n)-q(n).
  • A204985 (program): Ordered differences of numbers 2^k for k>=1.
  • A204988 (program): The index j < k such that n divides 2^k - 2^j, where k is the least index (A204987) for which such j exists.
  • A205083 (program): Parity of A070885.
  • A205084 (program): a(n)=n 4’s sandwiched between two 1’s.
  • A205085 (program): a(n) = n 5’s sandwiched between two 1’s.
  • A205086 (program): a(n) = n 6’s sandwiched between two 1’s.
  • A205087 (program): a(n)=n 7’s sandwiched between two 1’s.
  • A205088 (program): a(n)=n 8’s sandwiched between two 1’s.
  • A205185 (program): Period 6: repeat [1, 8, 9, 8, 1, 0].
  • A205187 (program): Number of (n+1)X2 0..1 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor
  • A205219 (program): Number of (n+1)X2 0..1 arrays with the number of equal 2X2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order
  • A205220 (program): Number of (n+1) X 3 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.
  • A205248 (program): Number of (n+1) X 2 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock the same.
  • A205249 (program): Number of (n+1) X 3 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock the same.
  • A205312 (program): Number of (n+1) X 3 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.
  • A205342 (program): Number of length 5 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
  • A205354 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.
  • A205382 (program): s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)=(2j-1)^2.
  • A205383 (program): a(n) = (1/n)*A205382(n).
  • A205565 (program): Number of ways of writing n = u + v with u <= v, and u,v having in ternary representation no 3.
  • A205593 (program): a(2) = 0, a(3k) = a(3k+1) = a(2k), a(3k+2) = a(2k+1) + 1 for k >= 1.
  • A205633 (program): Expansion of f(x^3, x^7) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A205646 (program): Number of empty faces in Freij’s family of Hansen polytopes.
  • A205651 (program): Period 6: repeat [1, 6, 5, 4, 9, 0].
  • A205745 (program): a(n) = card d d*p = n, d odd, p prime
  • A205794 (program): Least positive integer j such that n divides C(k)-C(j) , where k, as in A205793, is the least number for which there is such a j, and C=A002808 (composite numbers).
  • A205808 (program): G.f.: Sum_ n=-oo..oo q^(9n^2 + 2n).
  • A205809 (program): G.f.: Sum_ n=-oo..oo q^(9n^2+4n).
  • A205825 (program): a(n) = n!/ceiling(n/2)!.
  • A205987 (program): G.f.: Sum_ n=-oo..oo q^(9n^2+8n).
  • A205988 (program): Expansion of f(x^1, x^9) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A206143 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
  • A206144 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
  • A206224 (program): Floor(n^2/4) appears 1+floor(n/2) times.
  • A206248 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having zero permanent.
  • A206258 (program): 1/8 the number of 2 X 2 -n..n arrays with a 2 X 2 -n..n inverse, i.e., with determinant +-1.
  • A206259 (program): Number of (n+1) X (n+1) 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206297 (program): Position of n in the canonical bijection from the positive integers to the positive rational numbers.
  • A206332 (program): Complement of A092754.
  • A206344 (program): Floor(n/2)^n.
  • A206350 (program): Position of 1/n in the canonical bijection from the positive integers to the positive rational numbers.
  • A206351 (program): a(n) = 7*a(n-1) - a(n-2) - 4 with a(1)=1, a(2)=3.
  • A206371 (program): 31*2^n + 1.
  • A206372 (program): 14*4^n - 1.
  • A206373 (program): (14*4^n + 1)/3.
  • A206374 (program): a(n) = (7*4^n - 1)/3.
  • A206399 (program): a(0) = 1; for n>0, a(n) = 41*n^2 + 2.
  • A206417 (program): (5F(n)+3L(n)-8)/2.
  • A206419 (program): Fibonacci sequence beginning 11, 7.
  • A206420 (program): Fibonacci sequence beginning 11, 8.
  • A206422 (program): Fibonacci sequence beginning 11, 9.
  • A206423 (program): Fibonacci sequence beginning 12, 7.
  • A206444 (program): Least n such that L(n)<-1 and L(n)<L(n-1), where L(k) means the least root of the polynomial p(k,x) defined at A206284, and a(1)=13.
  • A206456 (program): Number of 0..n arrays of length n+2 avoiding the consecutive pattern 0..n
  • A206492 (program): Sums of rows of the sequence of triangles with nonnegative integers and row widths defined by A004738.
  • A206525 (program): a(n) = 113*(n-1) - a(n-1) with n>1, a(1)=51.
  • A206526 (program): a(n) = 137*(n-1) - a(n-1) with n>1, a(1)=31.
  • A206543 (program): Period 10: repeat 1, 3, 5, 7, 9, 9, 7, 5, 3, 1.
  • A206544 (program): Period 12: repeat 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1.
  • A206545 (program): Period length 16: repeat 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1.
  • A206546 (program): Period 8: repeat [1, 7, 11, 13, 13, 11, 7, 1].
  • A206564 (program): Fibonacci sequence beginning 14, 13.
  • A206601 (program): 3^(n(n+1)/2) - 1.
  • A206605 (program): Fibonacci sequence beginning 14, 11.
  • A206607 (program): Fibonacci sequence beginning 13, 11.
  • A206608 (program): Fibonacci sequence beginning 13, 10.
  • A206609 (program): Fibonacci sequence beginning 13, 9.
  • A206610 (program): Fibonacci sequence beginning 13, 8.
  • A206611 (program): Fibonacci sequence beginning 13, 7.
  • A206612 (program): Fibonacci sequence beginning 13, 6.
  • A206641 (program): Fibonacci sequence beginning 14, 9.
  • A206687 (program): Number of n X 2 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.
  • A206694 (program): Number of n X 2 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.
  • A206723 (program): a(n) = 7*( ((3 + sqrt(5))/2)^n + ((3 - sqrt(5))/2)^n - 2 ).
  • A206735 (program): Triangle T(n,k), read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A206776 (program): a(n) = 3a(n-1) + 2a(n-2) for n>1, a(0)=2, a(1)=3.
  • A206787 (program): Sum of the odd squarefree divisors of n.
  • A206802 (program): a(n) = (1/2)*A185382(n).
  • A206803 (program): Sum_ 0<j<k<=n P(k)-P(j), where P(j)=A065091(j) is the j-th odd prime.
  • A206804 (program): (1/2)*A206803.
  • A206805 (program): Position of 2^n when 2^j and 3^k are jointly ranked; complement of A206807.
  • A206806 (program): Sum_ 0<j<k<=n s(k)-s(j), where s(j)=A002620(j) is the j-th quarter-square.
  • A206807 (program): Position of 3^n when 2^j and 3^k are jointly ranked; complement of A206805.
  • A206808 (program): Sum_ 0<j<n n^3-j^3.
  • A206809 (program): Sum_ 0<j<k<=n k^3-j^3.
  • A206816 (program): Sum_ 0<j<n (n!-j!).
  • A206817 (program): Sum_ 0<j<k<=n (k!-j!).
  • A206857 (program): Number of n X 2 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.
  • A206905 (program): n+[nr/t]+[ns/t], where []=floor, r=3, s=sqrt(3), t=1/s.
  • A206906 (program): n+[ns/r]+[nt/r], where []=floor, r=1/3, s=sqrt(3), t=1/s.
  • A206908 (program): a(n) = 4*n + floor(n/sqrt(3)).
  • A206912 (program): Position of log(n+1) when the partial sums of the harmonic series are jointly ranked with the set log(k+1) ; complement of A206911.
  • A206913 (program): Greatest binary palindrome <= n; the binary palindrome floor function.
  • A206915 (program): The index (in A006995) of the greatest binary palindrome <= n; also the ‘lower inverse’ of A006995.
  • A206916 (program): Index of the least binary palindrome >=n; also the “upper inverse” of A006995.
  • A206917 (program): Sum of binary palindromes in the half-open interval [2^(n-1), 2^n).
  • A206918 (program): Sum of binary palindromes p < 2^n.
  • A206919 (program): Sum of binary palindromes <= n.
  • A206927 (program): Minimal numbers of binary length n+1 such that the number of contiguous palindromic bit patterns in the binary representation is minimal.
  • A206981 (program): Number of nX2 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal
  • A207020 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207021 (program): Number of nX5 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A207025 (program): Number of 2 X n 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207064 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207069 (program): Number of 2 X n 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207106 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207165 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207166 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207168 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A207188 (program): Numbers matching polynomials y(k,x) that have x as a factor; see Comments.
  • A207255 (program): Number of 4 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
  • A207262 (program): a(n) = 2^(4n - 2) + 1.
  • A207332 (program): Double factorials (prime(n)-2)!!.
  • A207336 (program): One half of smallest positive nontrivial even solution of the congruence x^2 == 1 (mod A001748(n+2)), n>=1.
  • A207361 (program): Displacement under constant discrete unit surge.
  • A207363 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A207399 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207401 (program): Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207436 (program): Number of n X 2 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207449 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207450 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207451 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207452 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207596 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207597 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207598 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207656 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207701 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207832 (program): Numbers x such that 20*x^2+1 is a perfect square.
  • A207836 (program): a(n) = n*A052530(n)/2.
  • A207846 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.
  • A207872 (program): Denominator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial.
  • A208035 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 0 1 vertically.
  • A208044 (program): Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
  • A208064 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208079 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 0 vertically.
  • A208086 (program): Number of 4 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208087 (program): Number of 6 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208088 (program): Number of 7 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208089 (program): Number of 8 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208104 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208114 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208124 (program): a(1)=2, a(n) = (4n/3)*(2n-1)!! (see A001147) for n>1.
  • A208131 (program): Partial products of A052901.
  • A208138 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208139 (program): Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208140 (program): Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208141 (program): Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208147 (program): Sequence generated from A089080.
  • A208148 (program): Number of n state 1 dimensional radius-1 totalistic cellular automata.
  • A208176 (program): a(n) = F(n+1)^2, if n>=0 is even (F=A000045) and a(n) = (L(2n+2)+8)/5, if n is odd (L=A000204).
  • A208251 (program): Number of refactorable numbers less than or equal to n.
  • A208259 (program): Numbers starting and ending with digit 1.
  • A208279 (program): Central terms of Pascal’s triangle mod 10 (A008975).
  • A208283 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A208296 (program): Smallest positive nontrivial odd solution of the congruence x^2 == 1 (mod A001748(n+2)), n >= 1.
  • A208309 (program): Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.
  • A208354 (program): Number of compositions of n with at most one even part.
  • A208355 (program): Right edge of the triangle in A208101.
  • A208375 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208376 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208377 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208378 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208387 (program): Number of nX3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors
  • A208402 (program): Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208428 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
  • A208528 (program): Number of permutations of n>1 having exactly 3 points P on the boundary of their bounding square.
  • A208529 (program): Number of permutations of n > 1 having exactly 2 points on the boundary of their bounding square.
  • A208536 (program): Number of 5-bead necklaces of n colors not allowing reversal, with no adjacent beads having the same color.
  • A208537 (program): Number of 7-bead necklaces of n colors not allowing reversal, with no adjacent beads having the same color.
  • A208545 (program): Number of 7-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color.
  • A208556 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208558 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208561 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.
  • A208570 (program): LCM of n and smallest nondivisor of n.
  • A208598 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
  • A208599 (program): Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
  • A208638 (program): Number of 3 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208648 (program): Denominators of Pokrovskiy’s lower bound on the ratio of e(G^n) the number of edges in the n-th power of a graph G, to E(G) the number of edges of G.
  • A208658 (program): Row sums of A208657.
  • A208665 (program): Numbers that match odd ternary polynomials; see Comments.
  • A208704 (program): Number of nX3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208705 (program): Number of n X 4 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208881 (program): Number of words either empty or beginning with the first letter of the ternary alphabet, where each letter of the alphabet occurs n times.
  • A208882 (program): Number of representations of square of prime(n) as a^2 + b^2 + c^2 with 0 < a <= b <= c.
  • A208884 (program): a(n) = (a(n-1) + n)/2^k where 2^k is the largest power of 2 dividing a(n-1) + n, for n>1 with a(1)=1.
  • A208891 (program): Pascal’s triangle matrix augmented with a right border of 1’s.
  • A208900 (program): Number of bitstrings of length n which (if having two or more runs) the last two runs have different lengths.
  • A208901 (program): Number of bitstrings of length n (with at least two runs) where the last two runs have different lengths.
  • A208902 (program): The sum over all bitstrings b of length n of the number of runs in b not immediately followed by a longer run.
  • A208903 (program): The sum over all bitstrings b of length n with at least two runs of the number of runs in b not immediately followed by a longer run.
  • A208946 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
  • A208950 (program): a(4n) = n(16n^2-1)/3, a(2n+1) = n(n+1)(2n+1)/6, a(4n+2) = (4n+1)(4n+2)(4*n+3)/6.
  • A208954 (program): n^4(n-1)(n+1)/12.
  • A208971 (program): Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first and second differences in -n..n.
  • A208981 (program): Number of iterations of the Collatz recursion required to reach a power of 2.
  • A208994 (program): Number of 3-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.
  • A208995 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.
  • A209008 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.
  • A209081 (program): Floor(A152170(n)/n^n). Floor of the expected value of the cardinality of the image of a function from [n] to [n].
  • A209084 (program): a(n) = 2a(n-1) + 4a(n-2) with n>1, a(0)=0, a(1)=4.
  • A209094 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A209116 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
  • A209188 (program): Smallest prime factor of n^2 + n - 1.
  • A209189 (program): Smallest prime factor of n^2 + n + 1.
  • A209197 (program): Column 1 of triangle A209196.
  • A209229 (program): Characteristic function of powers of 2, cf. A000079.
  • A209231 (program): Number of binary words of length n such that there is at least one 0 and every run of consecutive 0’s is of length >= 4.
  • A209262 (program): a(n) = 1 + 2n^2 + 3n^3 + 4*n^4.
  • A209263 (program): a(n) = 1 + 2n^2 + 3n^3 + 4n^4 + 5n^5.
  • A209264 (program): a(n) = 1 + 2n^2 + 3n^3 + 4n^4 +5n^5 + 6*n^6.
  • A209265 (program): a(n) = 1 + 2n^2 + 3n^3 + 4n^4 +5n^5 + 6n^6 + 7n^7.
  • A209267 (program): 1 + 2n^2 + 3n^3 + 4n^4 + 5n^5 + 6n^6 + 7n^7 + 8*n^8.
  • A209275 (program): a(n) = 1 + 2n^2 + 3n^3 + 4n^4 + 5n^5 + 6n^6 + 7n^7 + 8n^8 + 9n^9.
  • A209281 (program): Start with first run [0,1] then, for n >= 2, the n-th run has length 2^n and is the concatenation of [a(1),a(2),…,a(2^n/2)] and [n-a(1),n-a(2),…,n-a(2^n/2)].
  • A209290 (program): Number of elements whose preimage is the empty set summed over all functions f: 1,2,…,n -> 1,2,…,n .
  • A209291 (program): Sum of the refactorable numbers less than or equal to n.
  • A209294 (program): a(n) = (7n^2 - 7n + 4)/2.
  • A209295 (program): Antidiagonal sums of the gcd(.,.) array A109004.
  • A209297 (program): Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n.
  • A209302 (program): Table T(n,k) = max n+k-1, n+k-1 n, k > 0, read by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1).
  • A209304 (program): Table T(n,k)=n+4*k-4 n, k > 0, read by antidiagonals.
  • A209345 (program): Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal
  • A209350 (program): Number of initially rising meander words, where each letter of the cyclic n-ary alphabet occurs twice.
  • A209356 (program): The function g(n), the inverse of f(k) the shortest length of a binary linear intersecting code.
  • A209359 (program): a(n) = 2^n * (n^4 - 4n^3 + 18n^2 - 52*n + 75) - 75.
  • A209427 (program): T(n,k) = binomial(n,k)^n.
  • A209466 (program): Final digit of n^n - n.
  • A209492 (program): a(0)=1; for n >= 1, let k = floor((1 + sqrt(8*n-7))/2), m = n - (k^2 - k+2)/2. Then a(n) = 2^k + 2^(m+1) - 1.
  • A209505 (program): Half the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having two or four distinct clockwise edge differences.
  • A209518 (program): Triangle by rows, reversal of A104712.
  • A209529 (program): Half the number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
  • A209530 (program): Half the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209531 (program): Half the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209532 (program): Half the number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209533 (program): Half the number of (n+1)X8 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
  • A209544 (program): Primes not expressed in form n<+>2, where operation <+> defined in A206853.
  • A209594 (program): Number of 3 X 3 0..n arrays with every element equal to a diagonal or antidiagonal reflection.
  • A209615 (program): Completely multiplicative with a(p^e) = 1 if p == 1 (mod 4), a(p^e) = (-1)^e otherwise.
  • A209628 (program): Number of squarefree numbers < n that are not prime.
  • A209634 (program): Triangle with (1,4,7,10,13,16…,(3*n-2),…) in every column, shifted down twice.
  • A209635 (program): a(n) = A008683(A000265(n)).
  • A209646 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209647 (program): Number of n X 5 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209648 (program): Number of n X 6 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209661 (program): a(n) = (-1)^A083025(n).
  • A209675 (program): Radon function at even positions: a(n) = A003484(2*n).
  • A209721 (program): 1/4 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209722 (program): 1/4 the number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209723 (program): 1/4 the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209724 (program): 1/4 the number of (n+1) X 6 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209725 (program): 1/4 the number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209726 (program): 1/4 the number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209876 (program): a(n) = 36*n - 6.
  • A209890 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having two distinct values, and new values 0..2 introduced in row major order.
  • A209899 (program): Floor of the expected number of empty cells in a random placement of 2n balls into n cells.
  • A209900 (program): Floor of the expected number of occupied cells in a random placement of 2n balls into n cells.
  • A209927 (program): Decimal expansion of sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + … )))).
  • A209931 (program): Numbers n such that smallest digit of all divisors of n is 1.
  • A209938 (program): Number of groups of order prime(n)^5 with nontrivial unramified Brauer groups.
  • A209971 (program): a(n) = A000129(n) + n.
  • A209978 (program): a(n) = A196227(n)/2.
  • A209979 (program): Number of unimodular 2 X 2 matrices having all elements in 1,2,…,n .
  • A209981 (program): Number of singular 2 X 2 matrices having all elements in -n,…,n .
  • A209982 (program): Number of 2 X 2 matrices having all elements in -n,…,n and determinant 1.
  • A209983 (program): (A209982)/2.
  • A210000 (program): Number of unimodular 2 X 2 matrices having all terms in 0,1,…,n .
  • A210032 (program): a(n)=n for n=1,2,3 and 4; a(n)=5 for n>=5.
  • A210062 (program): Number of digits in 7^n.
  • A210100 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.
  • A210241 (program): Partial sums of A073093.
  • A210251 (program): Residues modulo 100 of odd squares.
  • A210256 (program): Differences of the sum of distinct values of floor(n/k), k=1,…,n .
  • A210277 (program): a(n) = (3*n)!/3^n.
  • A210357 (program): Location of the maximum modulus in the inverse of Hilbert’s matrix.
  • A210370 (program): Number of 2 X 2 matrices with all elements in 0,1,…,n and odd determinant.
  • A210373 (program): Number of 2 X 2 matrices with all elements in 0,1,…,n and positive odd determinant.
  • A210374 (program): Number of 2 X 2 matrices with all terms in 0,1,…,n and (sum of terms) = n+2.
  • A210375 (program): Number of 2 X 2 matrices with all terms in 0,1,…,n and (sum of terms) = n + 3.
  • A210378 (program): Number of 2 X 2 matrices with all terms in 0,1,…,n and even trace.
  • A210379 (program): Number of 2 X 2 matrices with all terms in 0,1,…,n and odd trace.
  • A210433 (program): Natural numbers k such that floor(v) * ceiling(v)^2 = k, where v = k^(1/3).
  • A210434 (program): Number of digits in 4^n.
  • A210435 (program): Number of digits in 5^n.
  • A210436 (program): Number of digits in 6^n.
  • A210437 (program): Greatest prime factor of reversal of digits of n.
  • A210440 (program): a(n) = 2n(n+1)*(n+2)/3.
  • A210448 (program): Total number of different letters summed over all ternary words of length n.
  • A210454 (program): Cipolla pseudoprimes to base 2: (4^p-1)/3 for any prime p greater than 3.
  • A210461 (program): Cipolla pseudoprimes to base 3: (9^p-1)/8 for any odd prime p.
  • A210464 (program): Number of bracelets with 2 blue, 2 red, and n black beads.
  • A210469 (program): a(n) = n - primepi(2n).
  • A210497 (program): 2*prime(n+1) - prime(n).
  • A210527 (program): a(n) = 9n^2 + 39n + 83.
  • A210530 (program): T(n,k) = (k + 3n - 2 - (k+n-2)(-1)^(k+n))/2 n, k > 0, read by antidiagonals.
  • A210535 (program): Second inverse function (numbers of columns) for pairing function A209293.
  • A210569 (program): a(n) = (n-3)(n-2)(n-1)n(n+1)/30.
  • A210615 (program): Least semiprime dividing n, or 0 if no semiprime divides n.
  • A210621 (program): Decimal expansion of 256/81.
  • A210622 (program): Decimal expansion of 377/120.
  • A210626 (program): Values of the prime-generating polynomial 4n^2 - 284n + 3449.
  • A210645 (program): Area A of the triangles such that A, the sides and one of the altitudes are four consecutive integers of an arithmetic progression d.
  • A210675 (program): a(n)=a(n-1)+a(n-2)+n+4, a(0)=0, a(1)=1.
  • A210677 (program): a(n)=a(n-1)+a(n-2)+n+1, a(0)=a(1)=1.
  • A210678 (program): a(n)=a(n-1)+a(n-2)+n+2, a(0)=a(1)=1.
  • A210695 (program): a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.
  • A210709 (program): Number of trivalent connected simple graphs with 2n nodes and girth at least 9.
  • A210728 (program): a(n) = a(n-1) + a(n-2) + n + 2 with n>1, a(0)=1, a(1)=2.
  • A210729 (program): a(n) = a(n-1) + a(n-2) + n + 3 with n>1, a(0)=1, a(1)=2.
  • A210730 (program): a(n) = a(n-1) + a(n-2) + n + 2 with n>1, a(0)=a(1)=0.
  • A210731 (program): a(n) = a(n-1) + a(n-2) + n + 3 with n>1, a(0) = a(1) = 0.
  • A210736 (program): Expansion of (1 + sqrt( (1 + 2x) / (1 - 2x))) / 2 in powers of x.
  • A210745 (program): The leaf weight sequence w_ 2,3,4 .
  • A210772 (program): Number of partitions of 2^n into powers of 2 less than or equal to 8.
  • A210826 (program): G.f.: Sum_ n>=1 a(n)*x^n/(1 - x^n) = Sum_ n>=1 x^(n^3).
  • A210840 (program): Sum of the 8th powers of the digits of n.
  • A210934 (program): Sum of prime factors of prime(n)+1 (counted with multiplicity).
  • A210936 (program): Sum of prime factors of prime(n)-1 (counted with multiplicity).
  • A210958 (program): Decimal expansion of 1 - (Pi/4).
  • A210977 (program): A005475 and positive terms of A000566 interleaved.
  • A210978 (program): A186029 and positive terms of A001106 interleaved.
  • A210981 (program): A062725 and positive terms of A051682 interleaved.
  • A210982 (program): Zero together with A126264 and positive terms of A051624 interleaved.
  • A210983 (program): Total number of pairs of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A210984 (program): Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A211004 (program): Number of distinct regions in the set of partitions of n.
  • A211006 (program): Pair (n,p) where n is the sum of adjacent nonprimes and p is the sum of adjacent primes.
  • A211007 (program): Surface area of the first n faces of the structure mentioned in A211006.
  • A211010 (program): Value on the axis “x” of the endpoint of the structure of A211000 at n-th stage.
  • A211012 (program): Total area of all squares and rectangles after 2^n stages in the toothpick structure of A139250, assuming the toothpicks have length 2.
  • A211013 (program): Second 13-gonal numbers: a(n) = n(11n+9)/2.
  • A211014 (program): Second 14-gonal numbers: n(6n+5).
  • A211065 (program): Number of 2 X 2 matrices having all terms in 1,…,n and odd determinant.
  • A211068 (program): Number of 2 X 2 matrices having all terms in 1,…,n and positive odd determinant.
  • A211159 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=n+1.
  • A211164 (program): Number of compositions of n with at most one odd part.
  • A211173 (program): (2n)!^n (modulo 2n+1).
  • A211197 (program): Table T(n,k) = 2n + ((-1)^n)(1/2 - (k-1) mod 2) - 1/2; n, k > 0, read by antidiagonals.
  • A211199 (program): Sum of the 16th powers of the decimal digits of n.
  • A211221 (program): For any partition of n consider the product of the sigma of each element. Sequence gives the maximum of such values.
  • A211227 (program): Row sums of A211226.
  • A211253 (program): Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211261 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=2n.
  • A211263 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=floor(n/2).
  • A211264 (program): Number of integer pairs (x,y) such that 0 < x < y <= n and x*y <= n.
  • A211265 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=n+1.
  • A211266 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=2n.
  • A211270 (program): Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=2n.
  • A211275 (program): Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= floor(n/2).
  • A211280 (program): Numerator of prime(n+1) - prime(n)/2.
  • A211317 (program): A211316(2n+1).
  • A211322 (program): Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211329 (program): Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211372 (program): Side length of smallest square containing n L’s with short sides 1, 2, …, n.
  • A211374 (program): Product of all the parts in the partitions of n into exactly 2 parts.
  • A211379 (program): Number of pairs of parallel diagonals in a regular n-gon.
  • A211385 (program): Values of n for which product_ p n, p prime 1 + 1/p > e^gamma*log(log(n)).
  • A211386 (program): Expansion of 1/((1-2x)^5(1-x)).
  • A211388 (program): Expansion of 1/((1-2x)^6(1-x)).
  • A211390 (program): The minimum cardinality of an n-qubit unextendible product basis.
  • A211412 (program): a(n) = 4*n^4 + 1.
  • A211422 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w^2 + x*y = 0.
  • A211430 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w^2+x+y=0.
  • A211431 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w^3+(x+y)^2=0.
  • A211433 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w+2x+4y=0.
  • A211434 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w+2x+5y=0.
  • A211435 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w+4x+5y=0.
  • A211438 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w+2x+2y=0.
  • A211439 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w+3x+3y=0.
  • A211440 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and 2w+3x+3y=0.
  • A211441 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w + x + y = 2.
  • A211466 (program): Number of (n+1) X (n+1) -8..8 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211480 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w + 2x + 3y = 1.
  • A211481 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and w+2x+3y=n.
  • A211483 (program): Number of ordered triples (w,x,y) with all terms in -n,…,0,…,n and (w+n)^2=x+y.
  • A211490 (program): Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211519 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w=2x-3y.
  • A211520 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w + 4y = 2x.
  • A211521 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w + 2x = 4y.
  • A211522 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w + 5y = 2x.
  • A211523 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w+2x=5y.
  • A211524 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w=3x+5y.
  • A211525 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set t,u,v in 0,1 ((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two or four distinct values for every i,j,k<=n.
  • A211533 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w=3x-5y.
  • A211534 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w = 3x + 3y.
  • A211535 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w=4x+5y.
  • A211538 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and 2w=2n-2x-y.
  • A211539 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and 2w = 2n - 2x + y.
  • A211540 (program): Number of ordered triples (w,x,y) with all terms in 1..n and 2w = 3x + 4y.
  • A211542 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and 2w=4y-3x.
  • A211543 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and 2w=3x+5y.
  • A211545 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and w+x+y>0.
  • A211546 (program): Number of ordered triples (w,x,y) with all terms in 1,…,n and w=3x-3y.
  • A211547 (program): The squares n^2, n >= 0, each one written three times.
  • A211549 (program): Number of (n+1) X (n+1) -9..9 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211562 (program): Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, and containing the value n-1.
  • A211612 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and w+x+y>=0.
  • A211613 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and w+x+y>1.
  • A211614 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and w+x+y>2.
  • A211615 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and -1<=w+x+y<=1.
  • A211616 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and -2<=w+x+y<=2.
  • A211617 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and 2w+x+y>0.
  • A211618 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and 2w+x+y>1.
  • A211620 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and -1<=2w+x+y<=1.
  • A211622 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and w+2x+3y>1.
  • A211623 (program): Number of ordered triples (w,x,y) with all terms in -n,…-1,1,…,n and -1<=w+2x+3y<=1.
  • A211661 (program): Number of iterations log_3(log_3(log_3(…(n)…))) such that the result is < 1.
  • A211662 (program): Number of iterations log_3(log_3(log_3(…(n)…))) such that the result is < 2.
  • A211663 (program): Number of iterations log(log(log(…(n)…))) such that the result is < 1, where log is the natural logarithm.
  • A211664 (program): Number of iterations (…f_4(f_3(f_2(n))))…) such that the result is < 1, where f_j(x):=log_j(x).
  • A211665 (program): Minimal number of iterations of log_10 applied to n until the result is < 1.
  • A211666 (program): Number of iterations log_10(log_10(log_10(…(n)…))) such that the result is < 2.
  • A211667 (program): Number of iterations sqrt(sqrt(sqrt(…(n)…))) such that the result is < 2.
  • A211668 (program): Number of iterations sqrt(sqrt(sqrt(…(n)…))) such that the result is < 3.
  • A211669 (program): Number of iterations f(f(f(…(n)…))) such that the result is < 2, where f(x) = cube root of x.
  • A211670 (program): Number of iterations (…f_4(f_3(f_2(n))))…) such that the result is < 2, where f_j(x):=x^(1/j).
  • A211703 (program): a(n) = n + [n/2] + [n/3] + [n/4], where [] = floor.
  • A211704 (program): a(n) = n + [n/2] + [n/3] + [n/4] + [n/5], where []=floor.
  • A211710 (program): Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.
  • A211715 (program): Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two or four distinct values.
  • A211773 (program): Prime-generating polynomial: 2n^2 - 108n + 1259.
  • A211775 (program): a(n) = 2n^2 - 212n + 5419.
  • A211784 (program): n^2 + floor(n^2/2) + floor(n^2/3).
  • A211786 (program): n^3 + floor(n^3/2).
  • A211813 (program): Number of (n+1) X (n+1) -10..10 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.
  • A211837 (program): Number of nonnegative integer arrays of length n+4 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.
  • A211850 (program): Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.
  • A211866 (program): (9^n - 5) / 4.
  • A211899 (program): Number of triangular n X n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any neighbor, and containing the value n(n+1)/2-2.
  • A211905 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-2.
  • A211911 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal, vertical, diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.
  • A211924 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal, vertical or antidiagonal neighbor, and containing the value n(n+1)/2-2
  • A211958 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.
  • A212012 (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.
  • A212013 (program): Triangle read by rows: total number of pairs of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A212014 (program): Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A212031 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element at a city block distance of two, and containing the value n(n+1)/2-2.
  • A212039 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-2.
  • A212068 (program): Number of (w,x,y,z) with all terms in 1,…,n and 2w=x+y+z.
  • A212069 (program): Number of (w,x,y,z) with all terms in 1,…,n and 3*w = x+y+z.
  • A212072 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2)^3.
  • A212088 (program): Number of (w,x,y,z) with all terms in 1,…,n and w<average x,y,z .
  • A212089 (program): Number of (w,x,y,z) with all terms in 1,…,n and w>=average x,y,z .
  • A212090 (program): Number of (w,x,y,z) with all terms in 1,…,n and w<x+y+z.
  • A212126 (program): Period 13: repeat (0,0,1,0,0,1,0,1,0,0,1,0,1).
  • A212133 (program): Number of (w,x,y,z) with all terms in 1,…,n and median=mean.
  • A212134 (program): Number of (w,x,y,z) with all terms in 1,…,n and median<=mean.
  • A212135 (program): Number of (w,x,y,z) with all terms in 1,…,n and median<mean.
  • A212156 (program): ((6*A023000(n))^3 + 1)/7^n, n >= 0.
  • A212158 (program): ((prime(n)- 1)/2)!, n >= 2.
  • A212159 (program): a(n) = (-1)^((prime(n) + 1)/2).
  • A212160 (program): Numbers congruent to 2 or 10 modulo 13.
  • A212161 (program): Numbers 6 or 10 modulo 17.
  • A212181 (program): Largest odd divisor of tau(n): a(n) = A000265(A000005(n)).
  • A212246 (program): Number of (w,x,y,z) with all terms in 1,…,n and w <= x > y <= z.
  • A212247 (program): Number of (w,x,y,z) with all terms in 1,…,n and 3w=x+y+z+n.
  • A212251 (program): Number of (w,x,y,z) with all terms in 1,…,n and 3w = x + y + z + n + 1.
  • A212252 (program): Number of (w,x,y,z) with all terms in 1,…,n and 3w=x+y+z+n+2.
  • A212254 (program): Number of (w,x,y,z) with all terms in 1,…,n and w=x+2y+3z-n.
  • A212262 (program): a(n) = 3^n + Fibonacci(n).
  • A212272 (program): a(n) = Fibonacci(n) + n^3.
  • A212291 (program): Number of permutations of n elements with at most one fixed point.
  • A212294 (program): Sums of (zero or more) distinct twin primes.
  • A212303 (program): a(n) = n!/([(n-1)/2]!*[(n+1)/2]!) for n>0, a(0)=0, and where [ ] = floor.
  • A212307 (program): Numerator of n!/3^n.
  • A212325 (program): Prime-generating polynomial: n^2 + 3*n - 167.
  • A212329 (program): Expansion of x(5+x)/(1-7x+7*x^2-x^3).
  • A212331 (program): a(n) = 5n(n+5)/2.
  • A212333 (program): n-th power of the n-th pentagonal number.
  • A212336 (program): Expansion of 1/(1 - 23x + 23x^2 - x^3).
  • A212337 (program): Expansion of 1/(1-4x+3x^2)^2.
  • A212342 (program): Sequence of coefficients of x^0 in marked mesh pattern generating function Q_ n,132 ^(0,3,0,0)(x).
  • A212343 (program): a(n) = (n+1)(n-2)(n-3)/2.
  • A212344 (program): Sequence of coefficients of x^(n-3) in marked mesh pattern generating function Q_ n,132 ^(0,3,0,0)(x).
  • A212346 (program): Sequence of coefficients of x^0 in marked mesh pattern generating function Q_ n,132 ^(0,4,0,0)(x).
  • A212347 (program): Sequence of coefficients of x^1 in marked mesh pattern generating function Q_ n,132 ^(0,4,0,0)(x).
  • A212350 (program): Maximal number of “good” manifolds in an n-serial polytope.
  • A212356 (program): Number of terms of the cycle index polynomial Z(D_n) for the dihedral group D_n.
  • A212415 (program): Number of (w,x,y,z) with all terms in 1,…,n and w=y<=z.
  • A212427 (program): a(n) = 17*n + A000217(n-1).
  • A212428 (program): a(n) = 18*n + A000217(n-1).
  • A212495 (program): Numbers all of whose base 11 digits are even.
  • A212501 (program): Number of (w,x,y,z) with all terms in 1,…,n and w > x < y >= z.
  • A212503 (program): Number of (w,x,y,z) with all terms in 1,…,n and w<2x and y<2z.
  • A212505 (program): Number of (w,x,y,z) with all terms in 1,…,n and w<2x and y>=2z.
  • A212506 (program): Number of (w,x,y,z) with all terms in 1,…,n and w<=2x and y<=2z.
  • A212518 (program): Number of (w,x,y,z) with all terms in 1,…,n and w>2x and y>3z.
  • A212519 (program): Number of (w,x,y,z) with all terms in 1,…,n and w>2x and y>=3z.
  • A212522 (program): Number of (w,x,y,z) with all terms in 1,…,n and w>=2x and y>3z.
  • A212523 (program): Number of (w,x,y,z) with all terms in 1,…,n and w+x<y+z.
  • A212530 (program): Difference between the sum of the first n primes s(n) and the nearest square < s(n).
  • A212555 (program): Values of   G*(n)   related to construction of graphs which contain all small trees.
  • A212560 (program): Number of (w,x,y,z) with all terms in 1,…,n and w+x<=y+z.
  • A212561 (program): Number of (w,x,y,z) with all terms in 1,…,n and w + x = 2y + 2z.
  • A212565 (program): Number of (w,x,y,z) with all terms in 1,…,n and w+x>=2y+2z.
  • A212568 (program): Number of (w,x,y,z) with all terms in 1,…,n and w< x-y + y-z .
  • A212570 (program): Number of (w,x,y,z) with all terms in 1,…,n and w-x = x-y + y-z .
  • A212573 (program): Number of (w,x,y,z) with all terms in 1,…,n and w-x > x-y + y-z .
  • A212574 (program): Number of (w,x,y,z) with all terms in 1,…,n and w-x >= x-y + y-z .
  • A212578 (program): Number of (w,x,y,z) with all terms in 1,…,n and w-x = 2* x-y - y-z .
  • A212591 (program): a(n) = smallest value of k for which A020986(k) = n.
  • A212595 (program): Let f(n) = 2n-7. Difference between f(n) and the nearest prime < f(n).
  • A212598 (program): a(n) = n - m!, where m is the largest number such that m! <= n.
  • A212656 (program): a(n) = 5*n^2 + 1.
  • A212668 (program): a(n) = (16/3)(n+1)n(n-1) + 8n^2 + 1.
  • A212669 (program): a(n) = 2/15 * (32n^5 + 80n^4 + 40n^3 - 20n^2 + 3*n).
  • A212673 (program): Number of (w,x,y,z) with all terms in 1,…,n and w<= x-y + y-z .
  • A212674 (program): Number of (w,x,y,z) with all terms in 1,…,n and w > x-y + y-z .
  • A212677 (program): Number of (w,x,y,z) with all terms in 1,…,n and w+y= x-y + y-z .
  • A212679 (program): Number of (w,x,y,z) with all terms in 1,…,n and x-y = y-z .
  • A212680 (program): Number of (w,x,y,z) with all terms in 1,…,n and x-y = y-z +1.
  • A212681 (program): Number of (w,x,y,z) with all terms in 1,…,n and x-y < y-z .
  • A212682 (program): Number of (w,x,y,z) with all terms in 1,…,n and x-y >= y-z .
  • A212683 (program): Number of (w,x,y,z) with all terms in 1,…,n and x-y = w + y-z .
  • A212684 (program): Number of (w,x,y,z) with all terms in 1,…,n and x-y =n-w+ y-z .
  • A212685 (program): Number of (w,x,y,z) with all terms in 1,…,n and w-x =w+ y-z .
  • A212686 (program): Number of (w,x,y,z) with all terms in 1,…,n and 2 w-x =n+ y-z .
  • A212688 (program): Number of (w,x,y,z) with all terms in 1,…,n and 2 w-x >=n+ y-z .
  • A212689 (program): Number of (w,x,y,z) with all terms in 1,…,n and 2 w-x >n+ y-z .
  • A212691 (program): Number of (w,x,y,z) with all terms in 1,…,n and w+ x-y <= x-z + y-z .
  • A212692 (program): Number of (w,x,y,z) with all terms in 1,…,n and w< x-y + y-z .
  • A212697 (program): a(n) = 2n3^(n-1).
  • A212698 (program): Main transitions in systems of n particles with spin 3/2.
  • A212699 (program): Main transitions in systems of n particles with spin 2.
  • A212700 (program): a(n) = 5n6^(n-1).
  • A212701 (program): Main transitions in systems of n particles with spin 3.
  • A212702 (program): Main transitions in systems of n particles with spin 7/2.
  • A212703 (program): Main transitions in systems of n particles with spin 4.
  • A212704 (program): a(n) = 9n10^(n-1).
  • A212714 (program): Number of (w,x,y,z) with all terms in 1,…,n and w-x >= w + y-z .
  • A212739 (program): a(n) = 2^(n^2) - 1.
  • A212740 (program): Number of (w,x,y,z) with all terms in 0,…,n and max w,x,y,z <2*min w,x,y,z .
  • A212742 (program): Number of (w,x,y,z) with all terms in 0,…,n and max w,x,y,z <=2*min w,x,y,z .
  • A212743 (program): Number of (w,x,y,z) with all terms in 0,…,n and max w,x,y,z >2*min w,x,y,z .
  • A212747 (program): Number of (w,x,y,z) with all terms in 0,…,n and 2w=floor((x+y+z)/2)).
  • A212748 (program): Number of (w,x,y,z) with all terms in 0,…,n and w=2*floor((x+y+z)/2)).
  • A212753 (program): Number of (w,x,y,z) with all terms in 0,…,n and at least one of these conditions holds: w<R, x<R, y>R, z>R, where R = max w,x,y,z - min w,x,y,z .
  • A212754 (program): Number of (w,x,y,z) with all terms in 0,…,n and at least one of these conditions holds: w<R, x>R, y>R, z>R, where R = max w,x,y,z - min w,x,y,z .
  • A212755 (program): Number of (w,x,y,z) with all terms in 0,…,n and w-x =max w,x,y,z -min w,x,y,z .
  • A212759 (program): Number of (w,x,y,z) with all terms in 0,…,n and w, x, and y even.
  • A212760 (program): Number of (w,x,y,z) with all terms in 0,…,n , w even, and x = y + z.
  • A212761 (program): Number of (w,x,y,z) with all terms in 0,…,n , w odd, x and y even.
  • A212762 (program): Number of (w,x,y,z) with all terms in 0,…,n , w and x odd, y even.
  • A212763 (program): Number of (w,x,y,z) with all terms in 0,…,n , and w, x and y odd.
  • A212764 (program): Number of (w,x,y,z) with all terms in 0,…,n , w, x and y odd, and z odd.
  • A212765 (program): Number of (w,x,y,z) with all terms in 0,…,n , w even and x, y, and z odd.
  • A212766 (program): Number of (w,x,y,z) with all terms in 0,…,n , w even and x odd.
  • A212767 (program): Number of (w,x,y,z) with all terms in 0,…,n , w even, x even, and w+x=y+z.
  • A212769 (program): p*q modulo (p+q) with p, q consecutive primes.
  • A212772 (program): Floor((n+1)(n-3)(n-4)/12).
  • A212790 (program): (prime(n) + n) mod (prime(n) - n).
  • A212793 (program): Characteristic function of cubefree numbers, A004709.
  • A212797 (program): Row 2 of array in A212796.
  • A212804 (program): Expansion of (1 - x)/(1 - x - x^2).
  • A212823 (program): Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.
  • A212831 (program): a(4n) = 2n, a(2n+1) = 2n+1, a(4n+2) = 2n+2.
  • A212832 (program): Decimal expansion of 5/24.
  • A212836 (program): Number of 0..n arrays of length 3 with 0 never adjacent to n.
  • A212837 (program): Number of 0..n arrays of length 4 with 0 never adjacent to n.
  • A212838 (program): Number of 0..n arrays of length 5 with 0 never adjacent to n.
  • A212839 (program): Number of 0..n arrays of length 6 with 0 never adjacent to n.
  • A212844 (program): a(n) = 2^(n+2) mod n.
  • A212850 (program): Number of n X 3 arrays with rows being permutations of 0..2 and no column j greater than column j-1 in all rows.
  • A212864 (program): Number of nondecreasing sequences of n 1..4 integers with no element dividing the sequence sum.
  • A212889 (program): Number of (w,x,y,z) with all terms in 0,…,n and even range.
  • A212890 (program): Number of (w,x,y,z) with all terms in 0,…,n and odd range.
  • A212892 (program): a(n) = n^4/8 if n is even, a(n) = (n^2-1)^2/8 if n is odd.
  • A212893 (program): Number of quadruples (w,x,y,z) with all terms in 0,…,n such that w-x, x-y, and y-z all have the same parity.
  • A212896 (program): Number of (w,x,y,z) with all terms in 0,…,n and (least gapsize)<2.
  • A212901 (program): Number of (w,x,y,z) with all terms in 0,…,n and equal consecutive gap sizes.
  • A212905 (program): Number of (w,x,y,z) with all terms in 0,…,n and w-x + x-y+ y-z =2n.
  • A212959 (program): Number of (w,x,y) such that w,x,y are all in 0,…,n and w-x = x-y .
  • A212960 (program): Number of (w,x,y) with all terms in 0,…,n and w-x != x-y .
  • A212963 (program): Number of (w,x,y) with all terms in 0,…,n and w-x != x-y != y-z .
  • A212964 (program): Number of (w,x,y) with all terms in 0,…,n and w-x < x-y < y-w .
  • A212965 (program): Number of (w,x,y) with all terms in 0,…,n and w=range w,x,y .
  • A212967 (program): Number of (w,x,y) with all terms in 0,…,n and w < range w,x,y .
  • A212968 (program): Number of (w,x,y) with all terms in 0,…,n and w>=range w,x,y .
  • A212969 (program): Number of (w,x,y) with all terms in 0,…,n and w!=x and x>range w,x,y .
  • A212970 (program): Number of (w,x,y) with all terms in 0,…,n and w!=x and x>range w,x,y .
  • A212971 (program): Number of (w,x,y) with all terms in 0,…,n and w<floor((x+y)/3)).
  • A212972 (program): Number of (w,x,y) with all terms in 0,…,n and w<floor((x+y)/3)).
  • A212973 (program): Number of (w,x,y) with all terms in 0,…,n and w<=floor((x+y)/3)).
  • A212974 (program): Number of (w,x,y) with all terms in 0,…,n and w>floor((x+y)/3)).
  • A212975 (program): Number of (w,x,y) with all terms in 0,…,n and even range.
  • A212976 (program): Number of (w,x,y) with all terms in 0,…,n and odd range.
  • A212977 (program): Number of (w,x,y) with all terms in 0,…,n and n/2 < w+x+y <= n.
  • A212978 (program): Number of (w,x,y) with all terms in 0,…,n and range = 2*n-w-x.
  • A212979 (program): Number of (w,x,y) with all terms in 0,…,n and range=average.
  • A212980 (program): Number of (w,x,y) with all terms in 0,…,n and w<x+y and x<y.
  • A212981 (program): Number of (w,x,y) with all terms in 0,…,n and w <= x + y and x < y.
  • A212982 (program): Number of (w,x,y) with all terms in 0,…,n and w<x+y and x<=y.
  • A212983 (program): Number of (w,x,y) with all terms in 0,…,n and w<=x+y and x<=y.
  • A212984 (program): Number of (w,x,y) with all terms in 0..n and 3w = x+y.
  • A212985 (program): Number of (w,x,y) with all terms in 0,…,n and 3w=3x+y.
  • A212986 (program): Number of (w,x,y) with all terms in 0,…,n and 2w = 3x+y.
  • A212987 (program): Number of (w,x,y) with all terms in 0,…,n and 3w = 2x+2*y.
  • A212988 (program): Number of (w,x,y) with all terms in 0,…,n and 4*w = x+y.
  • A212989 (program): Number of (w,x,y) with all terms in 0,…,n and 4w = 4x+y.
  • A213029 (program): a(n) = floor(n/2)^2 - floor(n/3)^2.
  • A213030 (program): [2n/3]^2 -[n/3]^2, where []=floor.
  • A213033 (program): n[n/2][n/3], where [] = floor.
  • A213034 (program): [3n/2]*[n/3], where [] = floor.
  • A213035 (program): n^2-[n/3]^2, where [] = floor.
  • A213036 (program): n^2-[2n/3]^2, where [] = floor.
  • A213037 (program): n^2-2*[n/2]^2, where [] = floor.
  • A213038 (program): a(n) = n^2 - 3*floor(n/2)^2.
  • A213039 (program): n^3-[n/3]^3, where [] = floor.
  • A213040 (program): Partial sums of A004738, leftmost column of the sequence of triangles defined in A206492.
  • A213041 (program): Number of (w,x,y) with all terms in 0..n and 2 w-x = max(w,x,y)-min(w,x,y).
  • A213042 (program): Convolution of (1,0,2,0,3,0,…) and (1,0,0,2,0,0,3,0,0,…); i.e., (A027656(n)) and (A175676(n+2)).
  • A213043 (program): Convolution of (1,-1,2,-2,3,-3,…) and A000045 (Fibonacci numbers).
  • A213045 (program): Number of (w,x,y) with all terms in 0,…,n and 2 w-x >max(w,x,y)-min(w,x,y).
  • A213046 (program): Convolution of Lucas numbers and positive integers repeated (A000032 and A008619).
  • A213064 (program): Bitwise AND of 2n with the one’s-complement of n.
  • A213071 (program): 3n(9n + 2)*(18n - 1), where n runs through the odd numbers 1, 3, 5,…
  • A213077 (program): a(n) = round(n^2 - sqrt(n)).
  • A213082 (program): Values of n for which the number of roots of the function sin(x)/x - 1/n increases.
  • A213083 (program): Each square n^2 appears n^2 number of times.
  • A213088 (program): The Manhattan distance to the origin while traversing the first quadrant in a taxicab geometry.
  • A213163 (program): Sequence of coefficients of x in marked mesh pattern generating function Q_ n,132 ^(3,0,-,0)(x).
  • A213164 (program): Sequence of coefficients of x in marked mesh pattern generating function Q_ n,132 ^(4,0,-,0)(x).
  • A213167 (program): a(n) = n! - (n-2)!.
  • A213169 (program): n!+n+1.
  • A213173 (program): a(n) = 4^floor(n/2), Powers of 4 repeated.
  • A213182 (program): Numbers which may represent a date in “condensed European notation” DDMMYY.
  • A213183 (program): Initialize a(1)=R=1. Repeat: copy the last R preceding terms to current position; increment R; do twice: append the least integer that has not appeared in the sequence yet.
  • A213184 (program): Numbers which may represent a date in “condensed American notation” MMDDYY.
  • A213194 (program): First inverse function (numbers of rows) for pairing function A211377.
  • A213222 (program): Minimum number of distinct slopes formed by n noncollinear points in the plane.
  • A213223 (program): 10^n + 10*n.
  • A213236 (program): a(n) = (-n)^(n-1).
  • A213243 (program): Number of nonzero elements in GF(2^n) that are cubes.
  • A213244 (program): Number of nonzero elements in GF(2^n) that are 5th powers.
  • A213245 (program): Number of nonzero elements in GF(2^n) that are 7th powers.
  • A213246 (program): Number of nonzero elements in GF(2^n) that are 9th powers.
  • A213247 (program): Number of nonzero elements in GF(2^n) that are 11th powers.
  • A213248 (program): Number of nonzero elements in GF(2^n) that are 13th powers.
  • A213255 (program): 2^(n-1) - floor((2^(n-1) - 1)/(n-1)).
  • A213269 (program): The number of edges in the directed graph of the 2-opt landscape of the symmetric TSP
  • A213283 (program): Number of 4-length words w over n-ary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.
  • A213326 (program): a(n) = (n+2)^n - (n+1)^n.
  • A213367 (program): Numbers that are not squares of primes.
  • A213370 (program): a(n) = n AND 2*n, where AND is the bitwise AND operator.
  • A213380 (program): a(n) = 132*binomial(n,12).
  • A213381 (program): a(n) = n^n mod (n+2).
  • A213387 (program): a(n) = 52^(n-1)-2-3n.
  • A213388 (program): Number of (w,x,y) with all terms in 0,…,n and 2 w-x >= max(w,x,y)-min(w,x,y).
  • A213389 (program): Number of (w,x,y) with all terms in 0,…,n and max(w,x,y) < 2*min(w,x,y).
  • A213390 (program): Number of (w,x,y) with all terms in 0,…,n and max(w,x,y) >= 2*min(w,x,y).
  • A213391 (program): Number of (w,x,y) with all terms in 0,…,n and 2max(w,x,y) < 3min(w,x,y).
  • A213393 (program): Number of (w,x,y) with all terms in 0,…,n and 2max(w,x,y) > 3min(w,x,y).
  • A213395 (program): Number of (w,x,y) with all terms in 0,…,n and max( w-x , x-y ) = w.
  • A213396 (program): Number of (w,x,y) with all terms in 0,…,n and 2*w < x+y-w .
  • A213397 (program): Number of (w,x,y) with all terms in 0,…,n and 2*w >= x+y-z .
  • A213398 (program): Number of (w,x,y) with all terms in 0,…,n and min( w-x , x-y ) = x.
  • A213399 (program): Number of (w,x,y) with all terms in 0,…,n and max( w-x , x-y ) = x.
  • A213432 (program): 2^(n-3)*binomial(n,4).
  • A213436 (program): Principal diagonal of the convolution array A212891.
  • A213443 (program): a(0)=5, thereafter a(n) = chromatic number (or Heawood number) Chi(n) of surface of genus n.
  • A213455 (program): 90*A002451(n).
  • A213472 (program): Period 20, repeat 1, 4, 0, 9, 1, 6, 4, 5, 9, 6, 6, 9, 5, 4, 6, 1, 9, 0, 4, 1.
  • A213479 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y = w+x+y.
  • A213480 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y != w+x+y.
  • A213481 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y <= w+x+y.
  • A213483 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y >= w+x+y.
  • A213484 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y + y-w >= w+x+y.
  • A213485 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y + y-w != w+x+y.
  • A213486 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y + y-w > w+x+y.
  • A213487 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y + y-w <= w+x+y.
  • A213488 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y + y-w < w+x+y.
  • A213489 (program): Number of (w,x,y) with all terms in 0,…,n and w-x + x-y + y-w >= w + x + y.
  • A213492 (program): Number of (w,x,y) with all terms in 0,…,n and w != min( w-x , x-y , y-w ).
  • A213495 (program): Number of (w,x,y) with all terms in 0,…,n and w = min( w-x , x-y , y-w ).
  • A213496 (program): Number of (w,x,y) with all terms in 0,…,n and x != max( w-x , x-y )
  • A213498 (program): Number of (w,x,y) with all terms in 0,…,n and w != max( w-x , x-y , y-w )
  • A213502 (program): Number of (w,x,y) with all terms in 0,…,n and x != min( w-x , x-y )
  • A213508 (program): The sequence Z(n) arising in the enumeration of balanced binary trees.
  • A213509 (program): The sequence Z’(n) arising in the enumeration of balanced binary trees.
  • A213510 (program): The sequence N(n) arising in the enumeration of balanced ternary trees.
  • A213511 (program): The sequence N’(n) arising in the enumeration of balanced ternary trees.
  • A213526 (program): a(n) = 3*n AND n, where AND is the bitwise AND operator.
  • A213544 (program): Sum of numerators of Farey Sequence of order n.
  • A213546 (program): Principal diagonal of the convolution array A213505.
  • A213547 (program): Antidiagonal sums of the convolution array A213505.
  • A213549 (program): Principal diagonal of the convolution array A213548.
  • A213560 (program): Antidiagonal sums of the convolution array A213558.
  • A213563 (program): Antidiagonal sums of the convolution array A213561.
  • A213569 (program): Principal diagonal of the convolution array A213568.
  • A213575 (program): Antidiagonal sums of the convolution array A213573.
  • A213578 (program): Antidiagonal sums of the convolution array A213576.
  • A213580 (program): Principal diagonal of the convolution array A213579.
  • A213581 (program): Antidiagonal sums of the convolution array A213571.
  • A213583 (program): Principal diagonal of the convolution array A213582.
  • A213585 (program): Principal diagonal of the convolution array A213584.
  • A213586 (program): Antidiagonal sums of the convolution array A213584.
  • A213604 (program): Cumulative sums of digital roots of A005891(n).
  • A213633 (program): [A000027/A007978], where [ ] = floor.
  • A213634 (program): n-[n/m], where m is the least nondivisor of n (as in A007978) and [ ] = floor.
  • A213635 (program): m*[n/m], where m is the least nondivisor of n (as in A007978) and [ ] = floor.
  • A213636 (program): Remainder when n is divided by its least nondivisor.
  • A213642 (program): Primes with subscript that equals odd part of n.
  • A213659 (program): a(n) = 3^n + 2^(2*n + 1).
  • A213667 (program): Number of dominating subsets with k vertices in all the graphs G(n) (n>=1) obtained by taking n copies of the path P_3 and identifying one of their endpoints (a star with n branches of length 2).
  • A213671 (program): The odd part of n^2 - n + 2.
  • A213673 (program): (n^2 - A000695(n))/4.
  • A213688 (program): a(n) = Sum_ i=0..n A000129(i)^3.
  • A213706 (program): Partial sums of A071542.
  • A213707 (program): Positions of zeros in A218254.
  • A213708 (program): a(n) is the least inverse of A071542, i.e., minimal i such that A071542(i) = n.
  • A213714 (program): Inverse function for injection A005187.
  • A213723 (program): a(n) = smallest natural number x such that x=n+A000120(x), otherwise zero.
  • A213724 (program): Largest natural number x such that x=n+A000120(x), or zero if no such number exists.
  • A213748 (program): Principal diagonal of the convolution array A213747.
  • A213749 (program): Antidiagonal sums of the convolution array A213747.
  • A213757 (program): Principal diagonal of the convolution array A213756.
  • A213758 (program): Antidiagonal sums of the convolution array A213756.
  • A213759 (program): Principal diagonal of the convolution array A213783.
  • A213763 (program): Principal diagonal of the convolution array A213762.
  • A213764 (program): Antidiagonal sums of the convolution array A213762.
  • A213769 (program): Principal diagonal of the convolution array A213768.
  • A213770 (program): Antidiagonal sums of the convolution array A213768.
  • A213772 (program): Principal diagonal of the convolution array A213771.
  • A213776 (program): Antidiagonal sums of the convolution array A213774.
  • A213779 (program): Principal diagonal of the convolution array A213778.
  • A213780 (program): Antidiagonal sums of the convolution array A213778.
  • A213782 (program): Principal diagonal of the convolution array A213781.
  • A213809 (program): Position of the maximum element in the simple continued fraction of Fibonacci(n+1)^5/Fibonacci(n)^5.
  • A213810 (program): a(n) = 4n^2 - 482n + 14561.
  • A213818 (program): Antidiagonal sums of the convolution array A213773.
  • A213820 (program): Principal diagonal of the convolution array A213819.
  • A213823 (program): Principal diagonal of the convolution array A213822.
  • A213824 (program): Antidiagonal sums of the convolution array A213822.
  • A213826 (program): Principal diagonal of the convolution array A213825.
  • A213827 (program): a(n) = n^2(n+1)(3*n+1)/4.
  • A213829 (program): Principal diagonal of the convolution array A213828.
  • A213830 (program): Antidiagonal sums of the convolution array A213828.
  • A213832 (program): Principal diagonal of the convolution array A213831.
  • A213834 (program): Antidiagonal sums of the convolution array A213833.
  • A213837 (program): Principal diagonal of the convolution array A213836.
  • A213839 (program): Principal diagonal of the convolution array A213838.
  • A213840 (program): a(n) = n(1 + n)(3 - 4n + 4n^2)/6.
  • A213842 (program): Principal diagonal of the convolution array A213841.
  • A213843 (program): Antidiagonal sums of the convolution array A213841.
  • A213845 (program): Principal diagonal of the convolution array A213844.
  • A213846 (program): Antidiagonal sums of the convolution array A213844.
  • A213848 (program): Principal diagonal of the convolution array A213847.
  • A213850 (program): Antidiagonal sums of the convolution array A213849.
  • A213852 (program): Least m>0 such that n+1+m and n-m are relatively prime.
  • A213857 (program): Least m such that n! <= 3^m.
  • A213859 (program): a(n) = 2^n mod (n+2).
  • A213902 (program): Number of integers of the form 6k+1 and 6k-1 between prime(n) and prime(n+1).
  • A213909 (program): Sum of all even numbers in Collatz (3x+1) trajectory of n.
  • A213911 (program): Number of runs of consecutive zeros in the Zeckendorf (binary) representation of n.
  • A213916 (program): Sum of all odd numbers in Collatz (3x+1) trajectory of n.
  • A213937 (program): Row sums a(n) of triangle A213936: number of representative necklaces with n beads (C_N symmetry) corresponding to all color signatures given by the partitions [1^n], [2,1^(n-2)],…[n-1,1], [n].
  • A214045 (program): Least m>0 such that n! <= 5^m.
  • A214055 (program): Least m>0 such that n!+2+m and n-m have a common divisor > 1.
  • A214059 (program): Least m>0 such that gcd(n^2+1+m, n-m) > 1.
  • A214060 (program): Least m>0 such that gcd(2*n-1+m, n-m) > 1.
  • A214061 (program): Least m>0 such that gcd(2n-1+m, 2n-m) > 1.
  • A214062 (program): Least m>0 such that gcd(2n+m, 2n-1-m) > 1.
  • A214066 (program): a(n) = floor( (3/2)floor(5n/2) ).
  • A214067 (program): [(5/2)[(5/2)n]], where [ ] = floor.
  • A214068 (program): a(n) = floor((3/2)floor((3/2)n)).
  • A214076 (program): a(n) = ceiling(e^(n/3)).
  • A214077 (program): a(n) = floor(e^(n/3)).
  • A214078 (program): a(n) = (ceiling (sqrt(n)))!.
  • A214080 (program): a(n) = (floor(sqrt(n)))!
  • A214085 (program): n^2 * (n^4 - n^2 + n + 1) / 2.
  • A214090 (program): Period 6: repeat [0, 0, 1, 0, 1, 1].
  • A214091 (program): a(n) = 3^n - 2^(n+2).
  • A214092 (program): Principal diagonal of the convolution array A213773.
  • A214135 (program): Number of 0..4 colorings on an nX3 array circular in the 3 direction with new values 0..4 introduced in row major order
  • A214142 (program): Number of 0..4 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.
  • A214151 (program): Numbers n from the set == 5 (mod 6) with the property that 3^((3*n-1)/2) == 3 (mod n) and 2^((n-1)/2) == (n-1) (mod n)
  • A214206 (program): a(n) = largest m such that m(m+1)/2 <= 14n.
  • A214210 (program): Trebled Thue-Morse sequence: the A010060 sequence replacing 0 with 0,0,0 and 1 with 1,1,1.
  • A214211 (program): Doubled Fibonacci word: the A003842 sequence replacing 1 with 1,1 and 2 with 2,2.
  • A214212 (program): Number of right special factors of length n in the Thue-Morse sequence A010060.
  • A214214 (program): Partial sums of A214212.
  • A214260 (program): First differences of A052980.
  • A214263 (program): Expansion of f(x^1, x^7) in powers of x where f() is Ramanujan’s general theta function.
  • A214264 (program): Expansion of f(x^3, x^5) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A214282 (program): Largest Euler characteristic of a downset on an n-dimensional cube.
  • A214283 (program): Smallest Euler characteristic of a downset on an n-dimensional cube.
  • A214284 (program): Characteristic function of squares or five times squares.
  • A214286 (program): a(n) = floor(Fibonacci(n)/7).
  • A214297 (program): a(0)=-1, a(1)=0, a(2)=-3; thereafter a(n+2) - 2*a(n+1) + a(n) has period 4: repeat -4, 8, -4, 2.
  • A214304 (program): Expansion of phi(q) + phi(q^2) - phi(q^4) in powers of q where phi() is a Ramanujan theta function.
  • A214315 (program): Floor of the real part of the zeros of the complex Fibonacci function on the right half-plane.
  • A214345 (program): Interleaved reading of A073577 and A053755.
  • A214392 (program): If n mod 4 = 0 then a(n) = n/4, otherwise a(n) = n.
  • A214393 (program): Numbers of the form (4k+3)^2+4 or (4k+5)^2-8.
  • A214394 (program): If n mod 6 = 0 then n/6 else n.
  • A214395 (program): Decimal expansion of 16/27.
  • A214400 (program): a(n) = binomial(n^2 + 3*n, n).
  • A214405 (program): Numbers of the form (4k+3)^2-8 or (4k+5)^2+4.
  • A214411 (program): The maximum exponent k of 7 such that 7^k divides n.
  • A214429 (program): Integers of the form (n^2 - 49) / 120.
  • A214438 (program): Numerator of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.
  • A214446 (program): n(n^2-2n-1)
  • A214489 (program): Numbers m such that A070939(m) = A070939(m + A070939(m)), A070939 = length of binary representation.
  • A214493 (program): Numbers of the form ((6k+5)^2+9)/2 or 2(3k+4)^2-9.
  • A214560 (program): Number of 0’s in binary expansion of n^2.
  • A214561 (program): Number of 1’s in binary expansion of n^n.
  • A214562 (program): Number of 0’s in binary expansion of n^n.
  • A214604 (program): Odd numbers by transposing the right half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, n), 1 <= k <= n.
  • A214606 (program): a(n) = gcd(n, 2^n - 2).
  • A214628 (program): Intersections of radii with the cycloid.
  • A214630 (program): a(n) is the reduced numerator of 1/4 - 1/A109043(n)^2 = (1 - 1/A026741(n)^2)/4.
  • A214647 (program): (n^n + n^2)/2.
  • A214656 (program): Floor of the imaginary part of the zeros of the complex Fibonacci function on the left half-plane.
  • A214657 (program): Floor of the moduli of the zeros of the complex Fibonacci function.
  • A214659 (program): a(n) = n(7n^2 - 3*n - 1)/3.
  • A214660 (program): 9n^2 - 11n + 3.
  • A214661 (program): Odd numbers by transposing the left half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, k), 1 <= k <= n.
  • A214671 (program): Floor of the real parts of the zeros of the complex Lucas function on the right half-plane.
  • A214672 (program): Floor of the imaginary parts of the zeros of the complex Lucas function on the left half-plane.
  • A214673 (program): Floor of the moduli of the zeros of the complex Lucas function.
  • A214675 (program): 9n^2 - 13n + 5.
  • A214682 (program): Remove 2s that do not contribute to a factor of 4 from the prime factorization of n.
  • A214684 (program): a(1)=1, a(2)=1, and, for n>2, a(n)=(a(n-1)+a(n-2))/5^k, where 5^k is the highest power of 5 dividing a(n-1)+a(n-2).
  • A214698 (program): (n^n - n^2)/2.
  • A214706 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=5.
  • A214720 (program): Least m>0 such that n^2-m and n-m are relatively prime.
  • A214721 (program): Least m>0 such that 2*n+1+m and n-m are not relatively prime.
  • A214731 (program): a(n) = n^3 - 2*n^2 - 1.
  • A214732 (program): a(n) = 25n^2 + 15n + 1021.
  • A214736 (program): Least m>0 such that n-m divides n+1+m.
  • A214745 (program): Least m>0 such that n-m divides 2*n-1+m.
  • A214748 (program): Least m>0 such that n-m divides (2*n-1)!!+m.
  • A214848 (program): First difference of A022846.
  • A214855 (program): Fibonacci numbers divisible by 10.
  • A214856 (program): Number of triangular numbers in interval ](n-1)^2, n^2] for n>0, a(0)=1.
  • A214857 (program): Number of triangular numbers in interval [0, n^2].
  • A214858 (program): Natural numbers missing from A214857.
  • A214860 (program): First differences of round(n*sqrt(3)) (A022847).
  • A214861 (program): First differences of round(n*sqrt(5)) (A022848).
  • A214863 (program): Numbers n such that n XOR 11 = n - 11.
  • A214864 (program): Numbers n such that n XOR 10 = n - 10.
  • A214865 (program): n such that n XOR 9 = n - 9.
  • A214877 (program): n ^ (last digit of n).
  • A214887 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=7.
  • A214916 (program): a(0) = a(1) = 1, a(n) = n! / a(n-2).
  • A214917 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Fibonacci(n+1+m).
  • A214918 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Fibonacci(n+2+m).
  • A214920 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Lucas(n+m).
  • A214922 (program): Numbers of the form x^2 + y^2 + z^3 + w^3 (x, y, z, w >= 0).
  • A214927 (program): Number of n-digit numbers N that do not end with 0 and are such that the reversal of N divides N but is different from N.
  • A214944 (program): Number of squarefree words of length 5 in an (n+1)-ary alphabet.
  • A214945 (program): Number of squarefree words of length 6 in an (n+1)-ary alphabet.
  • A214946 (program): Number of squarefree words of length 7 in an (n+1)-ary alphabet.
  • A214955 (program): Number of solid standard Young tableaux of shape [[n,n-1],[1]].
  • A214962 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Fibonacci(2n+2m).
  • A214971 (program): Integers k for which the base-phi representation of k includes 1.
  • A214972 (program): a(n) = a(floor(2*(n-1)/3)) + 1, where a(0) = 0.
  • A214982 (program): a(n) = (Fibonacci(5n)/Fibonacci(n) - 5)/50.
  • A214993 (program): Power floor sequence of (golden ratio)^5.
  • A214994 (program): Power ceiling sequence of (golden ratio)^5.
  • A215004 (program): a(0) = a(1) = 1; for n>1, a(n) = a(n-1) + a(n-2) + floor(n/2).
  • A215005 (program): a(n) = a(n-2) + a(n-1) + floor(n/2) + 1 for n > 1 and a(0)=0, a(1)=1.
  • A215006 (program): a(0)=0, a(n+1) is the least k>a(n) such that k+a(n)+n+1 is a Fibonacci number.
  • A215020 (program): a(n) = log_2( A182105(n) ).
  • A215036 (program): 2 followed by “1,0” repeated.
  • A215039 (program): a(n) = Fibonacci(2*n)^3, n>=0.
  • A215040 (program): a(n) = F(2*n+1)^3, n>=0, with F = A000045 (Fibonacci).
  • A215044 (program): a(n) = F(2*n)^5 with F=A000045 (Fibonacci numbers).
  • A215045 (program): a(n) = F(2*n+1)^5 with n >= 0, F=A000045 (Fibonacci numbers).
  • A215052 (program): a(n) = (binomial(n,5) - floor(n/5)) / 5.
  • A215053 (program): a(n) = 1/7*( binomial(n,7) - floor(n/7) ).
  • A215054 (program): a(n) = 1/11*(binomial(n,11) - floor(n/11)).
  • A215088 (program): a(n)=Sum d(i)2^i: i=0,1,…,m , where Sum d(i)5^i: i=0,1,…,m is the base 5 representation of n.
  • A215089 (program): a(n)=Sum d(i)6^i: i=0,1,…,m , where Sum d(i)2^i: i=0,1,…,m is the base 2 representation of n.
  • A215090 (program): a(n) = Sum_ i=0..m d(i)3^i, where Sum_ i=0..m d(i)4^i is the base-4 representation of n.
  • A215095 (program): a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a Jacobsthal number.
  • A215097 (program): a(n) = n^3 - a(n-2) for n >= 2 and a(0)=0, a(1)=1.
  • A215098 (program): a(0)=0, a(1)=1, a(n) = n*(n-1) - a(n-2).
  • A215108 (program): a(n) = A215082(2*n)
  • A215137 (program): a(n) = 17*n + 1.
  • A215144 (program): a(n) = 19*n + 1.
  • A215145 (program): a(n) = 20*n + 1.
  • A215146 (program): a(n) = 21*n + 1.
  • A215147 (program): For n odd, a(n)= 1^2+2^2+3^2+…+n^2; for n even, a(n)=(1^2+2^2+3^2+…+n^2) + 1.
  • A215148 (program): a(n) = 23*n + 1.
  • A215149 (program): a(n) = n * (1 + 2^(n-1)).
  • A215159 (program): a(n) = floor(n^n / (n+1)).
  • A215176 (program): Number of nXnXn triangular 0..2 arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value
  • A215191 (program): Number of arrays of 4 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.
  • A215203 (program): a(0) = 0, a(n) = a(n - 1)*2^(n + 1) + 2^n - 1. That is, add one 0 and n 1’s to the binary representation of previous term.
  • A215229 (program): Number of length-6 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic “squarefree”).
  • A215230 (program): Number of length-7 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic “squarefree”).
  • A215247 (program): A Beatty sequence: a(n) = floor((n-1/2)(2 + 2sqrt(2))).
  • A215265 (program): (n-1)^(n+1) - n^n.
  • A215270 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=6.
  • A215271 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=8.
  • A215272 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=9.
  • A215414 (program): Unix epoch timestamp for start of year, beginning with 1970.
  • A215415 (program): a(2n) = n, a(4n+1) = 2n-1, a(4n+3) = 2*n+3.
  • A215418 (program): Number of Regular and Stellar polytopes in n-dimensional Euclidean space, or -1 if infinite.
  • A215448 (program): a(0)=1, a(1)=0, a(n) = a(n-1) + a(n-2) + Sum_ i=0…n-1 a(i).
  • A215459 (program): Arises in quick gossiping without duplicate transmission.
  • A215465 (program): a(n) = (Lucas(4n) - Lucas(2n))/4.
  • A215476 (program): Minimum number of comparisons needed to find the median of n elements.
  • A215480 (program): Characteristic function of numbers n with exactly two distinct prime factors
  • A215486 (program): n - 1 mod phi(n), where phi(n) is Euler’s totient function.
  • A215495 (program): a(4n) = a(4n+2) = a(2n+1) = 2n + 1.
  • A215530 (program): The limit of the string “0, 1” under the operation ‘repeat string twice and append 0’.
  • A215531 (program): The limit of the string “0, 1” under the operation ‘append first k terms, k=k+2’ with k=1 initially.
  • A215532 (program): The limit of the string “0, 1” under the operation ‘append first k terms, increment k’ with k=2 initially.
  • A215537 (program): Lowest k such that k is representable as both the sum of n and of n+1 nonzero squares.
  • A215543 (program): Number of standard Young tableaux of shape [3n,3].
  • A215544 (program): Number of standard Young tableaux of shape [4n,4].
  • A215545 (program): Number of standard Young tableaux of shape [5n,5].
  • A215573 (program): a(n) = n(n+1)(2n+1)/6 modulo n.
  • A215580 (program): Partial sums of A215602.
  • A215602 (program): a(n) = L(n)*L(n+1), where L = A000032 (Lucas numbers).
  • A215604 (program): a(0)=0, a(n) = (n + a(floor(n/2))) mod 3.
  • A215630 (program): Triangle read by rows: T(n,k) = n^2 - n*k + k^2, 1 <= k <= n.
  • A215646 (program): n * (11n^2 + 6n + 1) / 6.
  • A215655 (program): Irregular triangle read by rows: reading the n-th row describes all the numbers seen in the triangle up to the end of the n-th row.
  • A215667 (program): 22n+1 is prime.
  • A215687 (program): Number of solid standard Young tableaux of shape [[2*n,2],[2]].
  • A215712 (program): Numerator of sum(i=1..n, 3*i/4^i )
  • A215713 (program): Denominator of sum(i=1..n, 3*i/4^i).
  • A215747 (program): a(n) = (-2)^n mod n.
  • A215761 (program): Numbers m with property that 36m+11 is prime.
  • A215773 (program): Number of undirected labeled graphs on n+3 nodes with exactly n cycle graphs as connected components.
  • A215781 (program): a(n) = ceiling(n*(sqrt(3)-1)).
  • A215814 (program): 60516n^2 - 61008n + 2481403.
  • A215848 (program): Primes > 3.
  • A215862 (program): Number of simple labeled graphs on n+2 nodes with exactly n connected components that are trees or cycles.
  • A215879 (program): Written in base 3, n ends in a(n) consecutive nonzero digits.
  • A215883 (program): When written in base 4, n ends in a(n) consecutive nonzero digits.
  • A215884 (program): Written in base 5, n ends in a(n) consecutive nonzero digits.
  • A215885 (program): a(n) = 3*a(n-1) - a(n-3), with a(0) = 3, a(1) = 3, and a(2) = 9.
  • A215887 (program): Written in decimal, n ends in a(n) consecutive nonzero digits.
  • A215928 (program): a(n) = 2*a(n-1) + a(n-2) for n > 2, a(0) = a(1) = 1, a(2) = 2.
  • A215942 (program): a(n) = sigma(6n) - 12n.
  • A215947 (program): Difference between the sum of the even divisors and the sum of the odd divisors of 2n.
  • A215960 (program): First differences of A016759.
  • A216038 (program): Number of isomorphism classes of unstretchable simplicial arrangements of n pseudolines in the real projective plane that satisfy Pappus’s theorem.
  • A216095 (program): a(n) = 2^n mod 10000.
  • A216096 (program): a(n) = 3^n mod 1000.
  • A216097 (program): 3^n mod 10000.
  • A216099 (program): Period of powers of 3 mod 10^n.
  • A216100 (program): 11^n mod 100.
  • A216106 (program): The Wiener index of the tetrameric 1,3-adamantane TA(n) (see the Fath-Tabar et al. reference).
  • A216108 (program): The Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216109 (program): The hyper-Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216110 (program): The Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216112 (program): The Wiener index of the para-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216113 (program): The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216114 (program): The Wiener index of a link of n fullerenes C_ 20 (see the Ghorbani and Hosseinzadeh reference).
  • A216125 (program): a(n) = 5^n mod 1000.
  • A216127 (program): a(n) = 6^n mod 1000.
  • A216129 (program): a(n) = 7^n mod 1000.
  • A216131 (program): a(n) = 11^n mod 1000.
  • A216147 (program): 2*n^n + 1.
  • A216156 (program): Period of powers of 11 mod 10^n.
  • A216164 (program): Period of powers of 7 mod 10^n.
  • A216172 (program): Number of all possible tetrahedra of any size, having reverse orientation to the original regular tetrahedron, formed when intersecting the latter by planes parallel to its sides and dividing its edges into n equal parts.
  • A216173 (program): Number of all possible tetrahedra of any size and orientation, formed when intersecting the original regular tetrahedron by planes parallel to its sides and dividing its edges into n equal parts.
  • A216175 (program): Number of all polyhedra (tetrahedra of any orientation and octahedra) of any size, formed when intersecting a regular tetrahedron by planes parallel to its sides and dividing its edges into n equal parts.
  • A216178 (program): Period 4: repeat [4, 1, 0, -3].
  • A216179 (program): a(n) = 10^n + 3.
  • A216194 (program): a(n) = Smallest b for which the base b representation of n contains at least one 2 (or 0 if no such base exists).
  • A216195 (program): Abelian complexity function of the period-doubling sequence (A096268).
  • A216197 (program): Abelian complexity function of A064990.
  • A216209 (program): Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n.
  • A216223 (program): Distance from Fibonacci(n) to the next perfect square.
  • A216225 (program): Distance between n^2 and next higher Fibonacci number.
  • A216230 (program): Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=2, T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
  • A216243 (program): Partial sums of the squares of Lucas numbers (A000032).
  • A216244 (program): a(n) = (prime(n)^2 - 1)/2 for n >= 2.
  • A216256 (program): Minimum length of a longest unimodal subsequence of a permutation of n elements.
  • A216257 (program): a(n) = 840n^2-23100n+86861.
  • A216325 (program): Number of divisors of the degree of the minimal polynomial for 2*cos(Pi/n), n >= 1.
  • A216326 (program): Number of divisors of the degree of the minimal polynomial of 2*cos(Pi/prime(n)), with prime = A000040, n >= 1.
  • A216414 (program): a(n) = (-1)^(n-3)*binomial(n,3) - 1.
  • A216430 (program): (-1)^A081603(n), parity of the number of 2’s in the ternary expansion of n.
  • A216443 (program): a(n) = n!! mod !n.
  • A216453 (program): Number of points hidden from the central point by a closer point in a hexagonal orchard of order n.
  • A216466 (program): n!! mod n!
  • A216475 (program): The number of numbers coprime to and less than n+2, excluding 2.
  • A216491 (program): 12*5^n.
  • A216522 (program): Integers of the form 2x + 3y with nonnegative x and y, with repetitions.
  • A216606 (program): Decimal expansion of 360/7.
  • A216607 (program): The sequence used to represent partition binary diagram as an array.
  • A216761 (program): n * floor(log_2(n)) * floor(log_2(log_2(n))) * floor(log_2(log_2(log_2(n)))) ….
  • A216762 (program): a(n) = n * ceiling(log_2(n)) * ceiling(log_2(log_2(n))) * ceiling(log_2(log_2(log_2(n)))) ….
  • A216778 (program): Number of derangements on n elements with an even number of cycles.
  • A216779 (program): Number of derangements on n elements with an odd number of cycles.
  • A216844 (program): 4k^2-8k+2 interleaved with 4k^2-4k+2 for k>=0.
  • A216852 (program): 18k^2-36k+9 interleaved with 18k^2-18k+9 for k>=0.
  • A216853 (program): 18k^2-12k-7 interleaved with 18k^2+6k+5 for k>=0.
  • A216865 (program): 16k^2-32k+8 interleaved with 16k^2-16k+8 for k>=0.
  • A216871 (program): 16k^2-16k-4 interleaved with 16k^2+4 for k>=0.
  • A216875 (program): 20k^2-40k+10 interleaved with 20k^2-20k+10 for k>=0.
  • A216876 (program): 20k^2-20k-5 interleaved with 20k^2+5 for k=>0.
  • A216913 (program): a(n) = Gauss_primorial(3n, 3) / Gauss_primorial(3n, 3*n).
  • A216938 (program): Number of side-2 hexagonal 0..n arrays with values nondecreasing E, SW and SE
  • A216972 (program): a(4n+2) = 2, otherwise a(n) = n.
  • A216973 (program): Exponential Riordan array [x*exp(x),x].
  • A216998 (program): Digit sum of n*7 mod 7.
  • A217009 (program): Multiples of 7 in base 8.
  • A217022 (program): Number of city-block distance 1, pressure limit 2 movements in an n X 2 array with each element moving exactly one horizontally or vertically and no element acquiring more than two neighbors.
  • A217038 (program): Number of powerful numbers < n.
  • A217094 (program): Least index k such that A011540(k) >= 10^n.
  • A217096 (program): Characteristic function of numbers that have a nonleading zero in their decimal representation (A011540). 0 itself is also included, so a(0) = 1.
  • A217123 (program): Number of possible ordered pairs (x, y) where x is the number of beads adjacent to at least one black bead and y the number of beads adjacent to at least one white bead in a binary necklace of length n.
  • A217140 (program): a(n) = m/n where m is the least number divisible by n such that phi(m) = phi(m+6n).
  • A217200 (program): Number of permutations in S_ n+2 containing an increasing subsequence of length n.
  • A217213 (program): 2*A002740(n).
  • A217233 (program): Expansion of (1-2x+x^2)/(1-3x-3*x^2+x^3).
  • A217238 (program): a(n) = n! * Sum_ k=1..n k!.
  • A217239 (program): n!(!n-1) = n!(Sum k!, k=1..n-1)
  • A217284 (program): a(n) = Sum_ k=0..n (n!/k!)^3.
  • A217285 (program): Irregular triangle read by rows: T(n,k) is the number of labeled relations on n nodes with exactly k edges; n>=0, 0<=k<=n^2.
  • A217290 (program): Integers n such that 2cos(2Pi/n) is an integer.
  • A217330 (program): The number of integer solutions to the equation x1 + x2 + x3 + x4 = n, with xi >= 0, and with x2 + x3 divisible by 3.
  • A217366 (program): a(n) = ((n+6) / gcd(n+6,4)) * (n / gcd(n,4)).
  • A217367 (program): a(n) = ((n+7) / gcd(n+7,4)) * (n / gcd(n,4)).
  • A217398 (program): Numbers starting with 5.
  • A217400 (program): Numbers starting with 7.
  • A217402 (program): Numbers starting with 9.
  • A217434 (program): n divided by the product of all its prime divisors smaller than the largest prime divisor.
  • A217441 (program): Numbers k such that 26*k+1 is a square.
  • A217447 (program): Number of n x n permutation matrices that disconnect their zeros.
  • A217471 (program): Partial sum of fifth power of the even-indexed Fibonacci numbers.
  • A217473 (program): Product of the first n+1 odd-indexed Lucas numbers A000032.
  • A217477 (program): Z-sequence for the Riordan triangle A111125;
  • A217482 (program): Quarter-square tetrahedrals: a(n) = k(k - 1)(k - 2)/6, k = A002620(n).
  • A217515 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123)*.
  • A217516 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234)*.
  • A217517 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345)*.
  • A217527 (program): a(n) = 2^(n-2)*(n-2)^2+2^(n-1).
  • A217528 (program): a(n) = (n-2)(n-3)2^(n-2)+2^n-2.
  • A217530 (program): n^4/2-5n^3/2+21n-30.
  • A217557 (program): The difference between the reversal of an 8-bit integer and the original integer.
  • A217562 (program): Even numbers not divisible by 5.
  • A217564 (program): Number of primes between prime(n)/2 and prime(n+1)/2.
  • A217570 (program): Numbers n such that floor(sqrt(n)) = floor(n/(floor(sqrt(n))-1))-1.
  • A217571 (program): a(n) = (2n(n+5) + (2n+1)(-1)^n - 1)/8.
  • A217573 (program): Number of integers between -(2n+1)Pi and (2n+2)Pi.
  • A217574 (program): (n^2)(n^2-1)(n^2-2)*(n^2-3).
  • A217575 (program): Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1.
  • A217585 (program): Number of triangles with endpoints of the form (x,x^2), x in -n,…,n , having at least one angle of 45 degrees.
  • A217586 (program): a(1) = 1 and, for all n >= 1, if a(n) = 0 then a(2n) = 1 and a(2n+1) = 0 whereas if a(n) = 1 then a(2n) = 0 and a(2n+1) = 0.
  • A217589 (program): Bit reversed 16-bit numbers.
  • A217619 (program): a(n) = m/(12n) where m is the least multiple of n that satisfies phi(m) = phi(m+6n).
  • A217628 (program): a(n) = 3^((n-1)*(n+2)/2).
  • A217652 (program): Number of isolated nodes over all labeled directed graphs on n nodes.
  • A217723 (program): a(n) = (sum of first n primorial numbers) minus 1.
  • A217748 (program): Number of regions with infinite area in the exterior of a regular n-gon with all diagonals drawn.
  • A217758 (program): Triangular numbers of the form k^2 + k - 1.
  • A217761 (program): Numbers whose square has a square number of decimal digits.
  • A217775 (program): a(n) = n(n+1) + (n+2)(n+3) + (n+4)*(n+5).
  • A217776 (program): a(n) = n(n+1) + (n+2)(n+3) + (n+4)(n+5) + (n+6)(n+7).
  • A217789 (program): Least difference between 2 palindromic numbers of length n.
  • A217831 (program): Triangle read by rows: label the entries T(0,0), T(1,0), T(0,1), T(2,0), T(1,1), T(0,2), T(3,0), … Then T(n,k)=T(k,n), T(0,0)=0, T(1,0)=1, and for n>1, T(n,0)=0 and T(n,in+j)=T(n-j,j) (i,j >= 0, not both 0).
  • A217855 (program): Numbers m such that 16m(3*m+1)+1 is a square.
  • A217871 (program): a(n)=b(n,1) where b(0,m)=m, b(n,m)=b(floor(n/4),m*2).
  • A217872 (program): a(n) = sigma(n)^n.
  • A217873 (program): 4n(n^2+2)/3.
  • A217893 (program): 50k^2-40k-17 interleaved with 50k^2+10k+13 for k=>0.
  • A217894 (program): 50k^2-20k-23 interleaved with 50k^2+30k+17 for k=>0.
  • A217923 (program): F-block elements for Janet periodic table.
  • A217947 (program): a(n) = (n+1)(n^3+15n^2+74*n+132)/12.
  • A217971 (program): a(n) = 2^(2n+1) * (2n+1)n^(2n).
  • A217975 (program): 2*n^2 - 7 is a square.
  • A217994 (program): a(n) = 2^((2 + n + n^2)/2).
  • A218008 (program): Sum of successive absolute differences of the binomial coefficients = 2*A014495(n)
  • A218036 (program): a(n) = (n+1) + (n+3/2)*H(n) - (H(n)^3)/2, where H(n)=A002024(n).
  • A218072 (program): Product of the nonzero digits (in base 10) of n^2.
  • A218073 (program): Number of profiles in domino tiling of a 2*n checkboard.
  • A218075 (program): a(n) = 2^(prime(n+1) - prime(n)).
  • A218078 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random 0..1 n X 2 array.
  • A218089 (program): a(n) = n*((n+1)^n - n^(n-1)).
  • A218101 (program): The number of simple labeled graphs on n nodes that have exactly n(n-1)/4 edges.
  • A218130 (program): Number of length 6 primitive (=aperiodic or period 6) n-ary words.
  • A218131 (program): Number of length 8 primitive (=aperiodic or period 8) n-ary words.
  • A218132 (program): Number of length 9 primitive (=aperiodic or period 9) n-ary words.
  • A218133 (program): Number of length 10 primitive (=aperiodic or period 10) n-ary words.
  • A218145 (program): Product of the nonzero digits (in base 10) of n^3.
  • A218148 (program): a(n) = 2^((6+5*n+n^3)/6).
  • A218151 (program): a(n) = 23^n5^(n(n-1)/2).
  • A218152 (program): a(n) = 1 + n + ((n-1)*n^2)/2.
  • A218155 (program): Numbers congruent to 2, 3, 6, 11 mod 12.
  • A218215 (program): Product of the nonzero digits (in base 10) of n^4.
  • A218234 (program): Infinitesimal generator for padded Pascal matrix A097805 (as lower triangular matrices).
  • A218245 (program): Nicolas’s sequence, whose nonnegativity is equivalent to the Riemann hypothesis.
  • A218255 (program): Next prime after 10*n.
  • A218272 (program): Infinitesimal generator for transpose of the Pascal matrix A007318 (as upper triangular matrices).
  • A218324 (program): Odd heptagonal pyramidal numbers
  • A218326 (program): Odd octagonal pyramidal numbers
  • A218327 (program): Even octagonal pyramidal numbers (A002414)
  • A218328 (program): Odd 9-gonal (nonagonal) pyramidal numbers.
  • A218344 (program): Smallest k such that k*(n-th composite)+1 is prime.
  • A218394 (program): Numbers such that sum(i<=n) binomial(n,i)binomial(2n-2*i, n-i) is not divisible by 5.
  • A218439 (program): a(n) = A001609(n)^2, where g.f. of A001609 is x(1+3x^2)/(1-x-x^3).
  • A218442 (program): a(n) = Sum_ k=0..n floor(n/(3*k + 1)).
  • A218443 (program): a(n) = Sum_ k=0..n floor(n/(3k+2)).
  • A218444 (program): a(n) = Sum_ k>=0 floor(n/(5*k + 1)).
  • A218445 (program): a(n) = Sum_ k>=0 floor(n/(5*k + 2)).
  • A218447 (program): a(n) = Sum_ k>=0 floor(n/(5*k + 4)).
  • A218451 (program): 10^n minus its binary weight.
  • A218460 (program): a(n) = prime(n)^(prime(n + 1) - prime(n)).
  • A218461 (program): Floor( prime(prime(n))/ prime(n) ).
  • A218470 (program): Partial sums of floor(n/9).
  • A218471 (program): a(n) = n(7n-3)/2.
  • A218507 (program): Number of partitions of n in which any two parts differ by at most 5.
  • A218530 (program): Partial sums of floor(n/11).
  • A218721 (program): a(n) = (18^n-1)/17.
  • A218722 (program): a(n) = (19^n-1)/18.
  • A218723 (program): a(n) = (256^n-1)/255.
  • A218724 (program): a(n) = (21^n - 1)/20.
  • A218725 (program): a(n) = (22^n-1)/21.
  • A218726 (program): a(n) = (23^n-1)/22.
  • A218727 (program): a(n) = (24^n-1)/23.
  • A218728 (program): a(n) = (25^n-1)/24.
  • A218729 (program): a(n) = (26^n-1)/25.
  • A218730 (program): a(n) = (27^n-1)/26.
  • A218731 (program): a(n) = (28^n-1)/27.
  • A218732 (program): a(n) = (29^n-1)/28.
  • A218733 (program): a(n) = (30^n-1)/29.
  • A218734 (program): a(n) = (31^n-1)/30.
  • A218736 (program): a(n) = (33^n-1)/32.
  • A218737 (program): a(n) = (34^n-1)/33.
  • A218738 (program): a(n) = (35^n-1)/34.
  • A218739 (program): a(n) = (36^n-1)/35.
  • A218740 (program): a(n) = (37^n-1)/36.
  • A218741 (program): a(n) = (38^n-1)/37.
  • A218742 (program): a(n) = (39^n-1)/38.
  • A218743 (program): a(n) = (40^n-1)/39.
  • A218744 (program): a(n) = (41^n-1)/40.
  • A218745 (program): a(n) = (42^n-1)/41.
  • A218746 (program): a(n) = (43^n-1)/42.
  • A218747 (program): a(n) = (44^n-1)/43.
  • A218748 (program): a(n) = (45^n-1)/44.
  • A218749 (program): a(n) = (46^n-1)/45.
  • A218750 (program): a(n) = (47^n-1)/46.
  • A218751 (program): a(n) = (48^n-1)/47.
  • A218752 (program): a(n) = (50^n-1)/49.
  • A218753 (program): a(n) = (49^n-1)/48.
  • A218767 (program): Total number of divisors and anti-divisors of n.
  • A218828 (program): Reluctant sequence of reverse reluctant sequence A004736.
  • A218832 (program): Number of positive integer solutions to the Diophantine equation x + y + 2z = n^2.
  • A218836 (program): Unmatched value maps: number of nX2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX2 array.
  • A218864 (program): Numbers of the form 9k^2 + 8k, k an integer.
  • A218930 (program): Number of maximal supersolvable conjugacy classes of subgroups of the symmetric group.
  • A218984 (program): Power floor sequence of 2+sqrt(6).
  • A218985 (program): Power ceiling sequence of 2+sqrt(6).
  • A218986 (program): Power floor sequence of 2+sqrt(7).
  • A218987 (program): Power ceiling sequence of 2+sqrt(7).
  • A218988 (program): Power floor sequence of 2+sqrt(8).
  • A218989 (program): Power ceiling sequence of 2+sqrt(8).
  • A218991 (program): Power floor sequence of 3+sqrt(10).
  • A218992 (program): Power ceiling sequence of 3+sqrt(10).
  • A219020 (program): Sum of the cubes of the first n even-indexed Fibonacci numbers divided by the sum of the first n terms.
  • A219028 (program): Number of non-primitive roots for prime(n), less than prime(n).
  • A219029 (program): a(n) = n - 1 - phi(phi(n)).
  • A219054 (program): (8n^3 + 3n^2 + n) / 6.
  • A219056 (program): 3*n^4.
  • A219085 (program): Floor((n + 1/2)^3).
  • A219086 (program): a(n) = floor((n + 1/2)^4).
  • A219088 (program): Floor((n + 1/2)^5).
  • A219089 (program): Floor((n + 1/2)^6).
  • A219091 (program): Floor((n + 1/2)^8).
  • A219092 (program): Floor(e^(n + 1/2)).
  • A219113 (program): Sequence of integers which are simultaneously a sum of consecutive squares and a difference of consecutive cubes.
  • A219116 (program): Number of semicomplete digraphs on n nodes with an “Emperor”.
  • A219167 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219190 (program): Numbers of the form n(5n+1), where n = 0,-1,1,-2,2,-3,3,…
  • A219191 (program): Numbers of the form k(7k+1), where k = 0,-1,1,-2,2,-3,3,…
  • A219196 (program): A subsequence of the denominators of the Bernoulli numbers: a(n) = A027642(A131577(n)).
  • A219205 (program): 3^(n-1)*(3^n - 1), n >= 0.
  • A219206 (program): Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.
  • A219211 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219227 (program): a(n) is the sum of n addends nested as follows: floor(f(floor(f(…(n)…)))) where f(x) = x^(1/3).
  • A219257 (program): Numbers k such that 11*k+1 is a square.
  • A219258 (program): Numbers k such that 27*k+1 is a square.
  • A219259 (program): Numbers k such that 25*k+1 is a square.
  • A219282 (program): Number of superdiagonal bargraphs with area n.
  • A219388 (program): Basic quantic arrangement for the 1 to 120 planetary electrons and elementary periods (circles I to XX) distributed by energy levels.
  • A219389 (program): Numbers k such that 13*k+1 is a square.
  • A219390 (program): Numbers k such that 14*k+1 is a square.
  • A219391 (program): Numbers k such that 21*k + 1 is a square.
  • A219392 (program): Numbers k such that 22*k+1 is a square.
  • A219393 (program): Numbers k such that 23*k+1 is a square.
  • A219394 (program): Numbers k such that 17*k+1 is a square.
  • A219395 (program): Numbers k such that 18*k+1 is a square.
  • A219396 (program): Numbers k such that 19*k+1 is a square.
  • A219428 (program): a(n) = n - 1 - phi(n).
  • A219462 (program): Sum_ k = 1..2n binomial(2n,k) * Fibonacci(2*k).
  • A219463 (program): Triangle read by rows: T(n,k) = 1 - A047999(n,k), 0 <= k <= n.
  • A219498 (program): Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 4 array.
  • A219527 (program): a(n) = (6n^2 + 7n - 9 + 2n^3)/12 - (-1)^n(n+1)/4.
  • A219529 (program): Coordination sequence for 3.3.4.3.4 Archimedean tiling.
  • A219621 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219636 (program): Complement of A035336.
  • A219637 (program): Numbers that occur twice in A219641.
  • A219640 (program): Numbers n for which there exists k such that n = k - (number of 1’s in Zeckendorf expansion of k); distinct values in A219641.
  • A219641 (program): a(n) = n minus (number of 1’s in Zeckendorf expansion of n).
  • A219642 (program): Number of steps to reach 0 starting with n and using the iterated process: x -> x - (number of 1’s in Zeckendorf expansion of x).
  • A219646 (program): Partial sums of A219642.
  • A219647 (program): Positions of zeros in A219649.
  • A219650 (program): The nonnegative integers n such that there exists a number k with A034968(n+k)=k.
  • A219651 (program): a(n) = n minus (sum of digits in factorial base expansion of n).
  • A219652 (program): Number of steps to reach 0 starting with n and using the iterated process: x -> x - (sum of digits in factorial expansion of x).
  • A219656 (program): Partial sums of A219652.
  • A219657 (program): Positions of zeros in A219659.
  • A219680 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219695 (program): For odd numbers 2n - 1, half the difference between the largest divisor not exceeding the square root, and the least divisor not less than the square root.
  • A219721 (program): Expansion of (1+7x+5x^2+7*x^3+x^4)/(1-x-x^4+x^5).
  • A219729 (program): Sum_ x <= n largest divisor of x that is <= sqrt(x).
  • A219730 (program): Sum_ x <= n smallest divisor of x that is >= sqrt(x).
  • A219754 (program): Expansion of x^4(1-x-x^2)/((1+x)(1-2x)(1-x-2*x^2)).
  • A219762 (program): Start with 0; repeatedly apply the map 0->012, 1->120, 2->201 to the odd-numbered terms and 0->210, 1->021, 2->102 to the even-numbered terms.
  • A219788 (program): Consider the succession rule (x, y, z) -> (z, y+z, x+y+z). Sequence gives z values starting at (0, 1, 2).
  • A219810 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219839 (program): a(n) is the number of odd integers in 2..(n-1) that have a common factor (other than 1) with n.
  • A219843 (program): Rows of A219463 seen as numbers in binary representation.
  • A219846 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219977 (program): Expansion of 1/(1+x+x^2+x^3).
  • A220000 (program): Sixty fourths of an inch in thousandths, rounded to nearest integer.
  • A220018 (program): Number of cyclotomic cosets of 3 mod 10^n.
  • A220020 (program): Number of cyclotomic cosets of 9 mod 10^n.
  • A220021 (program): Number of cyclotomic cosets of 11 mod 10^n.
  • A220029 (program): Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 5 array.
  • A220033 (program): Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 3 X n array.
  • A220071 (program): Difference between number of halving steps and number of tripling steps needed to reach 1 in ‘3x+1’ problem.
  • A220073 (program): Mirror of the triangle A130517.
  • A220082 (program): Numbers k such that 10*k-1 is a square.
  • A220083 (program): a(n) = (15n^2 + 9n + 2)/2.
  • A220084 (program): a(n) = (n + 1)(20n^2 + 19*n + 6)/6.
  • A220087 (program): 2^n - 27.
  • A220088 (program): a(n) = 2^n - 81.
  • A220089 (program): a(n) = 2^n - 243.
  • A220094 (program): Sum of the n-digit base-ten numbers whose digits are nonzero.
  • A220096 (program): a(1)=0, n-1 if n is prime, else largest proper divisor of n.
  • A220098 (program): Manhattan distances between 2n and 1 in the double spiral with positive integers and 1 at the center.
  • A220101 (program): Number of ordered set partitions of 1,…,n into n-1 blocks avoiding the pattern 123.
  • A220104 (program): n appears n*(n+1) times.
  • A220105 (program): 2^(n-1) mod n^2.
  • A220114 (program): Largest k >= 0 such that k = n - x - y where n = x*y, x > 0, y > 0, or -1 if no such k exists.
  • A220128 (program): 1 followed by period 6: (1, 3, 2, 3, 1, 4) repeated; offset 0.
  • A220129 (program): 1 followed by period 12: (1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11) repeated; offset 0.
  • A220147 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A220154 (program): Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.
  • A220182 (program): Number of changes of parity in the Collatz trajectory of n.
  • A220185 (program): Numbers n such that n^2 + n(n+1) is an oblong number (A002378).
  • A220186 (program): Numbers n >= 0 such that n^2 + n*(n+1)/2 is a square.
  • A220212 (program): Convolution of natural numbers (A000027) with tetradecagonal numbers (A051866).
  • A220236 (program): Binary palindromic numbers with only two 0 bits, both in the middle.
  • A220280 (program): Reluctant sequence of reluctant sequence A002260.
  • A220414 (program): a(n) = 6*a(n-1) - a(n-2), with a(1) = 13, a(2) = 73.
  • A220416 (program): Table T(n,k) = ((n+k-1)*(n+k-2)/2+n)^n, n,k >0 read by antidiagonals.
  • A220425 (program): a(n) = n^2 + 2*n + 2^n.
  • A220436 (program): a(n) = A127546(n)^2.
  • A220443 (program): a(n) = Sum_ i=1..n (3i)^2.
  • A220452 (program): Number of unordered full binary trees with labels from a set of n labels.
  • A220464 (program): Reverse reluctant sequence of reluctant sequence A002260.
  • A220465 (program): Reverse reluctant sequence of reverse reluctant sequence A004736.
  • A220466 (program): a((2n-1)2^p) = 4^p(n-1) + 2^(p-1)(1+2^p), p >= 0 and n >= 1.
  • A220492 (program): Number of primes p between quarter-squares, Q(n) < p <= Q(n+1), where Q(n) = A002620(n).
  • A220494 (program): Number of toothpicks and D-toothpicks after n-th stage in the structure of the D-toothpick “wide” triangle of the first kind.
  • A220495 (program): Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220494.
  • A220506 (program): Number of primes <= n-th quarter-square.
  • A220509 (program): n^3 + 3n + 3^n.
  • A220511 (program): n^5 + 5n + 5^n.
  • A220588 (program): a(n) = 2^n - n^2 - n.
  • A220633 (program): Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.
  • A220655 (program): For n with a unique factorial base representation n = duu! + … + d22! + d11! (each di in range 0..i, cf. A007623), a(n) = (du+1)u! + … + (d2+1)2! + (d1+1)1!; a(n) = n + A007489(A084558(n)).
  • A220656 (program): The positions of those permutations in A030298 where the first element is not fixed.
  • A220657 (program): Partial sums of A084558+1.
  • A220660 (program): Irregular table, where the n-th row consists of numbers 0..(n!-1).
  • A220661 (program): Irregular table, where the n-th row consists of numbers 1..n!
  • A220695 (program): Complement of A220655.
  • A220696 (program): The positions of those permutations in A030298 where the first element is one (fixed).
  • A220739 (program): Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.
  • A220753 (program): Expansion of (1+4x+5x^2-x^3)/((1-x)(1+x)(1-2*x^2)).
  • A220779 (program): Exponent of highest power of 2 dividing the sum 1^n + 2^n + … + n^n.
  • A220780 (program): Nonzero terms of A220779: exponent of highest power of 2 dividing an even sum 1^n + 2^n + … + n^n.
  • A220844 (program): Sum of inclusive heights of complete 4-ary trees on n nodes.
  • A220845 (program): Sum of exclusive heights of complete 3-ary trees on n nodes.
  • A220847 (program): a(n) = numerator of the fraction whose Engel expansion has the positive divisors of n as its terms.
  • A220848 (program): a(n) = sum_(d n) product_(d_x n, d_x<=d) d_x.
  • A220853 (program): Denominators of the fraction (30n+7) * binomial(2n,n)^2 * 2F1([1/2 - n/2, -n/2], [1], 64)/(-256)^n, where 2F1 is the hypergeometric function.
  • A220888 (program): a(n) = F(n+7) - (1/2)(n^3+2n^2+13*n+26) where F(i) is a Fibonacci number (A000045).
  • A220892 (program): G.f.: (1+8x+22x^2+8*x^3+x^4)/(1-x)^6.
  • A220932 (program): Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.
  • A220944 (program): Expansion of (1+3x+5x^2-x^3)/((1-x^2)(1-3x^2).
  • A220946 (program): Expansion of (1+2x+2x^2-x^3)/((1-x)(1+x)(1-3x^2)).
  • A220978 (program): a(n) = 3^(2n+1) - 3^(n+1) + 1: The left Aurifeuillian factor of 3^(6n+3) + 1.
  • A220989 (program): 12^(2n+1) - 6 * 12^n + 1: the left Aurifeuillian factor of 12^(6n+3) + 1.
  • A220990 (program): 12^(2n+1) + 6 * 12^n + 1: the right Aurifeuillian factor of 12^(6n+3) + 1.
  • A221049 (program): Expansion of (1+2x+3x^2-x^3)/((1-x)(1+x)(1-2x)(1+2*x)).
  • A221130 (program): a(n) = 2^(2*n - 1) + n.
  • A221151 (program): The generalized Fibonacci word f^[4].
  • A221152 (program): The generalized Fibonacci word f^[5].
  • A221162 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor.
  • A221217 (program): T(n,k) = ((n+k)^2-2n+3-(n+k-1)(1+2*(-1)^(n+k)))/2; n , k > 0, read by antidiagonals.
  • A221364 (program): The simple continued fraction expansion of F(x) := product n = 0..inf (1 - x^(4n+3))/(1 - x^(4n+1)) when x = 1/2*(3 - sqrt(5)).
  • A221366 (program): The simple continued fraction expansion of F(x) := product n = 0..inf (1 - x^(4n+3))/(1 - x^(4n+1)) when x = 1/2(7 - 3sqrt(5)).
  • A221374 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, with no occupancy greater than 2.
  • A221414 (program): Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with every occupancy equal to zero or two
  • A221440 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.
  • A221461 (program): Number of 0..6 arrays of length n with each element unequal to at least one neighbor, starting with 0
  • A221462 (program): Number of 0..7 arrays of length n with each element unequal to at least one neighbor, starting with 0
  • A221464 (program): Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.
  • A221465 (program): Number of 0..n arrays of length 6 with each element unequal to at least one neighbor, starting with 0.
  • A221466 (program): Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.
  • A221543 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.
  • A221564 (program): The number of FO4C3 moves required to restore a packet of n playing cards to its original state (order and orientation), where each move Flips Over the top four (4) as a unit and then Cuts three (3) cards from the top to bottom.
  • A221574 (program): Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1.
  • A221575 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1.
  • A221597 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.
  • A221652 (program): Number of n X 2 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns.
  • A221672 (program): Length of shortest non-constant arithmetic progression (AP) containing n squares.
  • A221684 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less, starting with 0
  • A221686 (program): Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less, starting with 0.
  • A221714 (program): Numbers written in base 2 with digits rearranged to be in decreasing order.
  • A221731 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns.
  • A221829 (program): Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.
  • A221837 (program): Number of integer Heron triangles of height n such that the angles adjacent to the base are not right.
  • A221838 (program): Number of integer Heron triangles of height n.
  • A221840 (program): Number of sets of n squares providing dissections of a square.
  • A221855 (program): Number of cyclotomic cosets of 13 mod 10^n.
  • A221881 (program): Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with (right) waist exactly k.
  • A221882 (program): Number of order-preserving or order-reversing full contraction mappings of an n-chain.
  • A221904 (program): 9^n + 10^n.
  • A221905 (program): 3^n + 3*n.
  • A221906 (program): 4^n + 4*n.
  • A221907 (program): 5^n + 5*n.
  • A221908 (program): 6^n + 6*n.
  • A221909 (program): 7^n + 7*n.
  • A221910 (program): a(n) = 8^n + 8*n.
  • A221911 (program): 9^n + 9*n.
  • A221912 (program): Partial sums of floor(n/12).
  • A221920 (program): a(n) = 3n/gcd(3n, n+3), n >= 3.
  • A221921 (program): a(n) = 4n/gcd(4n,n+4), n >= 4.
  • A221953 (program): a(n) = 5^(n-1) * n! * Catalan(n-1).
  • A221954 (program): a(n) = 3^(n-1) * n! * Catalan(n-1).
  • A221955 (program): a(n) = 6^(n-1) * n! * Catalan(n-1).
  • A221969 (program): Number of -n..n arrays of length 6 with the sum ahead of each element differing from the sum following that element by n or less.
  • A221975 (program): Triangle read by rows of the numbers that are the sum of some consecutive Mersenne numbers A000225.
  • A222001 (program): Number of n X 3 arrays with each row a permutation of 1..3 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.
  • A222066 (program): Decimal expansion of 1/sqrt(128).
  • A222132 (program): Decimal expansion of sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + … )))).
  • A222133 (program): Decimal expansion of sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - … )))).
  • A222134 (program): Decimal expansion of sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + … )))).
  • A222135 (program): Decimal expansion of sqrt(5 - sqrt(5 - sqrt(5 - sqrt(5 - … )))).
  • A222138 (program): Number of nX2 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero
  • A222170 (program): a(n) = n^2 + 2*floor(n^2/3).
  • A222182 (program): Numbers m such that 2*m+11 is a square.
  • A222256 (program): Lexicographically earliest injective sequence of nonnegative integers such that the sum of 6 consecutive terms is always divisible by 6.
  • A222257 (program): Lexicographically earliest injective sequence of positive integers such that the sum of 6 consecutive terms is always divisible by 6.
  • A222258 (program): Lexicographically earliest injective sequence of nonnegative integers such that the sum of 8 consecutive terms is always divisible by 8.
  • A222259 (program): Lexicographically earliest injective sequence of positive integers such that the sum of 8 consecutive terms is always divisible by 8.
  • A222260 (program): Lexicographically earliest injective sequence of nonnegative integers such that the sum of 10 consecutive terms is always divisible by 10.
  • A222261 (program): Lexicographically earliest injective sequence of positive integers such that the sum of 10 consecutive terms is always divisible by 10.
  • A222308 (program): Let P be a one-move “rider” with move set M= (1,2) ; a(n) is the number of non-attacking positions of two indistinguishable pieces P on an n X n board.
  • A222312 (program): a(n) = n + A001222(n) - 1.
  • A222335 (program): Number of nX2 0..6 arrays with no entry increasing mod 7 by 6 rightwards or downwards, starting with upper left zero
  • A222346 (program): Number of (n+2)X1 arrays of occupancy after each element moves up to +-n places including 0
  • A222408 (program): Partial sums of A008531, or crystal ball sequence for A_4 * lattice.
  • A222410 (program): Partial sums of A008534, or crystal ball sequence for A_6 * lattice.
  • A222416 (program): If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention).
  • A222464 (program): (n+6)/gcd(n*6,n+6), n >= 6.
  • A222465 (program): a(n) = 4*n^2 + 3.
  • A222548 (program): a(n) = Sum_ k=1..n floor(n/k)^2.
  • A222591 (program): Numerators of (n*(n - 3)/6) + 1, arising as the maximum possible number of triple lines for an n element set.
  • A222621 (program): a(n) = (2n-1)^(2n).
  • A222655 (program): a(n) = 16n^4 + 4.
  • A222657 (program): a(n) = 2 * floor( (2*n + 1) / 3) + 1.
  • A222716 (program): Numbers which are both the sum of n+1 consecutive triangular numbers and the sum of the n-1 immediately following triangular numbers.
  • A222740 (program): Denominators of 1/16 - 1/(4 + 8*n)^2.
  • A222822 (program): Number of idempotent 3X3 0..n matrices
  • A222834 (program): Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.
  • A222939 (program): Number of n X 1 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.
  • A222945 (program): Number of distinct sums i+j+k with i , j , k , ijk <= n.
  • A222947 (program): Number of distinct sums i+j+k with i , j , k , ijk <= n and gcd(i,j,k) <= 1.
  • A222963 (program): a(n) = (p-3)*(p+3)/4 where p is the n-th prime.
  • A222964 (program): Numbers n such that 25n+36 is a square.
  • A223082 (program): Number of n-digit numbers N with distinct digits such that N divides the reversal of N.
  • A223133 (program): Number of distinct sums i+j+k with i,j,k >= 0, ijk <= n and gcd(i,j,k) <= 1.
  • A223134 (program): Number of distinct sums i+j+k with i,j,k >= 0, ijk <= n.
  • A223139 (program): Decimal expansion of (sqrt(13) - 1)/2.
  • A223140 (program): Decimal expansion of (sqrt(29) + 1)/2.
  • A223141 (program): Decimal expansion of (sqrt(29) - 1)/2.
  • A223181 (program): Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.
  • A223211 (program): 3 X 3 X 3 triangular graph coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223241 (program): 3-loop graph coloring a rectangular array: number of n X 2 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223249 (program): Two-loop graph coloring a rectangular array: number of n X 2 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223291 (program): 4-loop graph coloring a rectangular array: number of n X 2 0..8 arrays where 0..8 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223373 (program): 3 X 3 square grid graph coloring a rectangular array: number of n X 2 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223395 (program): 4 X 4 square grid graph coloring a rectangular array: number of n X 1 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223451 (program): Number of idempotent 2X2 -n..n matrices of rank 1
  • A223454 (program): Number of idempotent 2 X 2 -n..n matrices.
  • A223544 (program): Triangle T(n,k), 0 < k <= n, T(n,1) = n - 1, T(n,k) = T(n,k-1) + n; read by rows.
  • A223552 (program): Petersen graph (3,1) coloring a rectangular array: number of n X 4 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.
  • A223564 (program): Number of nX3 0..1 arrays with antidiagonals unimodal
  • A223577 (program): Positive integers n for which there is exactly one negative integer m such that -n = floor(cot(Pi/(2*m))).
  • A223578 (program): Positive integers n for which f(-n-1) < f(-n) < f(-n+1), where f(m) = floor(cot(Pi/(2m))).
  • A223659 (program): Number of n X 1 [0..3] arrays with row sums unimodal and column sums inverted unimodal.
  • A223711 (program): Number of n X 2 0..1 arrays with row sums and column sums unimodal.
  • A223718 (program): Number of nX1 0..2 arrays with rows, antidiagonals and columns unimodal.
  • A223719 (program): Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.
  • A223756 (program): Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal.
  • A223764 (program): Number of n X 2 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
  • A223833 (program): Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A223925 (program): a(2n+1) = 2*n-1; a(2n)= 4^n.
  • A223950 (program): Number of 3 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
  • A224000 (program): Number of 2 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
  • A224039 (program): Number of 3 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
  • A224134 (program): Number of 3 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.
  • A224141 (program): Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A224195 (program): Ordered sequence of numbers of form (2^n - 1)*2^m + 1 where n >= 1, m >= 1.
  • A224233 (program): Decimal expansion of number of inches in a meter.
  • A224251 (program): Numbers, a(n) where binomial(a(n), 5n-1) == 0 (mod 5) and binomial(a(n), k) != 0 (mod 5) for k != 5n - 1.
  • A224274 (program): a(n) = binomial(4*n,n)/4.
  • A224317 (program): a(n) = a(n-1) + 3 - a(n-1)!.
  • A224327 (program): Number of idempotent n X n 0..2 matrices of rank n-1.
  • A224328 (program): Number of idempotent n X n 0..3 matrices of rank n-1
  • A224329 (program): Number of idempotent n X n 0..4 matrices of rank n-1.
  • A224330 (program): Number of idempotent n X n 0..5 matrices of rank n-1.
  • A224331 (program): Number of idempotent n X n 0..6 matrices of rank n-1.
  • A224332 (program): Number of idempotent n X n 0..7 matrices of rank n-1.
  • A224334 (program): Number of idempotent 3 X 3 0..n matrices of rank 2.
  • A224335 (program): Number of idempotent 4X4 0..n matrices of rank 3.
  • A224336 (program): Number of idempotent 5X5 0..n matrices of rank 4.
  • A224337 (program): Number of idempotent 6X6 0..n matrices of rank 5.
  • A224338 (program): Number of idempotent 7 X 7 0..n matrices of rank 6.
  • A224380 (program): Table read by antidiagonals of numbers of form (2^n -1)*2^(m+2) + 3 where n>=1, m>=1.
  • A224384 (program): a(n) = 1 + 17^n.
  • A224440 (program): a(n) = sigma(n)^(n-1).
  • A224446 (program): Denominators of certain rationals approximating sqrt(3).
  • A224454 (program): The Wiener index of the linear phenylene with n hexagons.
  • A224455 (program): The hyper-Wiener index of the linear phenylene with n hexagons.
  • A224456 (program): The Wiener index of the cyclic phenylene with n hexagons (n>=3).
  • A224459 (program): The Wiener index of the straight pentachain of n pentagonal rings (see Fig. 2.1 in the A. A. Ali et al. reference).
  • A224512 (program): Gray code variant of A147582.
  • A224513 (program): Gray code variant of A147562.
  • A224520 (program): Numbers a(n) with property a(n) + a(n+4) = 2^(n+4) - 1 = A000225(n+4).
  • A224521 (program): Numbers a(n) with property a(n) + a(n+5) = 2^(n+5) - 1 = A000225(n+5).
  • A224525 (program): Number of idempotent 3 X 3 0..n matrices of rank 1.
  • A224534 (program): Primes numbers that are the sum of three distinct prime numbers.
  • A224535 (program): Odd numbers that are the sum of three distinct prime numbers.
  • A224613 (program): a(n) = sigma(6*n).
  • A224666 (program): Number of 4 X 4 0..n matrices with each 2 X 2 subblock idempotent.
  • A224667 (program): Number of 5 X 5 0..n matrices with each 2 X 2 subblock idempotent.
  • A224668 (program): Number of 6 X 6 0..n matrices with each 2 X 2 subblock idempotent.
  • A224669 (program): Number of (n+1) X 2 0..2 matrices with each 2 X 2 subblock idempotent.
  • A224692 (program): Expansion of (1+5x+7x^2-x^3)/((1-2x^2)(1-x)*(1+x)).
  • A224701 (program): Table read by antidiagonals of numbers of form (2^n - 1)*2^(m+3) + 5 where n>=1, m>=1.
  • A224710 (program): The number of unordered partitions a,b of 2n-1 such that a and b are composite.
  • A224715 (program): The number of unordered partitions a,b of prime(n) such that a or b is a nonnegative composite and the other is prime.
  • A224779 (program): One half of the even numbers that are a primitive sum of four nonzero squares at least once.
  • A224783 (program): Denominator of Bernoulli(n,1/2) - Bernoulli(n,0).
  • A224790 (program): a(n) = 3*9^n + 8.
  • A224868 (program): a(1) = greatest k such that H(k) - H(4) < 1/3 + 1/4; a(2) = greatest k such that H(k) - H(a(1)) < H(a(1)) - H(4); and for n > 2, a(n) = greatest k such that H(k) - H(a(n-1) > H(a(n-1)) - H(a(n-2)), where H = harmonic number.
  • A224869 (program): a(n) = n*( a(n-1)+1 ), initialized by a(1) = -1.
  • A224880 (program): a(n) = 2n + sum of divisors of n.
  • A224895 (program): Let p = prime(n). Smallest odd number m > p such that m + p is semiprime.
  • A224900 (program): n!*((n+1)!)^2.
  • A224911 (program): Greatest prime dividing A190339(n).
  • A224915 (program): a(n) = Sum_ k=0..n n XOR k where XOR is the bitwise logical exclusive-or operator.
  • A224920 (program): Fifth powers expressed in base 3.
  • A224923 (program): Sum_ i=0..n Sum_ j=0..n (i XOR j), where XOR is the binary logical exclusive-or operator.
  • A224977 (program): n^2 minus sum of digits of n^2.
  • A224995 (program): Floor(1/f(x^(1/n))) for x = 3/2, where f computes the fractional part.
  • A224996 (program): Floor(1/f(x^(1/n))) for x = 2, where f computes the fractional part.
  • A225007 (program): Number of n X 5 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225008 (program): Number of n X 6 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225009 (program): Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225015 (program): Number of sawtooth patterns of length 1 in all Dyck paths of semilength n.
  • A225018 (program): Number of cusps in a class of degree-3n complex algebraic surfaces.
  • A225043 (program): Pascal’s triangle with row n reduced modulo n+1.
  • A225051 (program): Numbers of the form x^3 + SumOfCubedDigits(x).
  • A225055 (program): Irregular triangle which lists the three positions of 2*n-1 in A060819 in row n.
  • A225058 (program): a(4n) = n-1. a(2n+1) = a(4n+2) = 2n+1.
  • A225081 (program): Gray code variant of A048896.
  • A225101 (program): Numerator of (2^n - 2)/n.
  • A225126 (program): Central terms of the triangle in A048152.
  • A225144 (program): a(n) = Sum_ i=n..2n i^2(-1)^i.
  • A225152 (program): Let b(k) be A036378, then a(n) is the number of b(k) terms such that 2^n < b(k) <= 2^(n+1).
  • A225190 (program): (n+2)^(n+2) mod n^n.
  • A225215 (program): Floor of the Euclidean distance of a point on the (1, 1, 1; 1, 1, 1) 3D walk.
  • A225232 (program): The number of FO3C2 moves required to restore a packet of n playing cards to its original state (order and orientation).
  • A225240 (program): The squares on a chessboard that are white, counting from top left corner and down.
  • A225367 (program): Number of palindromes of length n in base 3 (A118594).
  • A225370 (program): Let f(S) = maximal m such that the string S contains two disjoint identical (scattered) substrings of length m (“twins”); a(n) = min f(S) over all binary strings of length n.
  • A225373 (program): a(n) = 1 + Sum_ i=0..floor(n/2) phi(n-2*i).
  • A225374 (program): Powers of 111.
  • A225381 (program): Elimination order of the first person in a Josephus problem.
  • A225399 (program): Number of nontrivial triangular numbers dividing triangular(n).
  • A225419 (program): Triangle read by rows: T(n,k) (0 <= k <= n) = binomial(2*n+2,k).
  • A225486 (program): Maximal frequency depth for the partitions of n.
  • A225491 (program): Maximal frequency depth for multisets over an alphabet of n letters.
  • A225530 (program): Number of ordered pairs (i,j) with i,j >= 0, i + j = n and gcd(i,j) <= 1.
  • A225531 (program): Number of ordered pairs (i, j) with i, j >= 0, i + j <= n and gcd(i, j) <= 1.
  • A225539 (program): Numbers n where 2^n and n have the same digital root.
  • A225551 (program): Longest checkmate in king and queen versus king endgame on an n X n chessboard.
  • A225553 (program): Longest checkmate in king and amazon versus king endgame on an n X n chessboard.
  • A225566 (program): The set of magic numbers for an idealized harmonic oscillator atomic nucleus with a biaxially deformed prolate ellipsoid shape and an oscillator ratio of 3:1
  • A225569 (program): Decimal expansion of Sum_ n>=0 1/10^(3^n), a transcendental number.
  • A225585 (program): Floor((3^n-1)/n).
  • A225586 (program): Floor((5^n-1)/n).
  • A225593 (program): The integer closest to n/e.
  • A225595 (program): Conjectured square array T(n,k) read by antidiagonals related to the existence of rectangles of size n*k in the toothpick structure of A139250.
  • A225605 (program): (1) = least k such that 1/3 < H(k) - 1/3; a(2) = least k such that H(a(1)) - H(3) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A225612 (program): Partial sums of the binomial coefficients C(4*n,n).
  • A225615 (program): Partial sums of the binomial coefficients C(5*n,n).
  • A225667 (program): Decimal expansion of 13-5*sqrt(5).
  • A225668 (program): a(n) = floor(4*log_2(n)).
  • A225690 (program): Number of Dyck paths of semilength n avoiding the pattern U^3 D^3 U D.
  • A225693 (program): Alternating sum of digits of n.
  • A225700 (program): Denominators of coefficients arising from q-expansion of Integrate[eta[q^4]^8/eta[q^2]^4, q]/q where eta is the Dedekind eta function.
  • A225743 (program): Triangular array: row n is least squarefree word of length n using positive integers.
  • A225773 (program): The squares on a chessboard that are black, counting from top left corner and down.
  • A225785 (program): Numbers n such that triangular(n) + triangular(2*n) is a triangular number.
  • A225786 (program): Numbers k such that oblong(2k) + oblong(k) is a square, where oblong(k) = A002378(k) = k(k+1).
  • A225810 (program): a(n) = (10^n)^2 + 4*(10^n) + 1.
  • A225813 (program): a(n) = (10^n)^2 + 7(10^n) + 1.
  • A225826 (program): Number of binary pattern classes in the (2,n)-rectangular grid: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225875 (program): We write the 1 + 4*k numbers once and twice the others.
  • A225883 (program): a(n) = (-1)^n * (1 - 2^n).
  • A225894 (program): Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than a single 1 has rows and columns in lexicographically nondecreasing order.
  • A225928 (program): a(n) = 416^n + 84^n + 17.
  • A225972 (program): The number of binary pattern classes in the (2,n)-rectangular grid with 3 ‘1’s and (2n-3) ‘0’s: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225975 (program): Square root of A226008(n).
  • A226008 (program): a(0) = 0; for n>0, a(n) = denominator(1/4 - 4/n^2).
  • A226023 (program): A142705 (numerators of 1/4-1/(4n^2)) sorted to natural order.
  • A226033 (program): Round(n * exp(-1 - 1/(2n))), an approximation to the number of daughters to wait before picking in the sultan’s dowry problem (Better that A225593).
  • A226044 (program): Period of length 8: 1, 64, 16, 64, 4, 64, 16, 64.
  • A226088 (program): a(n) is the number of the distinct quadrilaterals in a regular n-gon, which Q3 type are excluded.
  • A226089 (program): Denominators of the series a(n+1) = (a(n)+k)/(1+a(n)*k); where k=1/(n+1), a(1)=1/2.
  • A226096 (program): Squares with doubled (4*n+2)^2.
  • A226097 (program): a(n) = ((-1)^n + 2n - 38)(2*n - 38) + 41.
  • A226107 (program): Number of strict partitions of n with Cookie Monster number 2.
  • A226122 (program): Expansion of (1+2x+x^2+x^3+2x^4+x^5)/(1-2*x^3+x^6).
  • A226123 (program): Number of terms of the form 2^k in Collatz(3x+1) trajectory of n.
  • A226140 (program): a(n) = Sum_ i=1..floor(n/2) (n-i)^i.
  • A226164 (program): Sequence used for the quadratic irrational number belonging to the principal indefinite binary quadratic form.
  • A226177 (program): a(n) = mu(n)*d(n), where mu(n) = A008683 and d(n) = A000005.
  • A226198 (program): Floor((n-1)!/n).
  • A226199 (program): 7^n + n.
  • A226200 (program): 6^n + n.
  • A226201 (program): 8^n + n.
  • A226202 (program): 9^n + n.
  • A226203 (program): a(5n) = a(5n+3) = a(5n+4) = 2n+1, a(5n+1) = 2n-3, a(5n+2) = 2n-1.
  • A226205 (program): a(n) = F(n)^2 - F(n-1)^2 or F(n+1) * F(n-2) where F(n) = A000045(n), the Fibonacci numbers.
  • A226233 (program): Ten copies of each positive integer.
  • A226238 (program): a(n) = (n^n - n)/(n - 1).
  • A226264 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226265 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226271 (program): Index of 1/n in the Fibonacci (or rabbit) ordering of the positive rationals.
  • A226275 (program): Number of new rationals produced at the n-th iteration by applying the map t -> t+1, -1/t to nonzero terms, starting with S[0] = 1 .
  • A226276 (program): Period 4: repeat [8, 4, 4, 4].
  • A226279 (program): a(4n) = a(4n+2) = 2n , a(4n+1) = a(4n+3) = 2n-1.
  • A226280 (program): The perfect numbers produced by the aspiring numbers (A063769).
  • A226292 (program): (10n^2+4n+(1-(-1)^n))/8.
  • A226293 (program): Class of sequences of (p-1)-tuples of reverse order of natural numbers for p = 7.
  • A226294 (program): Period 2: repeat [6, 4].
  • A226308 (program): a(n) = a(n-1) + a(n-2) + 2*a(n-3) with a(0)=2, a(1)=1, a(2)=5.
  • A226315 (program): (n^2/8+3n/8-2)2^n+3.
  • A226323 (program): Number of ordered pairs (i,j) with i * j <= n and gcd(i,j) <= 1.
  • A226355 (program): Number of ordered pairs (i,j) with i * j <= n.
  • A226405 (program): Expansion of x/((1-x-x^3)*(1-x)^3).
  • A226449 (program): a(n) = n(5n^2-8*n+5)/2.
  • A226450 (program): a(n) = n(3n^2 - 5*n + 3).
  • A226451 (program): a(n) = n(7n^2-12*n+7)/2.
  • A226470 (program): a(n) = n^2 XOR triangular(n), where XOR is the bitwise logical exclusive-or operator.
  • A226488 (program): a(n) = n(13n - 9)/2.
  • A226489 (program): a(n) = n(15n-11)/2.
  • A226490 (program): a(n) = n(19n-15)/2.
  • A226491 (program): a(n) = n(21n-17)/2.
  • A226492 (program): a(n) = n(11n-5)/2.
  • A226493 (program): Closed walks of length n in K_4 graph.
  • A226500 (program): Triangular numbers representable as 3 * x^2.
  • A226508 (program): a(n) = Sum_ i=3^n..3^(n+1)-1 i.
  • A226511 (program): 3*(5^n-3^n)/2.
  • A226514 (program): Column 3 of array in A226513.
  • A226523 (program): a(n) = 0 if p=2, 1 if 2 is a square mod p, -1 otherwise, where p = prime(n).
  • A226538 (program): a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.
  • A226555 (program): Numerators of row sums of the triangular enumeration of rational numbers A226314(n,k) / A054531(n,k), 1 <= k <= n.
  • A226570 (program): Sum_ k=1..n (k+1)! mod n
  • A226576 (program): Smallest number of integer-sided squares needed to tile a 3 X n rectangle.
  • A226577 (program): Smallest number of integer-sided squares needed to tile a 4 X n rectangle.
  • A226595 (program): Lengths of maximal nontouching increasing paths in n X n grids.
  • A226602 (program): Number of ordered triples (i,j,k) with ijk = n, i,j,k >= 0 and gcd(i,j,k) <= 1.
  • A226639 (program): a(n) = n^4/8 + (5n^3)/12 - n^2/8 - (5n)/12 + 1.
  • A226720 (program): Complement of A122437.
  • A226721 (program): Position of 2^n in the joint ranking of all the numbers 2^j for j>=0 and 5^k for k>=1; complement of A123384.
  • A226725 (program): Denominator of the median of 1, 1/2, 1/3, …, 1/n .
  • A226731 (program): a(n) = (2n - 1)!/(2n).
  • A226737 (program): 11^n + n.
  • A226741 (program): Column 4 of array in A226513.
  • A226765 (program): Decimal expansion of (13-5*sqrt(5))/2.
  • A226782 (program): If n=0 (mod 2) then a(n)=0, otherwise a(n)=4^(-1) in Z/nZ*.
  • A226786 (program): If n=0 (mod 2) then a(n)=0, otherwise a(n)=8^(-1) in Z/nZ*.
  • A226787 (program): If n=0 (mod 3) then a(n)=0, otherwise a(n)=9^(-1) in Z/nZ*.
  • A226843 (program): a(n) = prime(prime(n + 1) - 2).
  • A226858 (program): Numbers n such that there are six distinct triples (k, k+n, k+2n) of squares.
  • A226866 (program): Number of n X 2 (-1,0,1) arrays of determinants of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
  • A226881 (program): Number of n-length binary words w with #(w,0) >= #(w,1) >= 1, where #(w,x) gives the number of digits x in w.
  • A226903 (program): Shiraishi numbers: a parametrized family of solutions c to the Diophantine equation a^3 + b^3 + c^3 = d^3 with d = c+1.
  • A226914 (program): Third column of A226518.
  • A226939 (program): A recursive variation of the Collatz-Fibonacci sequence: a(n) = 1 + min(a(C(n)),a(C(C(n)))) where C(n) = A006370(n), the Collatz map.
  • A226954 (program): Numbers n such that there are seven distinct triples (k, k+n, k+2n) of squares.
  • A226982 (program): a(n) = ceiling(n/2) - primepi(n).
  • A226998 (program): The number of descents over all functions f: 1,2,…,n -> 1,2,…,n .
  • A227012 (program): a(n) = floor(M(g(n-1)+1, …, g(n))), where M = harmonic mean and g(n) = n^3.
  • A227013 (program): a(n) = floor(M(g(n-1)+1,..,g(n))), where M is the harmonic mean and g(n) = n^4.
  • A227015 (program): a(n) = floor(M(g(n-1)+1, …, g(n))), where M = harmonic mean and g(n) = n^3 + n^2 + n + 1.
  • A227017 (program): Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(3n-1)/2 = A000326(n).
  • A227043 (program): Numerator of harmonic mean H(n,2), n>= 0.
  • A227047 (program): Expansion of x^2(1+x^2) / ( (x^2-x+1)(-x^2-x+1)*(1+x+x^2) ).
  • A227052 (program): a(n) = (n^2)! / (n^2-n)! = number of ways of placing n labeled balls into n^2 labeled boxes with at most one ball in each box.
  • A227071 (program): Let s(m) = the set of k > 0 such that k^m ends with k. Then a(n) = least m such that s(m) = s(n).
  • A227106 (program): Numerators of harmonic mean H(n,3), n >= 0.
  • A227107 (program): Numerators of harmonic mean H(n,4), n >= 0.
  • A227108 (program): Denominators of harmonic mean H(n,5), n >= 0.
  • A227109 (program): Numerators of harmonic mean H(n, 5), n >= 0.
  • A227121 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227140 (program): a(n) = n/gcd(n,2^5), n >= 0.
  • A227161 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227168 (program): a(n) = gcd(2n, n(n+1)/2)^2.
  • A227177 (program): n occurs n^2 - n + 1 times.
  • A227179 (program): After initial 0, integers from 0 to n(n-1) followed by integers from 0 to n(n+1) and so on.
  • A227181 (program): Irregular table: integers from n to n^2 followed by integers from (n+1) to (n+1)^2.
  • A227183 (program): a(n) = sum of parts of the unique unordered partition encoded in the run lengths of the binary expansion of n; row sums of A227739 for n>=1.
  • A227185 (program): The largest part in the unordered partition encoded in the runlengths of the binary expansion of n.
  • A227192 (program): Sum of the partial sums of the run lengths of binary expansion of n, when starting scanning from the least significant end; Row sums of A227188 and A227738.
  • A227209 (program): Expansion of 1/((1-x)^2(1-2x)(1-4x)).
  • A227241 (program): a(n) = sigma(n)( 2sigma(n)+1 ).
  • A227252 (program): Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
  • A227259 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227265 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of three or less, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227291 (program): Characteristic function of squarefree numbers squared (A062503).
  • A227308 (program): Given an equilateral triangular grid with side n consisting of n(n+1)/2 points, a(n) is the maximum number of points that can be painted so that, if any 3 of the painted ones are chosen, they do not form an equilateral triangle with sides parallel to the grid.
  • A227316 (program): a(n) = n(n+1) if n == 0 or 1 (mod 4), otherwise a(n) = n(n+1)/2.
  • A227327 (program): Number of non-equivalent ways to choose two points in an equilateral triangle grid of side n.
  • A227347 (program): Number of lattice points in the closed region bounded by the graphs of y = (5/6)*x^2, x = n, and y = 0, excluding points on the x-axis.
  • A227353 (program): Number of lattice points in the closed region bounded by the graphs of y = 3*x/5, x = n, and y = 0, excluding points on the x-axis.
  • A227362 (program): Distinct digits of n arranged in decreasing order.
  • A227380 (program): Doubling the first two of every four nonnegative numbers.
  • A227394 (program): The maximum value of x^4(n-x)(x-1) for x in 1..n is reached for x = a(n).
  • A227400 (program): Decimal expansion of 5/(3*phi^2) where phi is the golden ratio.
  • A227417 (program): Integer triples a(3n-2) = n, a(3n-1) = n+4, and a(3n) = n+7.
  • A227456 (program): Number of permutations i_0, i_1, …, i_n of 0, 1, …, n with i_0 = 0 and i_n = 1 such that all the n+1 numbers i_0^2+i_1, i_1^2+i_2, …, i_ n-1 ^2+i_n, i_n^2+i_0 are of the form (p+1)/4 with p a prime congruent to 3 modulo 4.
  • A227471 (program): Position of first 0 in the binary representation of prime(n), starting the count of positions at 1 for the least significant bit.
  • A227512 (program): Floor(-1/n + 1/log((2n+1)/(2n-1))).
  • A227513 (program): Round(-1/n + 1/log((2n+1)/(2n-1))).
  • A227541 (program): a(n) = floor(13*n^2/4).
  • A227546 (program): n! + n^2 + 1.
  • A227547 (program): a(n) = a(n-1) + prime(n-1), with a(1)=3.
  • A227554 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having nonzero determinant, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227559 (program): Number of partitions of n into distinct parts with boundary size 2.
  • A227568 (program): Largest k such that a partition of n into distinct parts with boundary size k exists.
  • A227582 (program): Expansion of (2+3x+2x^2+2x^3+3x^4+x^5-x^6)/(1-2x+x^2-x^5+2x^6-x^7).
  • A227589 (program): Maximum label within a minimal labeling of n identical 4-sided dice yielding the most possible sums.
  • A227625 (program): Indicator sequence of primes p > 3: k = p mod 6, if k = 5 then a(n) = -1, if k = 1 then a(n) = 1 else a(n) = 0, a(2) = -1, a(3) = 1.
  • A227637 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.
  • A227653 (program): a(1) = least k such that 1/2 + 1/3 < H(k) - H(3); a(2) = least k such that H(a(1)) - H(3) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A227683 (program): Number of digits in n-th Mersenne number.
  • A227703 (program): The Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference.
  • A227704 (program): The hyper-Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference.
  • A227707 (program): The terminal Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.
  • A227712 (program): a(n) = 92^n - 3n - 5.
  • A227719 (program): Floor(1/s(n)), where s(n) = n*log(1+1/n) - (2n-1)/(2n).
  • A227720 (program): Round(1/s(n)), where s(n) = n*log(1+1/n) - (2n-1)/(2n).
  • A227721 (program): Floor(1/s(n)), where s(n) = (2n+1)/(2n+2) - n*log((n+1)/n).
  • A227726 (program): a(n) = [x^n] (1 + x)/(1 - x)^(2*n+1).
  • A227742 (program): Fixed points of permutation A227741.
  • A227776 (program): a(n) = 6*n^2 + 1.
  • A227786 (program): Take squares larger than 1, subtract 3 from even squares and 2 from odd squares; a(n) = a(n-1) + A168276(n+1) (with a(1) = 1).
  • A227790 (program): Difference between 3n^2 and the nearest square number.
  • A227804 (program): a(1) = greatest k such that H(k) - H(8) < H(8) - H(4); a(2) = greatest k such that H(k) - H(a(1)) < H(a(1)) - H(8), and for n > 2, a(n) = greatest k such that H(k) - H(a(n-1) > H(a(n-1)) - H(a(n-2)), where H = harmonic number.
  • A227805 (program): Sum of even numbers starting at 2, alternating signs.
  • A227832 (program): Sum of odd numbers starting with 1, alternating signs (beginning with plus)
  • A227841 (program): Partial sums of A014817.
  • A227842 (program): First differences of A014817.
  • A227849 (program): a(n) = 2 * floor( 3/14 * n^2) if n even, a(n) = 2 * round( 3/14 * n^2) -1 if n odd.
  • A227863 (program): Numbers congruent to 1,49 mod 120.
  • A227871 (program): Sum of digits of 14^n.
  • A227881 (program): Sum of digits of 17^n.
  • A227906 (program): Coins left after packing heart patterns (fixed orientation) into n X n coins.
  • A227944 (program): Number of iterations of “take odd part of phi” (A053575) to reach 1 from n.
  • A227970 (program): Triangular arithmetic on half-squares: b(n)*(b(n) - 1)/2 where b(n) = floor(n^2/2).
  • A227978 (program): a(0)=1, a(1)=2; for n>1, a(n) = n*(2^n+4)/4.
  • A227990 (program): 3^a(n) is the highest power of 3 dividing prime(n)+1.
  • A227991 (program): Highest power of 3 dividing prime(n)+1.
  • A228016 (program): a(1) = least k such that 1/1+1/2+1/3+1/4+1/5 < H(k) - H(5); a(2) = least k such that H(a(1)) - H(5) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A228017 (program): Numbers n divisible by the sum of any k-subset of digits of n with k >= 1.
  • A228025 (program): a(1) = least k such that 1/2+1/3+1/4+1/5 < H(k) - H(5); a(2) = least k such that H(a(1)) - H(5) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A228039 (program): Thue-Morse sequence along the squares: A010060(n^2).
  • A228071 (program): Write n in binary and interpret as a decimal number; a(n) is this quantity minus n.
  • A228078 (program): a(n) = 2^n - Fibonacci(n) - 1.
  • A228081 (program): 64^n + 1.
  • A228105 (program): a(n) = 432*n^6.
  • A228121 (program): Numbers n such that 3n - 4 is prime.
  • A228124 (program): Number of blocks in a Steiner Quadruple System of order A047235(n+1).
  • A228137 (program): Numbers that are congruent to 1, 4 mod 12.
  • A228138 (program): Number of blocks in a Steiner system S(2, 4, A228137(n+1)).
  • A228141 (program): Numbers that are congruent to 1, 5 mod 20.
  • A228142 (program): Number of blocks in a Steiner system S(2, 5, A228141(n+1)).
  • A228157 (program): Numbers n which are anagrams of n+9.
  • A228158 (program): Numbers n such that the cardinality of (natural numbers <=n with a first digit of 1) = n/2.
  • A228219 (program): Number of second differences of arrays of length 4 of numbers in 0..n.
  • A228220 (program): Number of second differences of arrays of length 5 of numbers in 0..n.
  • A228221 (program): Number of second differences of arrays of length 6 of numbers in 0..n.
  • A228229 (program): Recurrence a(n) = n(n + 1)a(n-1) + 1 with a(0) = 1.
  • A228230 (program): Recurrence a(n) = 1/2n(n + 1)*a(n-1) + 1 with a(0) = 1.
  • A228245 (program): The integers occurring in the song “Ten green bottles”.
  • A228261 (program): Number of third differences of arrays of length 5 of numbers in 0..n.
  • A228274 (program): a(n) = Sum_ d n, n/d odd n * d.
  • A228290 (program): a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n.
  • A228291 (program): a(n) = Sum_ k=1..7 n^k.
  • A228292 (program): a(n) = Sum_ k=1..8 n^k.
  • A228293 (program): a(n) = Sum_ k=1..9 n^k.
  • A228294 (program): a(n) = Sum_ k=1..10 n^k.
  • A228295 (program): The ‘Honeycomb’ or ‘Beehive’ sequence: a(n) = ceiling(12^(1/4)*n).
  • A228297 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5.
  • A228298 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=7.
  • A228305 (program): a(1) = 3; for n >= 1, a(2n) = 2^(n+1), a(2n+1) = 5*2^(n-1).
  • A228306 (program): The Wiener index of the Kneser graph K(n,2) (n>=5).
  • A228307 (program): The hyper-Wiener index of the Kneser graph K(n,2) (n>=5).
  • A228310 (program): The hyper-Wiener index of the hypercube graph Q(n) (n>=2).
  • A228317 (program): The hyper-Wiener index of the triangular graph T(n) (n >= 1).
  • A228318 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the star graph K(1,n).
  • A228319 (program): The hyper-Wiener index of the graph obtained by applying Mycielski’s construction to the star graph K(1,n).
  • A228320 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the cycle graph C(n).
  • A228321 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the path graph on n vertices (n>=2).
  • A228329 (program): a(n) = Sum_ k=0..n (k+1)^2*T(n,k)^2 where T(n,k) is the Catalan triangle A039598.
  • A228344 (program): Floor(3*n^2/4) - 1.
  • A228361 (program): The number of all possible covers of L-length line segment by 2-length line segments with allowed gaps < 2.
  • A228366 (program): Toothpick sequence from a diagram of compositions of the positive integers (see Comments lines for definition).
  • A228367 (program): n-th element of the ruler function plus the highest power of 2 dividing n.
  • A228368 (program): Difference between the n-th element of the ruler function and the highest power of 2 dividing n.
  • A228372 (program): Number of nontrivial divisors in the first n composites.
  • A228394 (program): The number of permutations of length n sortable by 2 prefix block transpositions.
  • A228396 (program): The number of permutations of length n sortable by 2 reversals.
  • A228398 (program): The number of permutations of length n sortable by 3 prefix reversals (in the pancake sorting sense).
  • A228403 (program): The number of boundary twigs for complete binary twigs. A twig is a vertex with one edge on the boundary and only one other descendant.
  • A228406 (program): Sequences from the quartic oscillator.
  • A228409 (program): a(n) = 4*mu(n) + 5, where mu is the Moebius function (A008683).
  • A228423 (program): Sum of the squared primes less than or equal to n.
  • A228437 (program): Denominator of n/24.
  • A228448 (program): floor(n! / 3^n).
  • A228451 (program): Recurrence: a(2n) = a(n), a(2n+1) = a(n) + 2n + 1, with a(0) = 0, a(1) = 1.
  • A228483 (program): a(n) = 2 - mu(n), where mu(n) is the Moebius function (A008683).
  • A228484 (program): a(n) = 2^n(3n)!/(n!(2n)!).
  • A228495 (program): Characteristic function of the odd odious numbers (A092246).
  • A228560 (program): Curvature of the circles (rounded down) inscribed in golden triangle arranged as spiral form.
  • A228564 (program): Largest odd divisor of n^2 + 1.
  • A228568 (program): a(n) = 2^n*A056236(n).
  • A228569 (program): Binomial transform of A006497.
  • A228587 (program): Sum of the squares (modulo n) of the odd numbers less than n.
  • A228593 (program): a(1) = 2, a(n) = a(n-1)prime(n-1)prime(n), where prime(n) denotes the n-th prime number.
  • A228597 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to a benzenoid consisting of a linear chain of n hexagons.
  • A228598 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the crown graph G(n) (n>=3).
  • A228600 (program): The Szeged index of the n-sunlet graph (n>=3).
  • A228602 (program): a(1) = 17, a(2) = 80, a(n) = 4*(a(n-1) + a(n-2)) for n >= 3.
  • A228603 (program): a(1) = 9, a(2) = 44, a(n) = 4*(a(n-1) + a(n-2)) (n >=3).
  • A228609 (program): Partial sums of the cubes of the tribonacci sequence A000073.
  • A228612 (program): Number of (possibly overlapping) occurrences of the subword given by the binary expansion of n in all binary words of length n.
  • A228620 (program): a(n) = n - phi(n) + mu(n).
  • A228647 (program): a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x(1+3x^2)/(1-x-x^3).
  • A228661 (program): Number of 2Xn binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228693 (program): Largest number of maximal independent sets of nodes in any tree on n nodes.
  • A228698 (program): a(n) = 8*Product i=1..n p(i) - 1, where p(i) = i-th odd prime.
  • A228705 (program): Expansion of (1-2x+4x^2-2x^3+x^4)/((1-x)^4(1+x^2)^2).
  • A228706 (program): Expansion of (1 - 3x + 5x^2 - 3x^3 + x^4)/((1-x)^4(1+x^2)^2).
  • A228718 (program): Sequence taken from Garvan’s paper (see slides 28, 29).
  • A228719 (program): Decimal expansion of 3*Pi/5.
  • A228721 (program): Decimal expansion of 7*Pi.
  • A228728 (program): a(1)=1, a(2)=2 and for n > 2, a(n) is the least integer > a(n-1) such that there is a permutation b(1), …, b(n) of a(1), …, a(n) with b(1) = a(1) and b(n) = a(n), and with the n numbers b(1)-b(2) , b(2)-b(3) , …, b(n-1)-b(n) , b(n)-b(1) pairwise distinct.
  • A228729 (program): Product of the positive squares less than or equal to n.
  • A228763 (program): a(n) = 2^L(n) - 1, where L(n) is the n-th Lucas number (A000032).
  • A228767 (program): Second bisection of the inverse binomial transform of the rational sequence with e.g.f. (x/2)*(exp(-x)+1)/(exp(x)-1).
  • A228778 (program): a(n) = 2^Fibonacci(n) + 1.
  • A228789 (program): a(n) = 2^L(n) + 1, where L(n) is A000032(n).
  • A228791 (program): Number of n X 3 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
  • A228797 (program): Number of 2 X n binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
  • A228824 (program): Decimal expansion of 4*Pi/5.
  • A228826 (program): Delayed continued fraction of sqrt(2).
  • A228840 (program): a(n) = 3^n*A228569(n).
  • A228842 (program): Binomial transform of A014448.
  • A228843 (program): a(n) = 4^n*A228842(n).
  • A228871 (program): Odd numbers producing 3 out-of-order odd numbers in the Collatz (3x+1) iteration.
  • A228873 (program): F(n) * F(n+1) * F(n+2) * F(n+3), the product of four consecutive Fibonacci numbers, A000045.
  • A228879 (program): a(n+2) = 3*a(n), starting 4,7.
  • A228887 (program): a(n) = binomial(3*n + 1,3).
  • A228888 (program): a(n) = binomial(3*n + 2, 3).
  • A228889 (program): a(n) = 3n(3n + 1)(3*n + 2).
  • A228906 (program): A diagonal of triangle A228904.
  • A228935 (program): a(n) = (3 - 6n)(-1)^n.
  • A228936 (program): Expansion of (1 + 3x - 3x^3 - x^4)/(1 + 2*x^2 + x^4).
  • A228941 (program): The n-th convergent of CF(e) is the a(n)-th convergent of DCF(e), the delayed continued fraction of e.
  • A228949 (program): Coins left when packing boomerangs into n X n coins.
  • A228958 (program): a(n) = 12 + 34 + 56 + 78 + 910 + 1112 + 13*14 + … + (up to n).
  • A228959 (program): Total sum of squared lengths of ascending runs in all permutations of [n].
  • A228967 (program): Table read by rows; T(n,k) = 2n for k = 1, T(n,k) = 9n for k = 2.
  • A229004 (program): Indices of Bell numbers divisible by 3.
  • A229013 (program): Number of arrays of median of three adjacent elements of some length-5 0..n array, with no adjacent equal elements in the latter.
  • A229014 (program): Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.
  • A229020 (program): Decimal expansion of 1 - 1/(12) + 1/(122) - 1/(1223) + …
  • A229039 (program): G.f.: Sum_ n>=0 (n+2)^n * x^n / (1 + (n+2)*x)^n.
  • A229065 (program): Numbers of the form 2^(p-1)+3, where p is prime.
  • A229067 (program): Sum of n-th prime and next perfect square.
  • A229093 (program): The clubs patterns appearing in n X n coins.
  • A229109 (program): a(n) = n plus the number of its distinct prime factors.
  • A229110 (program): Sum of non-divisors of n reduced modulo n.
  • A229118 (program): Distance from the n-th triangular number to the nearest square.
  • A229127 (program): Number of n-digit numbers containing the digit ‘0’.
  • A229135 (program): n * (2 + 2^(2*n - 1)).
  • A229144 (program): Partial sums of (Fibonacci numbers mod 3).
  • A229146 (program): a(n) = n^3(5n+3)/2.
  • A229147 (program): a(n) = n^4(3n+2).
  • A229148 (program): a(n) = n^5(7n+5)/2.
  • A229149 (program): a(n) = n^6(4n+3).
  • A229151 (program): a(n) = n^8(5n+4).
  • A229152 (program): a(n) = n^9(11n+9)/2.
  • A229154 (program): The clubs patterns appearing in n X n coins, with rotation allowed.
  • A229183 (program): a(n) = n*(n^2 + 3)/2.
  • A229232 (program): Number of undirected circular permutations pi(1), …, pi(n) of 1, …, n with the n numbers pi(1)pi(2)-1, pi(2)pi(3)-1, …, pi(n-1)pi(n)-1, pi(n)pi(1)-1 all prime.
  • A229253 (program): Total number of elements of nonempty subsets of divisors of n.
  • A229274 (program): Composite squarefree numbers n such that p+tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).
  • A229277 (program): Number of ascending runs in 1,…,3 ^n.
  • A229278 (program): Number of ascending runs in 1,…,4 ^n.
  • A229279 (program): Number of ascending runs in 1,…,5 ^n.
  • A229324 (program): Composite squarefree numbers n such that p + tau(n) divides n - phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).
  • A229337 (program): Sum of products of elements of nonempty subsets of divisors of n.
  • A229341 (program): a(n) = tau(n’), the number of divisors of the arithmetic derivative of n.
  • A229347 (program): a(1) = 1, for n > 1 a(n) = n*2^(omega(n)-1) where omega is A001221.
  • A229354 (program): Total sum of n-th powers of parts in all partitions of 3.
  • A229422 (program): Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
  • A229439 (program): Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229446 (program): Number of 3 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229447 (program): Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229463 (program): Expansion of 1/((1-x)^2(1-26x)).
  • A229470 (program): Positions of 2 in decimal expansion of 0.1231232331232332333…, whose definition is given below.
  • A229472 (program): Number of defective 4-colorings of an n X 1 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229473 (program): Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229481 (program): Final digit of 1^n + 2^n + … + n^n.
  • A229489 (program): Conjecturally, possible differences between prime(k)^2 and the next prime for some k.
  • A229504 (program): Number of defective 3-colorings of an n X 2 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229505 (program): Number of defective 3-colorings of an n X 3 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229522 (program): Final digit (in decimal system) of (n^n)^n, i.e., (n^n)^n mod 10.
  • A229525 (program): Sum of coefficients of the transform ax^2 + (4a/k - b)x + 4a/k^2 + 2b/k + c = 0 for a,b,c = 1,-1,-1, k = 1,2,3…
  • A229526 (program): The c coefficients of the transform ax^2 + (4a/k - b)x + 4a/k^2 + 2b/k + c= 0 for a,b,c = 1,-1,-1, k = 1,2,3…
  • A229535 (program): Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229554 (program): 7*n! + 1.
  • A229572 (program): Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229573 (program): Number of defective 4-colorings of an n X 3 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229580 (program): Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229581 (program): Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229582 (program): Number of defective 3-colorings of an n X 4 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229587 (program): Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order
  • A229593 (program): Number of boomerang patterns appearing in n X n coins, rotation not allowed.
  • A229598 (program): Voids left when packing boomerangs into n X n coins.
  • A229611 (program): Expansion of 1/((1-x)^3*(1-11x))
  • A229620 (program): Incorrect version of A045949.
  • A229701 (program): Squares of triangular numbers, written backwards.
  • A229718 (program): Number of arrays of length 2 that are sums of n consecutive elements of length 2+n-1 permutations of 0..2+n-2, and no two consecutive rises or falls in the latter permutation.
  • A229762 (program): a(n) = (n XOR floor(n/2)) AND floor(n/2), where AND and XOR are bitwise logical operators.
  • A229763 (program): a(n) = (2*n) XOR n AND n, where AND and XOR are bitwise logical operators.
  • A229764 (program): Nim sequence of MARK: the game on n counters in which the legal moves are to remove 1 counter or to halve the number of counters and round down.
  • A229780 (program): Decimal expansion of (3+sqrt(5))/10.
  • A229785 (program): Partial sums of A157129.
  • A229786 (program): Primes modulo 23.
  • A229787 (program): Primes modulo 24.
  • A229788 (program): 62^n - n^2 - 5n - 6.
  • A229795 (program): Number of 2 X 2 0..n arrays with rows and columns in lexicographically nondecreasing order.
  • A229803 (program): Domination number for rook graph HR(n) on a triangular board of hexagonal cells. The rook can move along any row of adjacent cells, in any of the three directions.
  • A229828 (program): 7*n! - 1.
  • A229829 (program): Numbers coprime to 15.
  • A229838 (program): Consider all primitive 60-degree triangles with sides A < B < C. The sequence gives the values of A.
  • A229852 (program): 3*h^2, where h is an odd integer not divisible by 3.
  • A229853 (program): 384*n + 1.
  • A229855 (program): 384*n + 257.
  • A229858 (program): Consider all 120-degree triangles with sides A < B < C. The sequence gives the values of A.
  • A229903 (program): (190/99)*(100^A001651(n)-1).
  • A229912 (program): a(n) = Fibonacci(n) * (2*Fibonacci(n) + 1).
  • A229939 (program): Decimal expansion of 9*Pi/10.
  • A229949 (program): Number of divisors of the n-th positive quarter-square.
  • A229968 (program): Numbers not divisible by 3 or 11.
  • A230018 (program): a(n) = (9n^3 + 5n)/2.
  • A230024 (program): Final nonzero digit of n^n in base 16.
  • A230038 (program): Distance between n^2 and the smallest triangular number >= n^2.
  • A230056 (program): G.f.: Sum_ n>=0 (n+3)^n * x^n / (1 + (n+3)*x)^n.
  • A230059 (program): Conjectural number of irreducible zeta values of weight 2*n+1 and depth three.
  • A230074 (program): Period 4: repeat [1, -2, 1, 0].
  • A230075 (program): Period 8: repeat [2, 1, 0, 1, -2, -1, 0, -1].
  • A230076 (program): (A007521(n)-1)/4.
  • A230088 (program): Partial sums of A010062.
  • A230089 (program): If n is divisible by 4 then 4, if n is divisible by 2 then 2, otherwise n.
  • A230096 (program): Number of tilings of an n X 1 rectangle (using tiles of dimension 1 X 1 and 2 X 1) that share no tile at the same position with their mirrored image.
  • A230101 (program): a(n) = product of n and all its nonzero digits.
  • A230128 (program): The number of multinomial coefficients over partitions with value equal to 4.
  • A230135 (program): Triangle read by rows: T(n, k) = 1 if ((k mod 4 = 2) and (n mod 2 = 1)) or ((k mod 4 = 0) and (n mod 2 = 0)) else T(n, k) = 0.
  • A230137 (program): a(n)/2^n is the expected value of the maximum of the number of heads and the number of tails when n fair coins are tossed.
  • A230149 (program): The number of multinomial coefficients over partitions with value equal to 5.
  • A230179 (program): Number of n X 3 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).
  • A230196 (program): Number of pairs (p,q) such that 2p + 3q = n and p != q.
  • A230197 (program): The number of multinomial coefficients over partitions with value equal to 7.
  • A230198 (program): The number of multinomial coefficients over partitions with value equal to 8.
  • A230239 (program): Values of N for which the equation x^2 - 4*y^2 = N has integer solutions.
  • A230269 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
  • A230276 (program): Voids left after packing 5-curves coins patterns into fountain of coins with base n.
  • A230297 (program): a(n) = A010062(n) written in binary: a(n+1) = a(n) + hammingweight(a(n)) in binary.
  • A230298 (program): a(n) = A010062(n) mod 2.
  • A230300 (program): a(n) = n + wt(n-1), where wt() = A000120() is the binary weight.
  • A230312 (program): Squares which cannot be written as the sum of a smaller nonzero square and twice a triangular number.
  • A230325 (program): (prime(n)^2 -1)*(prime(n)^2 - prime(n))/2.
  • A230388 (program): a(n) = binomial(11n+1,n)/(11n+1).
  • A230402 (program): Integer areas of orthic triangles of integer-sided triangles.
  • A230403 (program): a(n) = the largest k such that (k+1)! divides n; the number of trailing zeros in the factorial base representation of n (A007623(n)).
  • A230404 (program): a(n) = the largest k such that (k+1)! divides 2n; the number of trailing zeros in the factorial base representation of even numbers.
  • A230405 (program): a(n) = A000217(A230404(n+1)); the first differences of A219650.
  • A230431 (program): After the first zero, integers from 0 to A219661(n)-1 followed by integers from 0 to A219661(n+1)-1, etc.
  • A230460 (program): Prime(2*prime(n)).
  • A230462 (program): Numbers congruent to 1, 11, 13, 17, 19, or 29 mod 30.
  • A230501 (program): Floor(Sum(d(k), k=1..n)/n), where d(k) is the number of divisors of k.
  • A230539 (program): a(n) = 3n2^(3*n-1).
  • A230540 (program): a(n) = 2n3^(2*n-1).
  • A230547 (program): a(n) = 3binomial(3n+9, n)/(n+3).
  • A230584 (program): Either two less than a square or two more than a square.
  • A230585 (program): First terms of first rows of zigzag matrices as defined in A088961.
  • A230586 (program): a(n) = n^5 - 5n^3 + 5n.
  • A230603 (program): Generalized Fibonacci word. Binary complement of A221150.
  • A230628 (program): Maximum number of colors needed to color a planar map of several empires, each empire consisting of n countries.
  • A230629 (program): a(0) = 0; thereafter a(n) = (1 + a(floor(n/2))) mod 3.
  • A230630 (program): a(1)=0; thereafter a(n) = (1 + a(floor(n/2))) mod 3.
  • A230631 (program): a(n) = n + (sum of digits in base-4 representation of n).
  • A230641 (program): a(n) = n + (sum of digits in base-3 representation of n).
  • A230664 (program): Floor(3^n / n^2).
  • A230724 (program): Digital sum of tribonacci numbers with a(0)=a(1)=0, a(2)=1.
  • A230774 (program): Number of primes less than first prime above square root of n.
  • A230775 (program): Smallest prime number greater than or equal to the square root of n.
  • A230799 (program): The number of distinct nonzero coefficients in the n-th cyclotomic polynomial.
  • A230846 (program): 1 + A075526(n).
  • A230847 (program): a(n) = 1 + A054541(n).
  • A230849 (program): A075526 and A000012 interleaved.
  • A230850 (program): A054541 and A000012 interleaved.
  • A230864 (program): log2*(n) (version 3): number of iterations log_2(log_2(log_2(…(n)…))) required for the result to be <= 1.
  • A230865 (program): a(n) = n + (sum of digits in base-5 representation of n).
  • A230874 (program): a(1)=1; thereafter a(n) = 2^a(ceiling(n/2)).
  • A230875 (program): a(1)=0; thereafter a(n) = 2^a(ceiling(n/2)).
  • A230877 (program): If n = Sum_ i=0..m c(i)2^i, c(i) = 0 or 1, then a(n) = Sum_ i=0..m (m+1-i)c(i).
  • A230900 (program): a(n) = 2^Lucas(n).
  • A230928 (program): Number of black-square subarrays of (n+2) X (1+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230929 (program): Number of black-square subarrays of (n+2) X (2+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230971 (program): Number of (n+2) X (2+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230980 (program): Number of primes <= n, starting at n=0.
  • A230981 (program): Decimal expansion of 3/(2^(1/2)).
  • A231001 (program): Number of years after which an entire year can have the same calendar, in the Julian calendar.
  • A231002 (program): Number of years after which it is possible to have a date falling on same day of the week, but the entire year does not have the same calendar, in the Julian calendar.
  • A231004 (program): Number of years after which it is not possible to have the same calendar for the entire year, in the Julian calendar.
  • A231057 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231087 (program): Number of perfect matchings in graph C_3 x C_ 2n
  • A231103 (program): Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231104 (program): Number of n X 4 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231149 (program): Greatest integer k such that n+1 + … + n+k <= 1 + … + n.
  • A231151 (program): Least integer k such that n+1 + … + n+k > 1 + … + n.
  • A231204 (program): If n = Sum_ i=0..m c(i)2^i, c(i) = 0 or 1, then a(n) = (m-i)c(i).
  • A231205 (program): Table of maximal number of guesses required to solve a Mastermind variant, read by columns.
  • A231209 (program): Smallest squarefree number k with 2^n ways to write k as k = x*y, where x, y = squarefree numbers, 1 <= x <= k, 1 <= y <= k.
  • A231233 (program): Triangle T(n,k) = greatest prime factor of n*k+1.
  • A231279 (program): a(n) = Jacobsthal(n^2), where Jacobsthal(n) = A001045(n), for n>=1.
  • A231303 (program): Recurrence a(n) = a(n-2) + n^M for M=4, starting with a(0)=0, a(1)=1.
  • A231304 (program): Recurrence a(n) = a(n-2) + n^M for M=5, starting with a(0)=0, a(1)=1.
  • A231305 (program): Recurrence a(n) = a(n-2) + n^M for M=6, starting with a(0)=0, a(1)=1.
  • A231306 (program): Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1.
  • A231307 (program): Recurrence a(n) = a(n-2) + n^M for M=8, starting with a(0)=0, a(1)=1.
  • A231308 (program): Recurrence a(n) = a(n-2) + n^M for M=9, starting with a(0)=0, a(1)=1.
  • A231309 (program): Recurrence a(n) = a(n-2) + n^M for M=10, starting with a(0)=0, a(1)=1.
  • A231317 (program): Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A231390 (program): Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A231470 (program): Largest integer less than 10, coprime to n.
  • A231471 (program): Largest integer less than 11 and coprime to n.
  • A231472 (program): Largest integer less than 12 and coprime to n.
  • A231475 (program): Largest integer less than 5 and coprime to n.
  • A231500 (program): a(n) = Sum_ i=0..n wt(i)^2, where wt(i) = A000120(i).
  • A231501 (program): a(n) = Sum_ i=0..n wt(i)^3, where wt() = A000120().
  • A231502 (program): a(n) = Sum_ i=0..n wt(i)^4, where wt() = A000120().
  • A231503 (program): a(n) = Sum_ i=0..n digsum_3(i)^2, where digsum_3(i) = A053735(i).
  • A231504 (program): a(n) = Sum_ i=0..n digsum_3(i)^3, where digsum_3(i) = A053735(i).
  • A231505 (program): a(n) = Sum_ i=0..n digsum_3(i)^4, where digsum_3(i) = A053735(i).
  • A231559 (program): a(n) = floor( A000326(n)/2 ).
  • A231560 (program): Floor(sum_ i=2..n 1/(i*log(i))).
  • A231562 (program): Numbers n such that A031971(8490421583559688410706771261086n) == n (mod 8490421583559688410706771261086n).
  • A231600 (program): Output of a finite state automaton generating the period doubling sequence, when fed with binary representation of n, read from right to left.
  • A231601 (program): Number of permutations of [n] avoiding ascents from odd to even numbers.
  • A231620 (program): a(n) = A000930(n^2), where A000930 is Narayana’s cows sequence.
  • A231621 (program): a(n) = A000930(n*(n+1)/2), where A000930 is Narayana’s cows sequence.
  • A231643 (program): a(n) = 5*2^n + 5.
  • A231664 (program): a(n) = Sum_ i=0..n digsum_4(i), where digsum_4(i) = A053737(i).
  • A231665 (program): a(n) = Sum_ i=0..n digsum_4(i)^2, where digsum_4(i) = A053737(i).
  • A231666 (program): a(n) = Sum_ i=0..n digsum_4(i)^3, where digsum_4(i) = A053737(i).
  • A231667 (program): a(n) = Sum_ i=0..n digsum_4(i)^4, where digsum_4(i) = A053737(i).
  • A231668 (program): a(n) = Sum_ i=0..n digsum_5(i), where digsum_5(i) = A053824(i).
  • A231669 (program): a(n) = Sum_ i=0..n digsum_5(i)^2, where digsum_5(i) = A053824(i).
  • A231670 (program): a(n) = Sum_ i=0..n digsum_5(i)^3, where digsum_5(i) = A053824(i).
  • A231671 (program): a(n) = Sum_ i=0..n digsum_5(i)^4, where digsum_5(i) = A053824(i).
  • A231672 (program): a(n) = Sum_ i=0..n digsum_6(i), where digsum_6(i) = A053827(i).
  • A231673 (program): a(n) = Sum_ i=0..n digsum_6(i)^2, where digsum_6(i) = A053827(i).
  • A231674 (program): a(n) = Sum_ i=0..n digsum_6(i)^3, where digsum_6(i) = A053827(i).
  • A231675 (program): a(n) = Sum_ i=0..n digsum_6(i)^4, where digsum_6(i) = A053827(i).
  • A231676 (program): a(n) = Sum_ i=0..n digsum_7(i), where digsum_7(i) = A053828(i).
  • A231677 (program): a(n) = Sum_ i=0..n digsum_7(i)^2, where digsum_7(i) = A053828(i).
  • A231678 (program): a(n) = Sum_ i=0..n digsum_7(i)^3, where digsum_7(i) = A053828(i).
  • A231679 (program): a(n) = Sum_ i=0..n digsum_7(i)^4, where digsum_7(i) = A053828(i).
  • A231680 (program): a(n) = Sum_ i=0..n digsum_8(i), where digsum_8(i) = A053829(i).
  • A231681 (program): a(n) = Sum_ i=0..n digsum_8(i)^2, where digsum_8(i) = A053829(i).
  • A231682 (program): a(n) = Sum_ i=0..n digsum_8(i)^3, where digsum_8(i) = A053829(i).
  • A231683 (program): a(n) = Sum_ i=0..n digsum_8(i)^4, where digsum_8(i) = A053829(i).
  • A231684 (program): a(n) = Sum_ i=0..n digsum_9(i), where digsum_9(i) = A053830(i).
  • A231685 (program): a(n) = Sum_ i=0..n digsum_9(i)^2, where digsum_9(i) = A053830(i).
  • A231686 (program): a(n) = Sum_ i=0..n digsum_9(i)^3, where digsum_9(i) = A053830(i).
  • A231687 (program): a(n) = Sum_ i=0..n digsum_9(i)^4, where digsum_9(i) = A053830(i).
  • A231688 (program): a(n) = Sum_ i=0..n digsum(i)^3, where digsum(i) = A007953(i).
  • A231689 (program): a(n) = Sum_ i=0..n digsum(i)^4, where digsum(i) = A007953(i).
  • A231712 (program): a(n) = n^n + n - 1.
  • A231721 (program): Partial sums of phitorials: a(n) = A001088(1)+A001088(2)+…+A001088(n).
  • A231722 (program): Partial sums of A001088 starting from its second term; a(1)=0, a(n) = A001088(2)+…+A001088(n).
  • A231821 (program): a(n) = mu(n) + 3, where mu is the Mobius function (A008683).
  • A231864 (program): Partial sums of the second power of arithmetic derivative function A003415.
  • A231896 (program): a(n) = 4*a(n-1) - a(n-2) with a(0) = 0, a(1) = 4.
  • A231946 (program): Partial sums of the third power of arithmetic derivative function A003415.
  • A232015 (program): Expansion of (1-2x)/((1+2x)(1-3x)).
  • A232059 (program): Number of n X 2 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal.
  • A232089 (program): Table read by rows, which consist of 1 followed by 2^k, 0 <= k < n ; n = 0,1,2,3,…
  • A232091 (program): Smallest square or promic (oblong) number greater than or equal to n.
  • A232096 (program): a(n) = largest m such that m! divides 1+2+…+n; a(n) = A055881(A000217(n)).
  • A232098 (program): a(n) is the largest m such that m! divides n^2; a(n) = A055881(n^2).
  • A232172 (program): Partial sums of second arithmetic derivative of natural numbers.
  • A232205 (program): a(0)=1; thereafter a(n) = na(n-1) if n is even, otherwise a(n) = 2n*a(n-1).
  • A232228 (program): a(1)=1; thereafter a(n) = 2^(number of bits in binary expansion of a(n-1)) + 1 + a(n-1).
  • A232229 (program): a(1)=9; thereafter a(n) = 8*10^(n-1) + 8 + a(n-1).
  • A232230 (program): Expansion of (1 - 2x + x^2 + x^3 + x^5) / ((1 - x)(1 - 2*x - x^3)).
  • A232245 (program): Sum of the number of ones in binary representation of n and n^2.
  • A232289 (program): Number of nX2 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally
  • A232324 (program): n(n+1)/2 modulo sigma(n).
  • A232395 (program): (ceiling(sqrt(n^3 + n^2 + n + 1)))^2 - (n^3 + n^2 + n + 1).
  • A232397 (program): a(n) = ceiling(sqrt(n^4 + n^3 + n^2 + n + 1))^2 - (n^4 + n^3 + n^2 + n + 1).
  • A232423 (program): a(n) = ceiling(sqrt(n^4 - n^3 - n^2 + n + 1))^2 - (n^4 - n^3 - n^2 + n + 1).
  • A232495 (program): 9n^3/2 - 21n^2/2 + 8*n - 4.
  • A232503 (program): Largest power of 2 in the Collatz (3x+1) trajectory of n.
  • A232508 (program): Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, diagonally or antidiagonally, with no adjacent elements equal.
  • A232533 (program): a(n) = Sum_ i=1…n Sum_ j=1..i lcm(i,j)/i.
  • A232555 (program): Nonsquare numbers whose sum of proper square divisors is a square greater than 1.
  • A232580 (program): Number of binary sequences of length n that contain at least one contiguous subsequence 011.
  • A232582 (program): Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.
  • A232584 (program): Number of (n+1)X(3+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal
  • A232599 (program): Alternating sum of cubes, i.e., Sum_ k=0..n k^p*q^k for p=3, q=-1.
  • A232600 (program): a(n) = Sum_ k=0..n k^p*q^k, where p=1, q=-2.
  • A232601 (program): a(n) = Sum_ k=0..n k^p*q^k for p = 2 and q = -2.
  • A232615 (program): Variant of the Chandra-sutra (A014701) using 3 instead of 2, and a mod argument using residues 1 and 2.
  • A232617 (program): Product of first n odd numbers plus product of first n even numbers: (2n-1)!! + (2n)!!, where k!! = A006882(k).
  • A232625 (program): Denominators of abs(n-8)/(2*n), n >= 1
  • A232713 (program): Doubly pentagonal numbers: a(n) = n(3n-2)(3n-1)(3n+1)/8.
  • A232746 (program): n occurs A030124(n) times; a(n) = one less than the least k such that A005228(k) > n.
  • A232747 (program): Inverse function to Hofstadter’s A005228.
  • A232748 (program): Partial sums of the characteristic function of Hofstadter’s A030124.
  • A232765 (program): Values of y solving x^2 = floor(y^2/3 + y).
  • A232771 (program): Values of x satisfying x^2 = floor(y^2/3 + y).
  • A232779 (program): Sum of iterated logs; a(n) = 0 if n = 0; otherwise n + a(floor(log_2(n)).
  • A232801 (program): a(2n) = (3^n - 1)/2, a(2n+1) = 3^n.
  • A232866 (program): Positions of the nonnegative integers in the sequence (or tree) of complex numbers generated by these rules: 0 is in S, and if x is in S, then x + 1 and i*x are in S, where duplicates are deleted as they occur.
  • A232867 (program): Positions of the negative integers in the sequence (or tree) of complex numbers generated by these rules: 0 is in S, and if x is in S, then x + 1 and i*x are in S, where duplicates are deleted as they occur.
  • A232893 (program): Numbers whose sum of square divisors is a palindrome in base 10 having at least two digits.
  • A232896 (program): a(n) = 3a(n-1) - 2a(n-2) - a(n-3) + a(n-4), where a(1) = 1, a(2) = 3, a(3) = 5, a(4) = 8.
  • A232921 (program): Number of 2 X n 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, diagonally or antidiagonally.
  • A232935 (program): Number of n X 2 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, vertically or antidiagonally.
  • A232970 (program): Expansion of (1-3x)/(1-5x+3*x^2+x^3).
  • A232983 (program): The Gauss factorial n_7!.
  • A232990 (program): Period 5: repeat [1,0,0,1,0].
  • A232991 (program): Period 6: repeat [1, 0, 0, 0, 1, 0].
  • A233035 (program): a(n) = n * floor(n/4).
  • A233036 (program): The maximum number of I-tetrominoes that can be packed into an n X n array of squares when rotation is allowed.
  • A233077 (program): Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233078 (program): Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233083 (program): Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233099 (program): Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233106 (program): Number of n X 1 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
  • A233123 (program): Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233196 (program): Number of n X 2 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
  • A233203 (program): Floor(n^n / 2^n).
  • A233211 (program): Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
  • A233247 (program): Expansion of ( 1-x^3-x^2 ) / ( (x^3-x^2-1)(x^3+2x^2+x-1) ).
  • A233272 (program): a(n) = n + 1 + number of nonleading zeros in binary representation of n (A080791).
  • A233273 (program): Bisection of A233272: a(n) = A233272(2n+1).
  • A233279 (program): Permutation of nonnegative integers: a(n) = A054429(A006068(n)).
  • A233280 (program): Permutation of nonnegative integers: a(n) = A003188(A054429(n)).
  • A233286 (program): Number of trailing zeros in the factorial base representation of n-th Fibonacci number; a(n) = A230403(A000045(n)) = A233285(n)-1.
  • A233325 (program): (2*6^(n+1) - 7) / 5.
  • A233326 (program): a(n) = (7^(n+1) - 4) / 3.
  • A233328 (program): a(n) = (2*8^(n+1) - 9) / 7.
  • A233329 (program): Expansion of (1+4x+x^2)/((1+x)^2(1-x)^5).
  • A233334 (program): a(1)=1; for n>1, a(n) is the smallest number > a(n-1) such that a(1) + a(2) +…+ a(n) is a composite number.
  • A233397 (program): floor(n^n / 3^n).
  • A233398 (program): n^n mod 3^n.
  • A233411 (program): The number of length n binary words with some prefix which contains two more 1’s than 0’s or two more 0’s than 1’s.
  • A233441 (program): Floor(2^n / n^3).
  • A233442 (program): 2^n mod n^3.
  • A233449 (program): a(n) = Sum_ k=0..n k! * 2^(n-k).
  • A233471 (program): a(n) = 3^n mod n^2.
  • A233473 (program): Least k such that there are n triangular numbers between triangular(k) and k^2.
  • A233522 (program): Expansion of 1 / (1 - x - x^4 + x^9) in powers of x.
  • A233543 (program): Table T(n,m) = m! read by rows.
  • A233581 (program): a(n) = 2a(n-1) - 3a(n-2) + a(n-3), a(0) = 1, a(1) = 0, a(2) = -1.
  • A233583 (program): Coefficients of the generalized continued fraction expansion e = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/….))).
  • A233656 (program): a(n) = 3a(n-1) - 2(n-1), with a(0) = 1.
  • A233774 (program): Total number of vertices in the first n rows of Sierpinski gasket, with a(0) = 1.
  • A233775 (program): Number of vertices in the n-th row of the Sierpinski gasket (cf. A047999).
  • A233795 (program): Number of triangular numbers between triangular(n) and n^2.
  • A233820 (program): Period 4: repeat [20, 5, 15, 10].
  • A233868 (program): Numbers that are not the sum of two evil numbers.
  • A233904 (program): a(2n) = a(n) - n, a(2n+1) = a(n) + n, with a(0)=0.
  • A233905 (program): a(2n) = a(n), a(2n+1) = a(n) + n, with a(0)=0.
  • A233931 (program): a(2n) = a(n) + n, a(2n+1) = a(n), with a(0)=0.
  • A234011 (program): The sums of 2 consecutive odious numbers (A000069).
  • A234016 (program): Partial sums of the characteristic function of A055938.
  • A234017 (program): Inverse function for injection A055938.
  • A234040 (program): a(n) = binomial(2(n+1),n) * gcd(n,2)/(2(n+1)).
  • A234041 (program): a(n) = binomial(n+2,2)*gcd(n,3)/3, n >= 0.
  • A234042 (program): a(n) = binomial(n+4,4)*gcd(n,5)/5.
  • A234043 (program): a(n) = C(5*(n+1),4)/5, with n >= 0.
  • A234044 (program): Period 7: repeat [2, -2, 1, 0, 0, 1, -2].
  • A234045 (program): Period 7: repeat [0, 0, 1, -1, -1, 1, 0].
  • A234046 (program): Period 7: repeat [0, 1, -1, 0, 0, -1, 1].
  • A234249 (program): Number of ways to choose 4 points in an n X n X n triangular grid.
  • A234253 (program): a(n) = sum_ i=1..n C(7+i,8)^2.
  • A234272 (program): G.f.: (1+4x+x^2)/(1-4x+x^2).
  • A234275 (program): Expansion of (1+2x+9x^2-4*x^3)/(1-x)^2.
  • A234306 (program): a(n) = n + 1 - d(2n), where d(n) is the number of divisors of n.
  • A234307 (program): a(n) = Sum_ i=1..n gcd(2*n-i, i).
  • A234319 (program): Smallest sum of n-th powers of k+1 consecutive positive integers that equals the sum of n-th powers of the next k consecutive integers, or -n if none.
  • A234349 (program): Maximal number of points that can be placed on a triangular grid of side n so that no three points are collinear.
  • A234373 (program): Row 4 of the square array A234951.
  • A234429 (program): Numbers which are the digital sum of the square of some prime.
  • A234431 (program): Numbers that are the sum of 2 successive evil numbers (A001969).
  • A234463 (program): Binomial(8n+4,n)/(2n+1).
  • A234528 (program): Binomial(10n+5,n)/(2n+1).
  • A234538 (program): (Number of positive digits of n written in base 3) modulo 3.
  • A234587 (program): Odd-indexed terms of A234586.
  • A234646 (program): Sum of the distinct prime divisors of n^3 + 1.
  • A234717 (program): Floor(n/(exp(1/(2*n))-1)).
  • A234740 (program): Sum of the eleventh powers of the first n primes.
  • A234779 (program): Number of (n+1) X (1+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases.
  • A234787 (program): Cubes (with at least two digits) that become squares when their rightmost digit is removed.
  • A234902 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3) after n rotations.
  • A234903 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 3, 2) after n rotations.
  • A234904 (program): a(n)*Pi is the total length of irregular spiral (center points: 2, 1, 3) after n rotations.
  • A234914 (program): Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant stress tilted 1 X 1 tilings).
  • A234933 (program): The number of binary sequences that contain at least two consecutive 1’s and contain at least two consecutive 0’s.
  • A234957 (program): Highest power of 4 dividing n.
  • A234959 (program): Highest power of 6 dividing n.
  • A235088 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4) after n rotations.
  • A235089 (program): a(n)*Pi is the total length of irregular spiral (center points: 2, 1, 3, 4) after n rotations.
  • A235115 (program): Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the star graph S_n (having n vertices; see A235114).
  • A235127 (program): Greatest k such that 4^k divides n.
  • A235136 (program): a(n) = (2*n - 1) * a(n-2) for n>1, a(0) = a(1) = 1.
  • A235162 (program): Decimal expansion of (sqrt(33) + 1) / 2.
  • A235204 (program): Number of integer lattice points inside the square ABCD with side length n>0 with A(0 0), B(n*sqrt(2)/2 n*sqrt(2)/2), C(0 nsqrt(2)) and D(-nsqrt(2)/2 n*sqrt(2)/2).
  • A235224 (program): a(0) = 0, and for n > 0, a(n) = largest k such that A002110(k-1) <= n, where A002110(k) gives the k-th primorial number.
  • A235269 (program): floor(s*t/(s+t)), where s(n) are the squares, t(n) the triangular numbers.
  • A235323 (program): Squared sum of the distinct prime factors of n, i.e., sopf(n)^2.
  • A235332 (program): a(n) = n(9n + 25)/2 + 6.
  • A235337 (program): Number of integer lattice points inside the square ABCD with side length n>0 with A(-n*sqrt(2)/2 0), B(n*sqrt(2)/2 0), C(0 nsqrt(2)/2) and D(-nsqrt(2)/2 0).
  • A235355 (program): 0 followed by the sum of (1),(2), (3,4),(5,6), (7,8,9),(10,11,12) from the natural numbers.
  • A235361 (program): Floor((n + Pi)^2).
  • A235367 (program): Sum of positive even numbers up to n^2.
  • A235378 (program): a(n) = (-1)^n*(n! - (-1)^n).
  • A235382 (program): a(n) = smallest number of unit squares required to enclose n units of area.
  • A235398 (program): Sum of digits of the cubes of prime numbers.
  • A235399 (program): Numbers which are the digital sum of the cube of some prime.
  • A235451 (program): Number of length n words on alphabet 0,1,2 of the form 0^(i)1^(j)2^(k) such that i=j or j=k.
  • A235496 (program): a(n) = round(n^n/n!).
  • A235497 (program): 2n concatenated with n.
  • A235498 (program): For k in 2,3,…,9 define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(2).
  • A235499 (program): For k in 2,3,…,9 define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(3).
  • A235509 (program): Decimal expansion of arccos(4/5).
  • A235534 (program): a(n) = binomial(6n, 2n) / (4*n + 1).
  • A235535 (program): a(n) = binomial(9n, 3n) / (6*n + 1).
  • A235536 (program): a(n) = binomial(8n, 2n) / (6*n + 1).
  • A235537 (program): Expansion of (6 + 13x - 8x^2 - 8x^3 + 6x^4)/((1 + x)^2*(1 - x)^3).
  • A235602 (program): a(n) = n/wt(n) if wt(n) divides n, otherwise a(n) = n, where wt(n) is the binary weight of n (A000120).
  • A235643 (program): Total number of sides of a tetraflake-like fractal after n iterations, a(1) = 16 (see comments).
  • A235699 (program): a(n+1) = a(n) + (a(n) mod 10) + 1, a(0) = 0.
  • A235700 (program): a(n+1) = a(n) + (a(n) mod 5), a(1)=1.
  • A235702 (program): Fixed points of A001175 (Pisano periods).
  • A235711 (program): Arithmetic derivative of quarter squares.
  • A235796 (program): 2*n - 1 - sigma(n).
  • A235799 (program): a(n) = n^2 - sigma(n).
  • A235800 (program): Length of n-th vertical line segment from left to right in a diagram of a two-dimensional version of the Collatz (or 3x + 1) problem.
  • A235801 (program): Length of n-th horizontal line segment in a diagram of a two-dimensional version of the Collatz (or 3x + 1) problem.
  • A235877 (program): Number of (n+1) X (1+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235878 (program): Number of (n+1) X (2+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235880 (program): Number of (n+1) X (4+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235885 (program): Number of (n+1)X(n+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
  • A235886 (program): Number of (n+1) X (1+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235887 (program): Number of (n+1) X (2+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235888 (program): Number of (n+1) X (3+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235889 (program): Number of (n+1) X (4+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235890 (program): Number of (n+1) X (5+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235918 (program): Largest m such that 1, 2, …, m divide n^2.
  • A235921 (program): Numbers n such that smallest number not dividing n^2 (A236454) is different from smallest prime not dividing n (A053669).
  • A235933 (program): Numbers coprime to 35.
  • A235944 (program): Digital roots of squares of Lucas numbers.
  • A235963 (program): n appears (n+1)/(1 + (n mod 2)) times.
  • A235988 (program): Sum of the partition parts of 3n into 3 parts.
  • A236182 (program): Sum of the sixth powers of the first n primes.
  • A236185 (program): Differences between terms of compacting Eratosthenes sieve for prime(4) = 7.
  • A236194 (program): a(n) = binomial(3n+1, n-1).
  • A236203 (program): Interleave A005563(n), A028347(n).
  • A236208 (program): Numbers not divisible by 2, 5 or 11.
  • A236209 (program): Sum of the seventh powers of the first n primes.
  • A236213 (program): Number of units in the imaginary quadratic field Q(sqrt(-d)), where d > 0 is the n-th squarefree number.
  • A236214 (program): Sum of the eighth powers of the first n primes.
  • A236215 (program): Sum of the ninth powers of the first n primes.
  • A236216 (program): Sum of the tenth powers of the first n primes.
  • A236218 (program): Sum of the twelfth powers of the first n primes.
  • A236222 (program): Sum of the fourteenth powers of the first n primes.
  • A236223 (program): Sum of the fifteenth powers of the first n primes.
  • A236224 (program): Sum of the sixteenth powers of the first n primes.
  • A236225 (program): Sum of the seventeenth powers of the first n primes.
  • A236226 (program): Sum of the eighteenth powers of the first n primes.
  • A236257 (program): a(n) = 2n^2 - 7n + 9.
  • A236267 (program): a(n) = 8n^2 + 3n + 1.
  • A236283 (program): The number of orbits of triples of 1,2,…,n under the action of the dihedral group of order 2n.
  • A236284 (program): a(n) = tau(n)^n, where tau(n) = A000005(n) = the number of divisors of n.
  • A236290 (program): Decimal expansion of (sqrt(33) - 1) / 2.
  • A236305 (program): The number of P-positions in the game of Nim with up to 3 piles, allowing for piles of zero, such that the number of objects in each pile does not exceed n.
  • A236312 (program): a(n) = floor((n + e)^2), where e is the natural logarithm base.
  • A236313 (program): Recurrence: a(2n) = 3a(n)-1, a(2n+1) = 1.
  • A236326 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 1) after n rotations.
  • A236327 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 2) after n rotations.
  • A236332 (program): The number of orbits of 4-tuples of the dihedral group of order 2n acting on 1,2,…,n .
  • A236337 (program): Expansion of (2 - x) / ((1 - x)^2 * (1 - x^3)) in powers of x.
  • A236343 (program): Expansion of (1 - x + 2*x^2 - x^3) / ((1 - x)^2 * (1 - x^3)) in powers of x.
  • A236348 (program): Expansion of (1 - x + 2*x^2 + x^3) / ((1 - x) * (1 - x^3)) in powers of x.
  • A236364 (program): Sum of all the middle parts in the partitions of 3n into 3 parts.
  • A236398 (program): Period 4: repeat 1,1,2,1.
  • A236399 (program): Left factorial !p, where p = prime(n).
  • A236403 (program): Numbers not in A236402.
  • A236428 (program): a(n) = F(n+1)^2 + F(n+1)*F(n) - F(n)^2, where F = A000045.
  • A236432 (program): a(n) = (2n-1)*210; numbers which are 210 times an odd number.
  • A236453 (program): Number of length n strings on the alphabet 0,1,2 of the form 0^i 1^j 2^k such that i,j,k>=0 and if i=1 then j=k.
  • A236454 (program): Smallest number not dividing n^2.
  • A236535 (program): a(n)*Pi is the total length of irregular spiral (center points: 2, 3, 1; pattern 1) after n rotations.
  • A236632 (program): Sum of all divisors of all positive integers <= n minus the total number of divisors of all positive integers <= n.
  • A236652 (program): Positive integers n such that n^2 divided by the digital root of n is a square.
  • A236653 (program): Positive integers n such that n^3 divided by the digital root of n is a cube.
  • A236677 (program): a(0)=1; for n>0, a(n) = (1-a(floor(log_2(n)))) * a(n-msb(n)); characteristic function of A079599.
  • A236678 (program): Partial sums of the characteristic function of A079599.
  • A236680 (program): Dimension of the space of spinors in n-dimensional real space.
  • A236682 (program): Values of a for triples (a,b,c) of positive integers such that 1/a + 1/b + 1/c = 1/2 and a <= b <= c, listed with multiplicity.
  • A236770 (program): a(n) = n(n + 1)(3n^2 + 3n - 2)/8.
  • A236771 (program): a(n) = n + floor(n/2 + n^2/3).
  • A236773 (program): a(n) = n + floor( n^2/2 + n^3/3 ).
  • A236840 (program): n minus number of runs in the binary expansion of n: a(n) = n - A005811(n).
  • A236916 (program): The first “octad” is 0, 1, 2, 2, 2, 2, 3, 3; thereafter add 4 to get the next octad.
  • A236965 (program): Number of nonzero quartic residues modulo the n-th prime.
  • A236967 (program): Expansion of (1+3x)^2/(1-3x)^2.
  • A236999 (program): Odd part of n*(n+3)/2-1 (A034856).
  • A237042 (program): UPC check digits.
  • A237109 (program): a(n) is the numerator of 2*n / ((n+2) * (n+3)).
  • A237128 (program): Angles n expressed in degrees such that 2*cos(n) = phi where phi is the golden ratio (A001622).
  • A237133 (program): Values of x in the solutions to x^2 - 3xy + y^2 + 19 = 0, where 0 < x < y.
  • A237250 (program): Values of x in the solutions to x^2 - 4xy + y^2 + 11 = 0, where 0 < x < y.
  • A237268 (program): a(1)=1; for n>1, a(n) is the smallest F(m)>F(n) such that F(n) divides F(m), where F(k) denotes the k-th Fibonacci number.
  • A237274 (program): a(n) = A236283(n) mod 9.
  • A237275 (program): Smallest k divisible by the n-th power of its last decimal digit > 1.
  • A237347 (program): First differences of A078633.
  • A237353 (program): For n=g+h, a(n) is the minimum value of omega(g)+omega(h).
  • A237415 (program): For k in 2,3,…,9 define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^3. This is k(2).
  • A237416 (program): Smallest multiple of 5 beginning with n.
  • A237420 (program): If n is odd, then a(n) = 0; otherwise, a(n) = n.
  • A237450 (program): Triangle read by rows, T(n,k) = !n + (k-1)*(n-1)!, with n>=1, 1<=k<=n; Position of the first n-letter permutation beginning with number k in the list of lexicographically sorted permutations A030299.
  • A237451 (program): Zero-based column index to irregular tables organized as successively larger square matrices.
  • A237514 (program): Numbers k such that 2^(k-1) < 3^(m-1) < 2^k < 3^m < 2^(k+1), for some m > 2, a(1) = 1.
  • A237516 (program): Pyramidal centered square numbers.
  • A237587 (program): Triangle read by rows in which row n lists the first n odd squares in decreasing order.
  • A237588 (program): Sigma(n) - 2n + 1.
  • A237589 (program): Sum of first n odd noncomposite numbers.
  • A237616 (program): a(n) = n(n + 1)(5*n - 4)/2.
  • A237617 (program): a(n) = n(n + 1)(17*n - 14)/6.
  • A237618 (program): a(n) = n(n + 1)(19*n - 16)/6.
  • A237622 (program): Interpolation polynomial through n points (0,1), (1,1), …, (n-2,1) and (n-1,n) evaluated at 2n, a(0)=1.
  • A237664 (program): Interpolation polynomial through n+1 points (0,1), (1,1), …, (n-1,1) and (n,n) evaluated at 2n.
  • A237684 (program): a(n) = floor(n*prime(n) / Sum_ i<=n prime(i).
  • A237881 (program): a(n) = 2-adic valuation of prime(n)+prime(n+1).
  • A237884 (program): a(n) = (n!m)/(m!(m+1)!) where m = floor(n/2).
  • A237930 (program): a(n) = 3^(n+1) + (3^n-1)/2.
  • A237991 (program): a(n) = 991*n^2 + 1.
  • A238015 (program): Denominator of (2n+1)!8Bernoulli(2n,1/2).
  • A238055 (program): a(n) = (13*3^n-1)/2.
  • A238192 (program): In the Collatz (3x+1) iteration of n, the last odd number before 1, or 0 if there is no such number.
  • A238236 (program): Expansion of (1-x-x^2)/((x-1)(x^3+3x^2+2*x-1)).
  • A238275 (program): a(n) = (4*7^n - 1)/3.
  • A238276 (program): a(n) = (9*8^n - 2)/7.
  • A238290 (program): a(n+1) = a(n) + 6 + 2(n - 2floor(n/2)) for n > 0, a(0) = 0.
  • A238303 (program): Triangle T(n,k), 0<=k<=n, read by rows given by T(n,0) = 1, T(n,k) = 2 if k>0.
  • A238327 (program): Recursively defined by a(0) = 1, a(n + 1) = p + 2, where p is the least prime greater than a(n).
  • A238328 (program): Sum of all the parts in the partitions of 4n into 4 parts.
  • A238340 (program): Number of partitions of 4n into 4 parts.
  • A238366 (program): a(n) = 5*a(n-2) + 2, a(0) = 1, a(1) = 2.
  • A238374 (program): Row sums of triangle in A204026.
  • A238375 (program): Row sums of triangle in A152719.
  • A238377 (program): Row sums of triangle in A204028.
  • A238383 (program): Row sums of triangle in A139040.
  • A238384 (program): Triangle of numbers related to A075535.
  • A238410 (program): a(n) = floor((3(n-1)^2 + 1)/2).
  • A238411 (program): a(n) = 2nfloor(n/2).
  • A238420 (program): a(n)=the Wiener index of the Lucas cube L_n.
  • A238468 (program): Period 7: repeat [0, 0, -1, 1, -1, 1, 0].
  • A238469 (program): Period 7: repeat [0, 1, 0, 0, 0, 0, -1].
  • A238470 (program): Period 7: repeat [0, 0, 1, 0, 0, -1, 0].
  • A238471 (program): C(5n+6, 4)/5 for n >= 0.
  • A238472 (program): C(5*n+7, 4)/5 for n>= 0.
  • A238473 (program): C(5*n+8, 4)/5 for n>= 0.
  • A238477 (program): a(n) = 32*n - 27 for n >= 1. Second column of triangle A238475.
  • A238526 (program): Record values of A238525.
  • A238531 (program): Expansion of (1 - x + x^2)^2 / (1 - x)^3 in powers of x.
  • A238533 (program): Number of solutions to gcd(x^2 + y^2 + z^2 + t^2 + h^2, n) = 1 with x,y,z,t,h in [0,n-1].
  • A238535 (program): Sum of divisors d of n where d > sqrt(n).
  • A238549 (program): a(n) is one fourth of the total number of free ends of 4 line segments expansion at n iterations (see Comments lines for definition).
  • A238598 (program): Largest integer k such that n >= k^2-k-1 = A165900(k).
  • A238604 (program): a(n) = Sum_ k=0..3 f(n+k)^2 where f=A130519.
  • A238642 (program): n if n+1 is prime; if n+1 is composite, n multiplied by smallest prime factor of n+1.
  • A238684 (program): a(1) = a(2) = 1; for n > 2, a(n) is the product of prime factors of the n-th Fibonacci number.
  • A238702 (program): Sum of the smallest parts of the partitions of 4n into 4 parts.
  • A238705 (program): Number of partitions of 4n into 4 parts with smallest part = 1.
  • A238720 (program): Number of nX2 0..2 arrays with no element equal to the sum modulo 3 of elements to its left or elements above it
  • A238737 (program): a(n) = 2*n+2 - A224911(n).
  • A238738 (program): Expansion of (1 + 2x + 2x^2)/(1 - x - 2x^3 + 2x^4 + x^6 - x^7).
  • A238803 (program): Number of ballot sequences of length 2n with exactly n fixed points.
  • A238806 (program): Number of n X 2 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the sum of elements above it, modulo 3.
  • A238845 (program): Prefix overlap between binary expansions of n and n+1.
  • A238846 (program): Expansion of (1-2x)/(1-3x+x^2)^2.
  • A238847 (program): Smallest k such that k*n^3 + 1 is prime.
  • A238874 (program): Strictly superdiagonal compositions: compositions (p1, p2, p3, …) of n such that pi > i.
  • A238923 (program): Number of (n+1) X (1+1) 0..3 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.
  • A238949 (program): Degree of divisor lattice D(n).
  • A238976 (program): a(n) = ((3^(n-1)-1)^2)/4.
  • A239024 (program): Number of n X 2 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.
  • A239031 (program): Number of 4 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.
  • A239035 (program): Product of 8 consecutive integers.
  • A239050 (program): a(n) = 4*sigma(n).
  • A239052 (program): Sum of divisors of 4*n-2.
  • A239053 (program): Sum of divisors of 4*n-1.
  • A239056 (program): Sum of the parts in the partitions of 4n into 4 parts with smallest part = 1.
  • A239057 (program): Sum of the parts in the partitions of 4n into 4 parts with smallest part equal to 1 minus the number of these partitions.
  • A239059 (program): Sum of the two smallest parts from the partitions of 4n into 4 parts with smallest part = 1.
  • A239072 (program): Maximum number of cells in an n X n square grid that can be painted such that no two orthogonally adjacent cells are painted and every unpainted cell can be reached from the edge of the grid by a series of orthogonal steps to unpainted cells.
  • A239086 (program): The sequence S = a(1), a(2), … is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e = f, and S is always extended with the smallest integer not yet present in S.
  • A239090 (program): The sequence S = a(1), a(2), … is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d >= e < f, and S is always extended with the smallest integer not yet present in S.
  • A239091 (program): Prefix overlap of dictionary consisting of binary expansions of 0 through n.
  • A239092 (program): Prefix overlap of dictionary consisting of decimal expansions of 0 through n.
  • A239094 (program): a(n) = (5n^9 - 30n^7 + 63n^5 - 50n^3 + 12*n)/360.
  • A239120 (program): Decimal expansion of 1/2 - Pi/8.
  • A239122 (program): Partial sums of A061019.
  • A239123 (program): a(n) = 128*n - 107 for n >= 1. Third column of triangle A238475.
  • A239124 (program): a(n) = 64*n - 11 for n >= 1. Third column of triangle A238476.
  • A239126 (program): Rectangular array showing the starting values M(n, k), k >= 1, for the Collatz operation (ud)^n, n >= 1, ending in an odd number, read by antidiagonals.
  • A239128 (program): a(n) = 32*n - 1, n >= 1. Fourth column of triangle A239126, related to the Collatz problem.
  • A239129 (program): a(n) = 18*n - 1, n >= 1, the second column of triangle A239127 related to the Collatz problem.
  • A239138 (program): The sequence S = a(1), a(2), … is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e > f, and S is always extended with the smallest integer not yet present in S.
  • A239140 (program): Number of strict partitions of n having standard deviation σ < 1.
  • A239141 (program): Number of strict partitions of n having standard deviation σ <= 1.
  • A239171 (program): Number of (n+1) X (1+1) 0..2 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.
  • A239186 (program): Sum of the largest two parts in the partitions of 4n into 4 parts with smallest part equal to 1.
  • A239195 (program): Sum of the next to smallest parts in the partitions of 4n into 4 parts with smallest part = 1.
  • A239229 (program): Euler characteristic of n-holed torus: 2 - 2*n.
  • A239278 (program): Smallest k > 1 such that n(n+1)…*(n+k-1) / (n+(n+1)+…+(n+k-1)) is an integer.
  • A239284 (program): a(n) = (15^n - (-1)^n)/16.
  • A239285 (program): a(n) = (15^n - (-2)^n)/17.
  • A239286 (program): Expansion of (x + 1)(3x^2 + 2*x + 1)/(x^2 + x + 1)^2.
  • A239287 (program): Triangle T(n,k), 0 <= k <= n, read by rows: T(n,k) = floor(n/2) - min(k,n-k).
  • A239294 (program): a(n) = (15^n - (-3)^n)/18.
  • A239308 (program): Size of smallest set S of integers such that 0,1,2,…,n is a subset of S-S, where S-S= abs(i-j) i,j in S .
  • A239325 (program): a(n) = 6n^2 + 8n + 1.
  • A239352 (program): van Heijst’s upper bound on the number of squares inscribed by a real algebraic curve in R^2 of degree n, if the number is finite.
  • A239364 (program): Numbers n such that (n^2-4)/10 is a square.
  • A239365 (program): Numbers n such that 10*n^2+4 is a square.
  • A239367 (program): The bisection of A238315 that remains constant with changes in the offset of the exponent of the second term.
  • A239442 (program): a(n) = phi(n^7).
  • A239443 (program): a(n) = phi(n^9), where phi = A000010.
  • A239447 (program): Partial sums of A030101.
  • A239449 (program): 7n^2 - 5n + 1.
  • A239459 (program): Concatenation of n^3 and n.
  • A239462 (program): A239459(n) / n.
  • A239463 (program): A239460(n) / n^2.
  • A239464 (program): A239461(n) / n^2.
  • A239492 (program): The fifth bicycle lock sequence: a(n) is the maximum value of min xy, (5-x)(n-y) over 0 <= x <= 5, 0 <= y <= n for integers x, y.
  • A239504 (program): Number of digits in the decimal expansion of n^10 (A008454).
  • A239568 (program): Number of ways to place 2 points on a triangular grid of side n so that they are not adjacent.
  • A239592 (program): (n^4 - n^3 + 4*n^2 + 2)/2.
  • A239607 (program): (1-2*n^2)^2.
  • A239608 (program): Sin( arcsin(n)- 2*arccos(n) )^2.
  • A239609 (program): Sin(arcsin(n)- 3 arccos(n))^2.
  • A239610 (program): Sin(arcsin(n) - 4 arccos(n))^2.
  • A239614 (program): a(n) = A239611(n) / A079458(n).
  • A239619 (program): Base 3 sum of digits of prime(n).
  • A239632 (program): Number of parts in all palindromic compositions of n.
  • A239636 (program): Distance between the two occurrences of n-th prime in A082500.
  • A239669 (program): Total number of prime factors counted with multiplicity of prime(n)-1 and prime(n)+1, where prime(n) is the n-th prime.
  • A239670 (program): Expansion of 1/((1-x)(1-81x)).
  • A239678 (program): Least numbers k such that k*2^n+1 is a square.
  • A239679 (program): Least number k > 0 such that k*2^n+1 is a cube.
  • A239683 (program): Number of digits in decimal expansion of n^5.
  • A239684 (program): Number of digits in the decimal expansion of n^4.
  • A239690 (program): Base 4 sum of digits of prime(n).
  • A239691 (program): Base 5 sum of digits of prime(n).
  • A239692 (program): Base 6 sum of digits of prime(n).
  • A239693 (program): Base 7 sum of digits of prime(n).
  • A239694 (program): Base 8 sum of digits of prime(n).
  • A239695 (program): Base 9 sum of digits of prime(n).
  • A239739 (program): a(n) = n4^(2n+1).
  • A239745 (program): a(n) = (32^(n+2) + n(n+5))/2 - 6.
  • A239767 (program): Degrees of polynomial on the fermionic side of the finite generalization of identity 46 from Slater’s List.
  • A239794 (program): 5n^2 + 4n - 15.
  • A239796 (program): 7n^2 + 2n - 15.
  • A239798 (program): Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.
  • A239844 (program): Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4.
  • A239868 (program): Sum of sigma(i) mod i for i from 1 to n.
  • A239876 (program): Partial sums of A229110, where A229110(n) = antisigma(n) mod n = A024816(n) mod n.
  • A239885 (program): a(n) = prime(n)*2^(n-2).
  • A239890 (program): Number of terms in consolidated series for normal reflectance of a three-layer thin film system of path length n.
  • A239904 (program): a(n) = n - wt(n) + (number of times 11 appears in binary expansion of n).
  • A239907 (program): Let cn(n,k) denote the number of times 11..1 (k 1’s) appears in the binary representation of n; a(n) = n - cn(n,1) + cn(n,2) - cn(n,3) + cn(n,4) - … .
  • A239968 (program): 0 unless n is a nonprime A018252(k) when a(n) = k.
  • A240001 (program): Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
  • A240022 (program): Total number of digits in palindromes with n digits.
  • A240025 (program): Characteristic function of quarter squares, cf. A002620.
  • A240052 (program): 2nd arithmetic derivative of products of 2 successive prime numbers (A006094).
  • A240053 (program): 3rd Arithmetic derivation of products of 2 successive prime numbers (A006094).
  • A240068 (program): Number of prime Lipschitz quaternions having norm prime(n).
  • A240114 (program): Maximal number of points that can be placed on a triangular grid of side n so that no three of them are vertices of an equilateral triangle in any orientation.
  • A240134 (program): Numerator of (n-1) * ceiling(n/2) / n.
  • A240137 (program): Sum of n consecutive cubes starting from n^3.
  • A240226 (program): 4-adic value of 1/n, n >= 1.
  • A240277 (program): Minimal number of people such that exactly n days are required to spread gossip.
  • A240328 (program): Inverse of 37th cyclotomic polynomial.
  • A240329 (program): Inverse of 41st cyclotomic polynomial.
  • A240330 (program): Inverse of 43rd cyclotomic polynomial.
  • A240331 (program): Inverse of 47th cyclotomic polynomial.
  • A240348 (program): Inverse of 53rd cyclotomic polynomial.
  • A240349 (program): Inverse of 59th cyclotomic polynomial.
  • A240355 (program): Inverse of 72nd cyclotomic polynomial.
  • A240388 (program): A sequence related to the Stern sequence s(n) (A002487), defined by w(n) = s(3n)/2.
  • A240400 (program): Numbers n having a partition into distinct parts of form 3^k-2^k.
  • A240434 (program): Binomial transform of the sum of the first n even squares (A002492).
  • A240437 (program): Number of non-palindromic n-tuples of 5 distinct elements.
  • A240438 (program): Greatest minimal difference between numbers of adjacent cells in a regular hexagonal honeycomb of order n with cells numbered from 1 through the total number of cells, the order n corresponding to the number of cells on one side of the honeycomb.
  • A240440 (program): Number of ways to place 3 points on a triangular grid of side n so that they are not vertices of an equilateral triangle of any orientation.
  • A240443 (program): Maximal number of points that can be placed on an n X n square grid so that no four of them are vertices of a square with any orientation.
  • A240450 (program): Greatest number of distinct numbers in the intersection of p and its conjugate, as p ranges through the partitions of n.
  • A240474 (program): Distance from prime(n) to the closest larger squarefree number.
  • A240506 (program): Number of length-n gap-free words on 1,2,3 .
  • A240525 (program): 2^(n-2)*(2^(n+4)-(-1)^n+5).
  • A240530 (program): a(n) = 4(2n)! / (n!)^2.
  • A240533 (program): a(n) = numerators of n!/10^n.
  • A240567 (program): a(n) = optimal number of tricks to throw in the game of One Round War (with n cards) in order to maximize the expected number of tricks won.
  • A240676 (program): Number of digits in the decimal expansion of n^7.
  • A240707 (program): Sum of the middle parts in the partitions of 4n-1 into 3 parts.
  • A240769 (program): Triangle read by rows: T(1,1) = 1; T(n+1,k) = T(n,k+1), 1 <= k < n; T(n+1,n) = 2T(n,1); T(n+1,n+1) = 2T(n,1) - 1.
  • A240803 (program): a(n) = 2 + product of first n odd primes.
  • A240804 (program): a(n) = -2 + product of first n odd primes.
  • A240826 (program): Number of ways to choose three points on a centered hexagonal grid of size n.
  • A240828 (program): a(1)=a(2)=0, a(3)=2; thereafter a(n) = Sum( a(n-i-s-a(n-i-1)), i=0..k-1 ), where s=0, k=3.
  • A240836 (program): Numbers n such that n^3 = xyz where 2 <= x <= y <= z , n^3+1 = (x-1)(y+1)(z+1).
  • A240846 (program): a(0)=0, a(1)=1, a(n) = a(n-1)*12 + 13.
  • A240848 (program): Sum of n, digitsum(n) and number of digits of n.
  • A240857 (program): Triangle read by rows: T(0,0) = 0; T(n+1,k) = T(n,k+1), 0 <= k < n; T(n+1,n) = T(n,0); T(n+1,n+1) = T(n,0)+1.
  • A240877 (program): Sum of the denominators of the Farey series of order n (A006843).
  • A240883 (program): Central terms of the triangle in A240857.
  • A240917 (program): a(n) = 23^(2n) - 3*3^n + 1.
  • A240924 (program): Digital root of squares of numbers not divisible by 2, 3 or 5.
  • A240926 (program): a(n) = 2 + L(2*n) = 2 + A005248(n), n >= 0, with the Lucas numbers (A000032).
  • A240930 (program): a(n) = n^7 - n^6.
  • A240931 (program): a(n) = n^8 - n^7.
  • A240932 (program): a(n) = n^9 - n^8.
  • A240933 (program): a(n) = n^10 - n^9.
  • A240951 (program): Maximum number of dividing subsets of a set of n natural numbers.
  • A240975 (program): The number of distinct prime factors of n^3-1.
  • A240988 (program): Denominators of the (reduced) rationals (((n-1)!!)/(n!! * 2^((1 + (-1)^n)/2)))^((-1)^n), where n is a positive integer.
  • A241038 (program): A000217(A058481(n)).
  • A241151 (program): Number of distinct degrees in the partition graph G(n) defined at A241150.
  • A241170 (program): Steffensen’s bracket function [n,n-3].
  • A241195 (program): Denominator of phi(prime(n)-1)/(prime(n)-1), where phi is Euler’s totient function and prime(n) is the n-th prime.
  • A241199 (program): Numbers n such that 4 consecutive terms of binomial(n,k) satisfy a quadratic relation for 0 <= k <= n/2.
  • A241200 (program): For the n in A241199, the index of the first of 4 terms in binomial(n,k) that satisfy a quadratic relation.
  • A241204 (program): Expansion of (1 + 2x)^2/(1 - 2x)^2.
  • A241217 (program): Largest number that when multiplied by 7 produces an n-digit number.
  • A241219 (program): Number of ways to choose two points on a centered hexagonal grid of size n.
  • A241235 (program): a(n) = number of times n appears in A006949.
  • A241271 (program): a(n) = 6a(n-1) + 3(2^(n-2)-1) for n > 2, a(0)=a(1)=a(2)=0.
  • A241275 (program): a(n) = 6a(n-1) + 5(2^(n-1)-1) for n > 0, a(0) = 0.
  • A241404 (program): Sum of n and the sum of the factorials of its digits.
  • A241406 (program): Numbers n such that n^2 == -1 (mod 61).
  • A241407 (program): Numbers n such that n^2 == -1 (mod 73).
  • A241422 (program): Limit-reverse of the infinite Fibonacci word A003849 with first term as initial block.
  • A241452 (program): a(n) = pg(3, n) + pg(4, n) + … + pg(n, n) where pg(m, n) is the n-th m-th-order polygonal number.
  • A241460 (program): Number of simple connected graphs g on n nodes with Aut(g) = 14
  • A241471 (program): Number of simple connected graphs g on n nodes with Aut(g) = 5040.
  • A241496 (program): Expansion of (1 + 4*x + x^2) / (1 - x^2)^3.
  • A241520 (program): Numbers n such that n^2 == -1 (mod 89).
  • A241521 (program): Numbers n such that n^2 == -1 (mod 97).
  • A241526 (program): Number of different positions in which a square with side length k, 1 <= k <= n - floor(n/3), can be placed within a bi-symmetric triangle of 1 X 1 squares of height n.
  • A241527 (program): n^3 + (3^n+1)/2.
  • A241566 (program): Number of 2-element subsets of 1,…,n whose sum has more than 2 divisors.
  • A241573 (program): 2^p + 3 where p is prime.
  • A241575 (program): Sturmian expansion of 1/2 in base sqrt(2)-1.
  • A241577 (program): n^3 + 4n^2 - 5n + 1.
  • A241676 (program): 2^p - 3 where p is prime.
  • A241677 (program): 2^p + 5 where p is prime.
  • A241678 (program): 2^p - 5 where p is prime.
  • A241679 (program): 2^p + 7 where p is prime.
  • A241680 (program): 2^p + 11 where p is prime.
  • A241683 (program): Total number of 2 X 2 squares appearing in the Thue-Morse sequence logical matrices after n stages.
  • A241685 (program): The total number of squares and rectangles appearing in the Thue-Morse sequence logical matrices after n stages.
  • A241717 (program): The number of P-positions in the game of Nim with up to 3 piles, allowing for piles of zero, such that the number of objects in the largest pile is n.
  • A241746 (program): Smallest number greater than n that CANNOT be scored using n darts on a standard dartboard.
  • A241748 (program): a(n) = n^2 + 12.
  • A241749 (program): a(n) = n^2 + 13.
  • A241750 (program): a(n) = n^2 + 15.
  • A241751 (program): a(n) = n^2 + 16.
  • A241755 (program): A finite sum of products of binomial coefficients: Sum_(m=0..n) binomial(-1/4, m)^2*binomial(-1/4, n-m)^2 (C. C. Grosjean’s problem, numerators).
  • A241756 (program): A finite sum of products of binomial coefficients: Sum_(m=0..n) binomial(-1/4, m)^2*binomial(-1/4, n-m)^2 (C. C. Grosjean’s problem, denominators).
  • A241765 (program): a(n) = n(n + 1)(n + 2)(3n + 17)/24.
  • A241814 (program): Number of distance-regular simple connected graphs on n nodes.
  • A241847 (program): a(n) = n^2 + 17.
  • A241848 (program): a(n) = n^2 + 18.
  • A241849 (program): a(n) = n^2 + 19.
  • A241850 (program): a(n) = n^2 + 20.
  • A241851 (program): a(n) = n^2 + 21.
  • A241888 (program): a(n) = 2^(4*n + 1) - 1.
  • A241889 (program): a(n) = n^2 + 23.
  • A241890 (program): a(n) = n^2 + 24.
  • A241892 (program): Total number of 2 X 2 squares appearing in the Thue-Morse sequence logical matrices (1, 0 version) after n stages.
  • A241893 (program): The total number of rectangles appearing in the Thue-Morse sequence logical matrices (1, 0 version) after n stages.
  • A241899 (program): Numbers n equal to the sum of all the two-digit numbers formed without repetition from the digits of n.
  • A241955 (program): a(n) = 2^(4*n+3) - 1.
  • A241976 (program): Values of k such that k^2 + (k+3)^2 is a square.
  • A241979 (program): (0,1) sequence such that lengths of three consecutive runs are always distinct.
  • A242026 (program): Number of non-palindromic n-tuples of 4 distinct elements.
  • A242062 (program): Expansion of x * (1 - x^12) / ((1 - x^3) * (1 - x^4) * (1 - x^7)) in powers of x.
  • A242063 (program): Analog clock times where the minute hand is on the hour hand (in hhmm format).
  • A242082 (program): Nim sequence of game on n counters whose legal moves are removing some number of counters in A027941.
  • A242083 (program): 3^p - 2^p - 1, where p is prime.
  • A242089 (program): Number of triples (a,b,c) with 0 < a < b < c < p and a + b + c == 0 mod p, where p = prime(n).
  • A242090 (program): Number of triples (a,b,c) with 0 < a < b < c < p and a + b + c == 0 mod p, where 2*b < p = prime(n).
  • A242096 (program): a(n) = (n mod 2) * pi( ceiling(n/2)-1 ), where pi is the prime counting function (A000720).
  • A242112 (program): a(n) = floor((2*n+6)/(5-(-1)^n)).
  • A242119 (program): Primes modulo 18.
  • A242120 (program): Primes modulo 20.
  • A242121 (program): Primes modulo 21.
  • A242122 (program): Primes modulo 22.
  • A242123 (program): Primes modulo 25.
  • A242124 (program): Primes modulo 26.
  • A242125 (program): Primes modulo 27.
  • A242126 (program): Primes modulo 28.
  • A242127 (program): Primes modulo 29.
  • A242135 (program): a(n) = n^3 - 2*n.
  • A242172 (program): a(n) = 2^n*binomial((n + 1 + (n mod 2))/2, 1/2).
  • A242179 (program): T(0,0) = 1, T(n+1,2k) = - T(n,k), T(n+1,2k+1) = T(n,k), k=0..n, triangle read by rows.
  • A242181 (program): Numbers with four X’s in Roman numerals.
  • A242182 (program): Numbers with four C’s in Roman numerals.
  • A242215 (program): a(n) = 18*n + 5.
  • A242278 (program): Number of non-palindromic n-tuples of 3 distinct elements.
  • A242285 (program): Number of terms in the greedy sum for the n-th triangular number.
  • A242312 (program): Digital roots in Pascal’s triangle, triangle read by rows, 0 <= k <= n.
  • A242328 (program): 5^n + 2.
  • A242329 (program): a(n) = 5^n + 4.
  • A242342 (program): a(n) = binomial(n, smallest non-divisor of n).
  • A242349 (program): Largest power of 2 <= n^2.
  • A242371 (program): Modified eccentric connectivity index of the cycle graph with n vertices, C[n].
  • A242374 (program): Number of digits in the decimal expansion of n^8.
  • A242388 (program): Triangle read by rows: T(n,k) = n*2^(k-1) + 1, 1 <= k <= n.
  • A242396 (program): Number of rows of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (0,0) or (1/2,0).
  • A242399 (program): Write n and 3n in ternary representation and add all trits modulo 3.
  • A242412 (program): a(n) = (2n-1)^2 + 14.
  • A242426 (program): floor(n! / n^3).
  • A242427 (program): n! mod n^3.
  • A242436 (program): n^5 - 2n.
  • A242448 (program): Number of distinct linear polynomials b+c*x in row n of array generated as in Comments.
  • A242475 (program): a(n) = 2^n + 8.
  • A242477 (program): Floor(3*n^2/4).
  • A242491 (program): Numbers avoiding subtractive notation when written in Roman numerals.
  • A242493 (program): a(n) is the number of not-sqrt-smooth numbers (“jagged” numbers) not exceeding n. This is the counting function of A064052.
  • A242563 (program): a(n) = 2a(n-1) - a(n-3) + 2a(n-4), a(0)=a(1)=0, a(2)=2, a(3)=3.
  • A242569 (program): n!-2n.
  • A242570 (program): Multiples of 252.
  • A242601 (program): Integers repeated twice in a canonical order.
  • A242602 (program): Integers repeated thrice in a canonical order.
  • A242603 (program): Largest divisor of n not divisible by 7. Remove factors 7 from n.
  • A242604 (program): a(n) = (n - 1)*(n^3 + 1) = n^4 - n^3 + n - 1, for n >= 1.
  • A242650 (program): For any number m there is a number k such that m-k^3 is congruent mod 96 to one of these 12 numbers.
  • A242658 (program): a(n) = 3n^2-3n+2.
  • A242659 (program): a(n) = n(n^2 - 3n + 4).
  • A242660 (program): Nonnegative numbers of the form x^2+xy-2y^2.
  • A242669 (program): a(n) = n*floor(n/3).
  • A242671 (program): Decimal expansion of k2, a Diophantine approximation constant such that the area of the “critical parallelogram” (in this case a square) is 4*k2.
  • A242709 (program): Nonequivalent ways to place two different markers (e.g., a pair of Go stones, black and white) on an n X n grid.
  • A242725 (program): Sequence with all (x, y) = (a(2m), a(2m+-1)) satisfying x y^2+y+1 and y x^2+1.
  • A242728 (program): Sequence a(n) with all (x,y)=(a(2m),a(2m+-1)) satisfying y x^2+1 and x y^2+y+1.
  • A242736 (program): Number of solutions of a^2 + b^2 congruent to -1 modulo the n-th prime.
  • A242771 (program): Number of integer points in a certain quadrilateral scaled by a factor of n (another version).
  • A242774 (program): a(n) = ceiling( n / 2 ) + ceiling( n / 3 ).
  • A242849 (program): Triangle read by rows: T(n,k) = A060828(n)/(A060828(k) * A060828(n-k)).
  • A242850 (program): 32n^5 - 32n^3 + 6*n.
  • A242851 (program): 64n^6 - 80n^4 + 24*n^2 - 1.
  • A242853 (program): 256n^8 - 448n^6 + 240n^4 - 40n^2 + 1.
  • A242856 (program): Number of 2-matchings of the n X n grid graph.
  • A242891 (program): Beginning with a centrally symmetric ‘Sun’ configuration of 8 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.
  • A242894 (program): Beginning with a central ‘Star’ configuration of a Penrose ‘Kite’ and ‘Dart’ tiling with rotational symmetry as the first step, number of tiles that can be added to the free edges of the current tiling.
  • A242954 (program): a(n) = Product_ i=1..n A234957(i).
  • A242963 (program): Numbers n such that A242962(n) = sigma(n) = A000203(n).
  • A242971 (program): Alternate n+1, 2^n.
  • A242983 (program): n/2 * (n^3 - 2n^2 - 2n + 5).
  • A242985 (program): a(n) = 4^n + 2^(n+1).
  • A242992 (program): Least k>n/2, k<n, such that 2^(n-k)-1 divides 2^k-2, or 0 if no such k exists.
  • A242998 (program): Number of integers k such that R = (2^k*Q - Q - 1)/(Q + 1 - 2^k) is a prime number, when Q = A000668(n) is the n-th Mersenne prime.
  • A243014 (program): Number of acyclic digraphs (DAGS) on n labeled nodes, where the indegree and outdegree of each node is at most 1.
  • A243036 (program): Number of entries of length n in A240602.
  • A243054 (program): a(0)=1, and for n >= 1, a(n) = p_n * A002110(n) / 2, where p_n is the n-th prime.
  • A243099 (program): A002061 and A000217 interleaved.
  • A243103 (program): Product of numbers m with 2 <= m <= n whose prime divisors all divide n.
  • A243111 (program): Difference between the smallest triangular number >= n-th prime and the n-th prime.
  • A243129 (program): a(n) = sigma(d(d(d(n)))), where d(n) is the number of divisors of n.
  • A243131 (program): 16n^5 - 20n^3 + 5*n.
  • A243132 (program): 32n^6 - 48n^4 + 18*n^2 - 1.
  • A243134 (program): 128n^8 - 256n^6 + 160n^4 - 32n^2 + 1.
  • A243138 (program): n^2 + 15*n + 13.
  • A243139 (program): a(n) = 2^prime(n) + prime(n).
  • A243201 (program): Odd octagonal numbers indexed by triangular numbers.
  • A243239 (program): a(n) = 10^n mod 97.
  • A243256 (program): Smallest distance of the n-th Fibonacci number to the set of all square integers.
  • A243282 (program): Partial sums of the characteristic function for A070003.
  • A243283 (program): One more than the partial sums of the characteristic function of A070003.
  • A243285 (program): Number of integers 1 <= k <= n which are not divisible by the square of their largest noncomposite divisor.
  • A243291 (program): Difference between n and the index of its largest prime factor: a(n) = n - A061395(n).
  • A243302 (program): Consider a triangular Go board graph with side length n; remove i nodes and let j be the number of nodes in the largest connected subgraph remaining; then a(n) = minimum (i + j).
  • A243305 (program): a(n) = 2^phi(n)+1 = A066781(n)+1.
  • A243306 (program): 2^phi(n) - phi(n).
  • A243307 (program): a(n) = 2^phi(n) + phi(n).
  • A243310 (program): Smallest k such that both prime(k)*prime(k+1) +/- 2^n are prime, or 0 if no such k exists.
  • A243319 (program): Number of simple connected graphs with n nodes that are bipartite and distance regular.
  • A243322 (program): Number of simple connected graphs with n nodes that are distance regular and Eulerian.
  • A243329 (program): Number of simple connected graphs with n nodes that are integral and distance regular.
  • A243334 (program): Number of simple connected graphs with n nodes that are distance regular and triangle-free.
  • A243339 (program): Number of simple connected graphs with n nodes that are distance regular and K_4 free.
  • A243383 (program): Number of length n+3 0..2 arrays with no four elements in a row with pattern abba (with a!=b) and new values 0..2 introduced in 0..2 order.
  • A243427 (program): Floored (rational) values of sqrt(xy) such that sqrt(x) + sqrt(y) = sqrt(xy).
  • A243501 (program): Permutation of even numbers: a(n) = 2*A048673(n).
  • A243502 (program): Permutation of even numbers: a(n) = 2 * A064216(n).
  • A243513 (program): Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order.
  • A243514 (program): Number of length n+2 0..5 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..5 introduced in 0..5 order.
  • A243520 (program): Numbers that are congruent to 0, 8 mod 11.
  • A243546 (program): Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to the bowtie graph.
  • A243554 (program): Number of simple connected graphs with n nodes that are distance-regular and have no subgraph isomorphic to bull graph.
  • A243561 (program): Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to diamond graph.
  • A243578 (program): Integers n of the form 8k+7 that are sum of distinct squares of the form m, m+1, m+2, m+4, where m == 1 (mod 4).
  • A243579 (program): Integers of the form 8k+7 that can be written as a sum of four distinct squares of the form m, m+2, m+4, m+5, where m == 1 (mod 4).
  • A243580 (program): Integers of the form 8k + 7 that can be written as a sum of four distinct squares of the form m, m + 1, m + 3, m + 5, where m == 2 (mod 4).
  • A243581 (program): Integers of the form 8k + 7 that can be written as a sum of four distinct squares of the form m, m + 2, m + 3, m + 4, where m == 2 (mod 4).
  • A243645 (program): Number of ways two L-tiles can be placed on an n X n square.
  • A243759 (program): Triangle T(m,k): exponent of the highest power of 3 dividing the binomial coefficient binomial(m,k).
  • A243762 (program): 4*n^3 + 5.
  • A243860 (program): 2^(n+1) - (n-1)^2.
  • A243869 (program): Expansion of x^4/[(1+x)Product_ k=1..3 (1-kx)].
  • A243883 (program): Numerator of circle radius r(n) at constant unit length sagitta and chord length = n.
  • A243887 (program): (p^2 - 3)/2 for odd primes p.
  • A243903 (program): Numbers n such that (number of primes <= n) is greater than or equal to (number of semiprimes <= n).
  • A243915 (program): a(n) = sigma(omega(n)).
  • A243980 (program): Four times the sum of all divisors of all positive integers <= n.
  • A243989 (program): Rounded down ratio of a lune area and a unit circle one, the lune is bounded by two unit circles whose centers are separated by a distance 1/n.
  • A244009 (program): Decimal expansion of 1 - log(2).
  • A244040 (program): Sum of digits of n in fractional base 3/2.
  • A244041 (program): Sum of digits of n written in fractional base 4/3.
  • A244042 (program): In ternary representation of n, replace 2’s with 0’s.
  • A244048 (program): Antisigma(n) minus the sum of remainders of n mod k, for k = 1,2,3,…,n.
  • A244049 (program): Sum of all proper divisors of all positive integers <= n.
  • A244050 (program): Partial sums of A243980.
  • A244056 (program): Maximum score achievable in the 2048 game on an n X n grid.
  • A244063 (program): Number of prime factors (with multiplicity) of the number of distinct prime factors of n; i.e., Omega(omega(n)).
  • A244082 (program): a(n) = 32*n^2.
  • A244151 (program): 0-additive sequence: start with a(1) = 2; thereafter, a(n) = smallest number not already in sequence which is not the sum of any previous two terms.
  • A244174 (program): Number of compositions of 3n in which the minimal multiplicity of parts equals n.
  • A244191 (program): a(n) = most common final digit for a prime < 10^n, or 0 if there is a tie.
  • A244239 (program): Number of partitions of n into 3 parts such that every i-th smallest part (counted with multiplicity) is different from i.
  • A244307 (program): Sum over each antidiagonal of A244306.
  • A244309 (program): a(n) = F(n)^3 - F(n)^2, where F(n) is the n-th Fibonacci number (A000045).
  • A244310 (program): a(n) = L(n)^3 - L(n)^2, where L(n) is the n-th Lucas number (A000032).
  • A244317 (program): n occurs A014138(n) times.
  • A244327 (program): a(n) = floor((n*(n+1)/2) / sigma(n)) = floor(A000217(n) / A000203(n)).
  • A244328 (program): a(1) = a(2) = 0; for n >= 3: a(n) = floor((n*(n+1)/2) / antisigma(n)) = floor(A000217(n) / A024816(n)).
  • A244329 (program): Floor(antisigma(n) / sigma(n)) = floor(A024816(n) / A000203(n)).
  • A244331 (program): Number of binary digits in the high-water marks of the terms of the continued fraction of the base-2 Champernowne constant.
  • A244334 (program): Decimal expansion of 64/169, the upper bound (as given by S. Finch) of the 2-dimensional simultaneous Diophantine approximation constant.
  • A244413 (program): Exponent of highest power of 8 dividing n.
  • A244414 (program): Remove highest power of 6 from n.
  • A244415 (program): Exponent of 4 appearing in the 4-adic value of 1/n, n >= 1, given in A240226(n).
  • A244416 (program): 6-adic value of 1/n for n >= 1.
  • A244417 (program): Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).
  • A244418 (program): Triangle read by rows T(n,m) = nm +(n-1)(m-1), for n >= m >= 1.
  • A244477 (program): a(1)=3, a(2)=2, a(3)=1; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
  • A244509 (program): Order of GL_2(p), the general linear group over F_p, where p runs through the primes.
  • A244576 (program): Sum of all proper divisors of all positive integers <= prime(n).
  • A244578 (program): Sum of all aliquot divisors of all positive integers <= prime(n).
  • A244583 (program): a(n) = sum of all divisors of all positive integers <= prime(n).
  • A244584 (program): a(n) = n OR 3.
  • A244586 (program): a(n) = n OR 4.
  • A244587 (program): a(n) = n OR 5.
  • A244588 (program): a(n) = n OR 6.
  • A244590 (program): a(n) = sum( floor(k*n/8), k=1..7 ).
  • A244591 (program): Zero followed by the terms of A032924 arranged to give the unique path to the n-th node of a complete, rooted and ordered binary tree.
  • A244593 (program): Decimal expansion of z_c = phi^5 (where phi is the golden ratio), a lattice statistics constant which is the exact value of the critical activity of the hard hexagon model.
  • A244630 (program): a(n) = 17*n^2.
  • A244631 (program): 19*n^2.
  • A244632 (program): 23*n^2.
  • A244633 (program): a(n) = 26*n^2.
  • A244634 (program): 27*n^2.
  • A244635 (program): 29*n^2.
  • A244636 (program): a(n) = 30*n^2.
  • A244644 (program): Consider the method used by Archimedes to determine the value of Pi (A000796). This sequence denotes the number of iterations of his algorithm which would result in a difference of less than 1/10^n from that of Pi.
  • A244663 (program): Binary representation of 4^n + 2^(n+1) - 1.
  • A244725 (program): a(n) = 5*n^3.
  • A244726 (program): 6*n^3.
  • A244727 (program): a(n) = 7*n^3.
  • A244728 (program): a(n) = 9*n^3.
  • A244729 (program): 10*n^3.
  • A244730 (program): a(n) = 2*n^4.
  • A244735 (program): a(n) = (prime(n) mod 5) mod 2.
  • A244738 (program): a(n) = (prime(n) mod 5) mod 3.
  • A244750 (program): 0-additive sequence: a(n) is the smallest number larger than a(n-1) which is not the sum of any subset of earlier terms, with initial values 0, 2, 3, 4 .
  • A244762 (program): a(n) = (53^n-2n-1)/4.
  • A244796 (program): Number of moduli m such that (prime(n) mod m) = 1.
  • A244797 (program): Number of moduli m such that (prime(n) mod m) = 2.
  • A244802 (program): The 60 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244803 (program): The 360 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244804 (program): The 300 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244805 (program): The 240 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244806 (program): The 180 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244841 (program): 4^p - 3^p - 1, where p is prime.
  • A244842 (program): a(n) = (10^n - 1)*(10^n - 10)/90.
  • A244845 (program): Binary representation of 4^n - 2^(n+1) - 1.
  • A244855 (program): a(n) = Fibonacci(n)^4-1.
  • A244864 (program): a(n) = binomial(n+5,5) + 4binomial(n+4,5) + 4binomial(n+3,5) + binomial(n+2,5).
  • A244870 (program): Number of magic labelings with magic sum n of 2nd graph shown in link.
  • A244879 (program): Number of magic labelings of the cycle-of-loops graph LOOP X C_6 having magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph.
  • A244882 (program): Expansion of (1 + 2x + 2x^2) / (1 - x)^6.
  • A244887 (program): Third column of triangle in A234950.
  • A244892 (program): a(n) = a(n-a(n-1)) with initial values 5,2,5,2.
  • A244893 (program): a(n) = a(n-a(n-1)) with initial values 2,3,2.
  • A244895 (program): Period 5 sequence [0, 1, 1, -1, -1, …].
  • A244919 (program): For odd prime p, largest k such that binomial(2p-1, p-1) is congruent to 1 modulo p^k.
  • A244953 (program): a(n) = Sum_ i=0..n (-i mod 4).
  • A244961 (program): Decimal equivalent of the binary string generated by the n X n antidiagonal matrix read by rows.
  • A244974 (program): Sum of numbers m <= n whose set of prime divisors is a subset of the set of prime divisors of n.
  • A244975 (program): (7^n - 2*n - 1)/4.
  • A244978 (program): Decimal expansion of Pi/32.
  • A244988 (program): a(n) = n - A244989(n).
  • A244989 (program): Partial sums of A244992: a(1) = 0, and for n >= 1, a(n) = A244992(n) + a(n-1); Inverse function for A244991.
  • A244992 (program): Characteristic function for A244991: a(n) = A000035(A061395(n)).
  • A245023 (program): Number of cases of tie (no winner) in the n-person rock-paper-scissors game.
  • A245032 (program): a(n) = 27(n - 6)^2 + 4(n - 6)^3 = ((n - 6)^2)(4n + 3).
  • A245033 (program): 4(n + 7)^3 - 27(n + 7)^2 = (4n +1)(n+7)^2.
  • A245034 (program): a(n) = prime(n)^2 - 4*prime(n).
  • A245070 (program): Smallest positive non-divisor of the n-th Lucas number (A000032).
  • A245071 (program): a(n) = 12n - prime(n).
  • A245087 (program): Largest number such that 2^a(n) is a divisor of (n!)!.
  • A245092 (program): The even numbers (A005843) and the values of sigma function (A000203) interleaved.
  • A245093 (program): Triangle read by rows in which row n lists the first n terms of A000203.
  • A245135 (program): Number of length 5 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope
  • A245176 (program): a(n) = 2a(n-1)+(n-2)a(n-2)-(n-1)*a(n-3) with initial terms (1,2,4).
  • A245179 (program): Numbers of the form 2^k+3 or 3*2^k+1, k >= 2.
  • A245187 (program): Trajectory of 1 under repeated applications of the morphism 0->12, 1->12, 2->00.
  • A245195 (program): a(n) = 2^A014081(n).
  • A245200 (program): Smallest positive solution to k == 0 mod 3 and k == 1 mod prime(n).
  • A245207 (program): a(n) = floor((n + sqrt(2))^2).
  • A245219 (program): Continued fraction expansion of the constant c in A245218; c = sup f(n,1) , where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A001951, else f(n,x) = 1/x.
  • A245222 (program): Continued fraction of the constant c in A245221; c = sup f(n,1) , where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A022838, else f(n,x) = 1/x.
  • A245231 (program): Maximum frustration of complete bipartite graph K(n,4).
  • A245235 (program): Repeat 2^(n*(n+1)/2) n+1 times.
  • A245288 (program): a(n) = (4n^2 - 2n - 1 + (2n^2 - 2n + 1)*(-1)^n)/16.
  • A245300 (program): Triangle T(n,k) = (n+k)*(n+k+1)/2 + k, 0 <= k <= n, read by rows.
  • A245301 (program): a(n) = n(7n^2 + 15*n + 8)/6.
  • A245306 (program): a(n) = Fibonacci(n)^2+1.
  • A245321 (program): Sum of digits of n written in fractional base 6/5.
  • A245335 (program): Sum of digits of n in fractional base 5/4.
  • A245336 (program): Sum of digits of n written in fractional base 8/7.
  • A245337 (program): Sum of digits of n in fractional base 7/6.
  • A245338 (program): Sum of digits of n written in fractional base 9/8.
  • A245339 (program): Sum of digits of n written in fractional base 10/9.
  • A245341 (program): Sum of digits of n written in fractional base 5/2.
  • A245342 (program): Sum of digits of n written in fractional base 7/2.
  • A245343 (program): Sum of digits of n written in fractional base 5/3.
  • A245344 (program): Sum of digits of n written in fractional base 7/3.
  • A245345 (program): Sum of digits of n written in fractional base 9/2.
  • A245346 (program): Sum of digits of n in fractional base 10/3.
  • A245347 (program): Sum of digits of n written in fractional base 8/3.
  • A245349 (program): Sum of digits of n in fractional base 7/4.
  • A245350 (program): Sum of digits of n written in fractional base 9/4.
  • A245352 (program): Sum of digits of n written in fractional base 7/5.
  • A245353 (program): Sum of digits of n written in fractional base 9/7.
  • A245354 (program): Sum of digits of n in fractional base 9/5.
  • A245355 (program): Sum of digits of n written in fractional base 8/5.
  • A245356 (program): Number of numbers whose base-4/3 expansion (see A024631) has n digits.
  • A245357 (program): Number of numbers with property that their base 5/4 expansion (see A024634) has n digits.
  • A245380 (program): (7n^5+5n^3)/12.
  • A245391 (program): a(n) = 2^nbinomial(2(n+1), n).
  • A245399 (program): Number of nonnegative integers with property that their base 6/5 expansion (see A024638) has n digits.
  • A245400 (program): Number of nonnegative integers with property that their base 9/8 expansion (see A024656) has n digits.
  • A245401 (program): Number of nonnegative integers with property that their base 8/7 expansion (see A024649) has n digits.
  • A245402 (program): Number of nonnegative integers with property that their base 7/6 expansion (see A024643) has n digits.
  • A245403 (program): Number of nonnegative integers with property that their base 10/9 expansion (see A024664) has n digits.
  • A245404 (program): Number of nonnegative integers with property that their base 7/2 expansion (see A024639) has n digits.
  • A245415 (program): Number of nonnegative integers with property that their base 5/2 expansion (see A024632) has n digits.
  • A245416 (program): Number of nonnegative integers with property that their base 9/2 expansion (see A024650) has n digits.
  • A245418 (program): Number of nonnegative integers with property that their base 5/3 expansion (see A024633) has n digits.
  • A245420 (program): Number of nonnegative integers with property that their base 8/5 expansion (see A024647) has n digits.
  • A245423 (program): Number of nonnegative integers with property that their base 7/5 expansion (see A024642) has n digits.
  • A245425 (program): Number of nonnegative integers with the property that their base 9/4 expansion (see A024652) has n digits.
  • A245426 (program): Number of nonnegative integers with property that their base 7/4 expansion (see A024641) has n digits.
  • A245429 (program): Number of nonnegative integers with property that their base 9/7 expansion (see A024655) has n digits.
  • A245430 (program): Number of nonnegative integers with property that their base 9/5 expansion (see A024653) has n digits.
  • A245447 (program): Permutation of natural numbers: a(n) = A048673(A048673(n)).
  • A245466 (program): a(n) = sigma_1(1) + sigma_2(2) + sigma_3(3) + … + sigma_n-1(n-1) + sigma_n(n).
  • A245467 (program): a(n) = ( 4n^2 - 2n + 1 - (2n^2 - 6n + 1) * (-1)^n )/16.
  • A245473 (program): Nearest integer to 2^log(n).
  • A245477 (program): Period 6: repeat [1, 1, 1, 1, 1, 2].
  • A245478 (program): Numbers n such that the n-th cyclotomic polynomial has a root mod 5.
  • A245489 (program): a(n) = (1^n + (-2)^n + 4^n)/3.
  • A245497 (program): a(n) = phi(n)^2/2, where phi(n) = A000010(n), the Euler totient function.
  • A245524 (program): a(n) = n^2 - floor(n/2)*(-1)^n.
  • A245534 (program): a(n) = n^2 + floor(n/2)*(-1)^n.
  • A245552 (program): G.f.: Sum_ n>=0 (2n+1)x^(n^2+n+1).
  • A245555 (program): Trajectory of 1 under the morphism 1 -> 12, 2 -> 23, 3 -> 31.
  • A245578 (program): The number of permutations of 0,0,1,1,…,n-1,n-1 that begin with 0 and in which adjacent elements are adjacent mod n.
  • A245579 (program): Number of odd divisors of n multiplied by n.
  • A245580 (program): Smallest Lucas number L(m) > L(n) that is divisible by the n-th Lucas number L(n) = A000204(n).
  • A245581 (program): (5 * (1 + (-1)^(1 + n)) + 2 * n^2) / 4.
  • A245599 (program): Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.
  • A245621 (program): Sequence of distinct least nonnegative numbers such that the average of the first n terms is a cube.
  • A245624 (program): Sequence of distinct least positive numbers such that the average of the first n terms is a cube.
  • A245626 (program): a(n)= 1 (respectively, a(n)= 3) if up to 2^n the number of A245622-terms is more (respectively, less) than the number of A245623-terms; or a(n)=0 if these numbers are equal.
  • A245627 (program): Base 10 digit sum of 11*n.
  • A245656 (program): Characteristic function of arithmetic numbers, cf. A003601.
  • A245679 (program): a(n) = pg(n, 3) + pg(n, 4) + … + pg(n, n) where pg(n, m) is the m-th n-th-order polygonal number.
  • A245685 (program): Sigma(2p)/2, for odd primes p.
  • A245710 (program): Number of nonzero evil numbers <= n, see A001969.
  • A245717 (program): Triangle read by rows: T(n,k) = gcd(n,k^2), 1 <= k <= n.
  • A245738 (program): Number of compositions of n into parts 1 and 2 with both parts present.
  • A245761 (program): Numbers with a maximal multiplicative persistence of 1 in any base.
  • A245764 (program): a(n) = 2(n^2 + 1) + n(1 + (-1)^n).
  • A245766 (program): a(n) = 2(n^2 + 1) - n(1 + (-1)^n).
  • A245779 (program): Numbers n such that (n/tau(n) - sigma(n)/n) < 1.
  • A245788 (program): n times the number of 1’s in the binary expansion of n.
  • A245804 (program): a(n) = 23^n - 32^n.
  • A245805 (program): a(n) = 12^n mod 11^n.
  • A245806 (program): 3^n + 10^n.
  • A245807 (program): 7^n + 10^n.
  • A245827 (program): Szeged index of the grid graph P_3 X P_n.
  • A245828 (program): Szeged index of the grid graph P_n X P_n.
  • A245829 (program): Szeged index of the prism graph C_n X P_2 (n >=3).
  • A245830 (program): The Szeged index of a benzenoid consisting of a linear chain of n hexagons.
  • A245838 (program): Arithmetic derivative of (3*n + 1), n >= 1, (A016777)’.
  • A245839 (program): Arithmetic derivative of (3*n + 2).
  • A245871 (program): Number of length 2+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
  • A245872 (program): Number of length 3+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
  • A245906 (program): Numbers of the form 4n^2 + 1 or 4n^2 + 8n + 1.
  • A245908 (program): The number of distinct prime factors of prime(n)^2-1.
  • A245909 (program): The number of distinct prime factors of prime(n)^3-1.
  • A245920 (program): Limit-reverse of the (2,1)-version of the infinite Fibonacci word A014675 with first term as initial block.
  • A245933 (program): Limit-reverse of A006337 (the difference sequence of Beatty sequence for sqrt(2)), with first term as initial block.
  • A245938 (program): Limit-reverse of the Thue-Morse sequence (A010060), with first term as initial block.
  • A245951 (program): Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.
  • A245968 (program): The edge independence number of the Lucas cube Lambda(n).
  • A245969 (program): The average Wiener index of the set of all fibonacenes with n hexagons.
  • A245977 (program): Limit-reverse of the infinite Fibonacci word A014675 = (s(0),s(1),…) = (2,1,2,2,1,2,1,2, …) using initial block (s(2),s(3)) = (2,2).
  • A245989 (program): Number of length n+2 0..2 arrays with no pair in any consecutive three terms totalling exactly 2.
  • A245990 (program): Number of length n+2 0..3 arrays with no pair in any consecutive three terms totalling exactly 3.
  • A245992 (program): Number of length n+2 0..5 arrays with no pair in any consecutive three terms totalling exactly 5
  • A245994 (program): Number of length n+2 0..7 arrays with no pair in any consecutive three terms totalling exactly 7
  • A245996 (program): Number of length 1+2 0..n arrays with no pair in any consecutive three terms totalling exactly n
  • A245997 (program): Number of length 2+2 0..n arrays with no pair in any consecutive three terms totalling exactly n
  • A246010 (program): a(n) = floor(5*prime(n)^2 / 4).
  • A246016 (program): a(n) = (-1)^A055941(n).
  • A246017 (program): Partial sums of A246016.
  • A246030 (program): a(n) = (52^(2n)+(-2)^(n+1))/3.
  • A246036 (program): Expansion of (1+4x)/((1+2x)(1-4x)).
  • A246046 (program): [Pi((n + Pi/2)/(Pi -1) - 1/2)]; complement of A062389.
  • A246057 (program): a(n) = (5*10^n - 2)/3.
  • A246058 (program): a(n) = (16*10^n-7)/9.
  • A246059 (program): (17*10^n-8)/9.
  • A246074 (program): Paradigm Shift Sequence for a (-4,5) production scheme with replacement.
  • A246075 (program): Paradigm shift sequence for a (-3,5) production scheme with replacement.
  • A246104 (program): Least m > 0 for which (s(m), …, s(n+m-1) = (s(0), …, s(n)), the first n+1 terms of the infinite Fibonacci word A003849.
  • A246105 (program): Least m > 0 for which (s(m),…,s(n+m-1) = (s(n),…,s(0)), the reverse of the first n+1 terms of the infinite Fibonacci word A003849.
  • A246127 (program): Limiting block extension of the (2,1)-version of the infinite Fibonacci word A014675 with first term as initial block.
  • A246130 (program): Binomial(2n,n)-2 mod n.
  • A246139 (program): 2^n + 10.
  • A246140 (program): Limiting block extension of A006337 (difference sequence of the Beatty sequence for sqrt(2)) with first term as initial block.
  • A246142 (program): Limiting block extension of A004539 (base-2 representation of sqrt(2)) with first term as initial block.
  • A246146 (program): Limiting block extension of A010060 (Thue-Morse sequence) with first term as initial block.
  • A246159 (program): Inverse function to the injection A048724.
  • A246160 (program): Inverse function to the injection A065621.
  • A246168 (program): 2^n - 10.
  • A246170 (program): Beatty sequence for sqrt(14).
  • A246171 (program): Beatty sequence for sqrt(15).
  • A246172 (program): a(n) = (n^2+9*n-8)/2.
  • A246260 (program): Characteristic function of A246261: a(n) = A000035(A048673(n)).
  • A246262 (program): Inverse function to injection A246261, partial sums of A246260.
  • A246264 (program): Inverse function for injection A246263.
  • A246331 (program): Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by “Rule 465”.
  • A246347 (program): Record values in A135141.
  • A246360 (program): a(1) = 1, then A007051 ((3^n)+1)/2 interleaved with A057198 (5*3^(n-1)+1)/2.
  • A246393 (program): Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) <= 0.
  • A246416 (program): A permutation of essentially the duplicate nonnegative numbers: a(4n) = n + 1/2 - (-1)^n/2, a(2n+1) = a(4n+2) = 2n+1.
  • A246425 (program): In the Collatz 3x+1 problem: start at an odd number 2n+1 and find the next odd number 2m+1 in the trajectory; then a(n) = m-n.
  • A246435 (program): Length of representation of n in fractional base 3/2.
  • A246447 (program): The odd primes squared plus 1 and the composites squared minus 1.
  • A246456 (program): a(n) = sigma(n + sigma(n)).
  • A246472 (program): Number of order-preserving (monotone) functions from the power set of 1 = 0 to the power set of n = 0, …, n-1 .
  • A246473 (program): Number of length n+3 0..2 arrays with no pair in any consecutive four terms totalling exactly 2.
  • A246474 (program): Number of length n+3 0..3 arrays with no pair in any consecutive four terms totalling exactly 3.
  • A246506 (program): a(n) is the number m_0 with the property that if m >= m_0, then every graph obtained from the complete bipartite graph K_ m,m+n by deleting two edges is chromatically unique.
  • A246508 (program): Digital root of numbers congruent to 1,7,11,13,17,19,23,29 modulo 30.
  • A246514 (program): Number of composite numbers between prime(n) and 2*prime(n) exclusive.
  • A246534 (program): Sum_ k=1,n 2^(T(k)-1), where T(k)=k(k+1)/2 are the triangular numbers A000217; for n=0 the empty sum a(0)=0.
  • A246552 (program): 2-adic valuation of the number of involutions of n (A000085).
  • A246554 (program): Concatenation of the n-th Fibonacci number with itself.
  • A246574 (program): a(n) = 2(n-1)Catalan(n).
  • A246591 (program): Smallest number that can be obtained by swapping 2 bits in the binary expansion of n.
  • A246604 (program): a(n) = Catalan(n) - n.
  • A246638 (program): Sequence a(n) = 2 + 3*A001519(n+1) appearing in a certain four circle touching problem together with A246639.
  • A246639 (program): Sequence a(n) = 3 + 5*A001519(n+1) appearing in a certain three circle touching problem, together with A246638.
  • A246640 (program): Sequence a(n) = 1 + A001519(n+1) appearing in a certain touching problem for three circles and a chord, together with A246638.
  • A246641 (program): Sequence a(n) = (1 + A007805(n))/2, appearing in a certain touching problem for three circles and a chord, together with A007805.
  • A246642 (program): Sequence appearing in the curvature of a certain four circle touching problem: (-3 + 5*A007805(n))/2.
  • A246669 (program): Catalan(prime(n)).
  • A246695 (program): Row sums of the triangular array A246694.
  • A246697 (program): Row sums of the triangular array A246696.
  • A246705 (program): Position of first n in A246694 (read as sequence with offset changed to 1); complement of A246706.
  • A246706 (program): Position of last n in A246694 (read as a sequence, with offset changed to 1); complement of A246705.
  • A246715 (program): n * Lucas(n) - (n - 1) * Lucas(n - 1).
  • A246723 (program): Decimal expansion of r_1, the smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_1.
  • A246724 (program): Decimal expansion of r_2, the second smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_2.
  • A246725 (program): Decimal expansion of r_3, the third smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_3.
  • A246767 (program): a(n) = n^4 - 2n.
  • A246780 (program): Strictly increasing terms of the sequence A246778: a(1)= A246778(1) and for n>0 a(n+1) is next term greater than a(n) after that a(n) appears in A246778 for the first time.
  • A246817 (program): Possible number of trailing zeros in hyperfactorials (A002109).
  • A246831 (program): a(n) is the concatenation of n and 3n in binary.
  • A246839 (program): Number of trailing zeros in A002109(n).
  • A246860 (program): Expected value of trace(O)^(2n), where O is a 4 X 4 orthogonal matrix randomly selected according to Haar measure.
  • A246862 (program): Expansion of phi(x) * f(x^3, x^5) in powers of x where phi(), f() are Ramanujan theta functions.
  • A246863 (program): Expansion of phi(x) * f(x^1, x^7) in powers of x where phi(), f() are Ramanujan theta functions.
  • A246880 (program): 6((10^n-1)/9)(10^(n+1))+9*(10^n-1)/9.
  • A246929 (program): Prime(11*n).
  • A246930 (program): Prime(12*n).
  • A246934 (program): The closest square to n-th prime.
  • A246943 (program): a(4n) = 4n , a(2n+1) = 8n+4 , a(4n+2) = 2*n+1.
  • A246960 (program): Directions of the lines in the (Heighway) Dragon Curve.
  • A246965 (program): Numbers n such that 19*n-(n+19) is a prime.
  • A246985 (program): Expansion of (1-8x+14x^2)/((1-2x)(1-3x)(1-6*x)).
  • A247000 (program): Maximal number of palindromes in a circular binary word of length n.
  • A247004 (program): Denominator of (n+4)/gcd(n, 4)^2, a 16-periodic sequence that associates A061037 with A106617.
  • A247014 (program): Number of binary centrosymmetric matrices of size n X n.
  • A247018 (program): Numbers of the form 3*z^2 + z + 3 for some integer z.
  • A247035 (program): Expansion of 2(x+1)(x^4+6x^3+5x^2+6x+1)/(x^6-18x^3+1).
  • A247049 (program): Rectangular array read upwards by columns: T = T(n,k) = number of paths from (0,0) to (n,k), where 0 >= k <= 2, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247060 (program): Dynamic Betting Game D(n,4,1).
  • A247061 (program): Dynamic Betting Game D(n,5,1).
  • A247062 (program): Dynamic Betting Game D(n,5,2).
  • A247063 (program): Dynamic Betting Game D(n,5,3).
  • A247110 (program): n + reversal of digits of n, when n is not palindromic
  • A247112 (program): Floor of sums of the cubes of the non-integer square roots of n, as partitioned by the integer roots: floor( sum( j from n^2+1 to (n+1)^2-1, j^(3/2) ) ).
  • A247128 (program): Positive numbers that are congruent to 0,5,9,13,17 mod 22.
  • A247146 (program): As a binary numeral, the bit 2^(m-1) of a(n) is 1 iff m is a proper divisor of n.
  • A247155 (program): 31n^2 + 1
  • A247157 (program): Greatest number of colors possible for interval edge-colorings of the complete graph K_ 2n .
  • A247159 (program): Sum of divisors of even semiprimes.
  • A247160 (program): Dynamic Betting Game D(n,4,3).
  • A247161 (program): Dynamic Betting Game D(n,4,2).
  • A247188 (program): a(0) = 0. a(n) is the number of repeating sums in the collection of all sums of any k elements in [a(0), … a(n-1)] chosen without replacement for 2 <= k <= n.
  • A247209 (program): Number of terms in generalized Swinnerton-Dyer polynomials.
  • A247215 (program): Integers k such that 3k+1 and 6k+1 are both squares.
  • A247281 (program): 4^n -(-1)^n.
  • A247309 (program): Rectangular array read upwards by columns: T = T(n,k) = number of paths from (0,1) to (n,k), where 0 <= k <= 2, consisting of segments given by the vectors (1,1), (1,0), (1,-1), (1,-2).
  • A247313 (program): a(n) = 5*a(n-1) - 2^n for n>0, a(0)=1.
  • A247328 (program): Odd deficient numbers.
  • A247335 (program): The curvature of touching circles inscribed in a special way in the larger segment of circle of radius 10/9 divided by a chord of length 4/3.
  • A247375 (program): Numbers n such that floor(n/2) is a square.
  • A247380 (program): First differences of A117495.
  • A247396 (program): Number of even numbers in classes of classification of the positive numbers defined in comment in A247395.
  • A247425 (program): A005206(A003259(n)).
  • A247426 (program): Complement of A247425.
  • A247431 (program): The largest integer m such that A001950(m) < A003231(n).
  • A247432 (program): Complement of A247431.
  • A247485 (program): Integer part of 2*sqrt(prime(n)) + 1.
  • A247534 (program): Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.
  • A247541 (program): a(n) = 7*n^2 + 1.
  • A247560 (program): a(n) = 3a(n-1) - 4a(n-2) with a(0) = a(1) = 1.
  • A247563 (program): a(n) = 3a(n-1) - 4a(n-2) with a(0) = 2, a(1) = 3.
  • A247608 (program): a(n) = Sum_ k=0..3 binomial(6,k)*binomial(n,k).
  • A247617 (program): a(4n) = n + 1/2 - (-1)^n/2 + (-1)^n, a(2n+1) = 2n + 5, a(4n+2) = 2n + 3.
  • A247618 (program): Start with a single square; at n-th generation add a square at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247619 (program): Start with a single pentagon; at n-th generation add a pentagon at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247620 (program): Start with a single hexagon; at n-th generation add a hexagon at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247643 (program): a(n) = ( 10n(n+1)+(2n+1)(-1)^n+7 )/8.
  • A247727 (program): Number of length 1+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum.
  • A247787 (program): Sum of divisors of 2*prime(n)-1.
  • A247792 (program): a(n) = 9*n^2 + 1.
  • A247817 (program): Sum(4^k, k=2..n).
  • A247840 (program): Sum(6^k, k=2..n).
  • A247841 (program): a(n) = Sum_ k=2..n 8^k.
  • A247842 (program): Sum(9^k, k=2..n).
  • A247903 (program): Start with a single square; at n-th generation add a square at each expandable vertex (this is the “vertex to side” version); a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247904 (program): Start with a single pentagon; at n-th generation add a pentagon at each expandable vertex (this is the “vertex to side” version); a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247905 (program): Start with a single hexagon; at n-th generation add a hexagon at each expandable vertex (this is the “vertex to side” version); a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247954 (program): a(n) = sigma(sigma(2n-1)).
  • A247964 (program): Beatty sequence for e^(1/3): a(n)=floor(n*(e^(1/3)))
  • A247968 (program): a(n) = least k such that (k!e^k)/(sqrt(2Pi)*k^(k+1/2)) - 1 < 1/2^n.
  • A247970 (program): a(n) is the smallest k such that prime(k+i) (mod 6) takes successively the values 5,1,5,1… for i = 0, 1,…,n-1 ending with 1 or 5.
  • A247974 (program): Numbers k such that A247973(k+1) = A247973(k).
  • A247983 (program): Least number k such that log(2) - sum 1/(h*2^h), h=1..k < 1/2^n.
  • A248038 (program): 3n concatenated with itself.
  • A248076 (program): Partial sums of the sum of the 5th powers of the divisors of n: Sum_ i=1..n sigma_5(i).
  • A248098 (program): a(n) = 1 + a(n-1) + a(n-2) + a(n-3) if n>=4; a(1) = a(2) = a(3) = 1.
  • A248121 (program): Floor(1 / (1/n - Pi^2/6 + sum 1/h^2, h = 1..n )).
  • A248155 (program): Expansion of (1 + x - x^2)/((1 + x)(1 + 2x)).
  • A248157 (program): Expansion of (1 - 2*x^2)/(1 + x)^2. First column of Riordan triangle A248156.
  • A248158 (program): Expansion of (1 - 2*x^2)/(1 + x)^3. Second column of Riordan triangle A248156.
  • A248170 (program): Nonnegative integer whose square is the closest square to prime(n).
  • A248174 (program): 2-adic order of the tribonacci sequence.
  • A248178 (program): Least k such that r - sum 1/F(n), h = 1..k < 1/2^(n+1), where F(n) = A000045 (Fibonacci numbers) and r = sum 1/F(n), h = 1..infinity .
  • A248179 (program): Decimal expansion of (2/27)(9 + 2sqrt(3)*Pi).
  • A248181 (program): Decimal expansion of Sum_ h >= 0 1/binomial(h, floor(h/2)).
  • A248183 (program): Least k such that 1/4 - sum 1/(h(h+1)(h+2)) , h = 1..k < 1/n^2.
  • A248185 (program): Numbers k such that A248183(k+1) = A248183(k) + 1.
  • A248205 (program): Indices of centered octagonal numbers (A016754) that are also pentagonal numbers (A000326).
  • A248216 (program): a(n) = 6^n - 2^n.
  • A248217 (program): a(n) = 8^n - 2^n.
  • A248225 (program): a(n) = 6^n - 3^n.
  • A248226 (program): a(n) = 10^n - 3^n.
  • A248230 (program): a(n) = floor(1/(zeta(4) - Sum_ h=1..n 1/h^4)).
  • A248231 (program): Least k such that zeta(5) - sum 1/h^5, h = 1..k < 1/n^4.
  • A248232 (program): Numbers k such that A248231(k+1) = A248231(k).
  • A248233 (program): Numbers k such that A248231(k+1) = A248231(k) + 1.
  • A248333 (program): Number of unit squares enclosed by n lattice points in and along the first quadrant of the coordinate plane starting from (0,0) and moving along each square gnomon starting on the y-axis and ending on the x-axis.
  • A248337 (program): 6^n - 4^n.
  • A248338 (program): 10^n - 4^n.
  • A248339 (program): a(n) = 22*n+19.
  • A248340 (program): 10^n - 5^n.
  • A248341 (program): 10^n - 7^n.
  • A248343 (program): 10^n - 8^n.
  • A248365 (program): 4n concatenated with itself.
  • A248375 (program): a(n) = floor(9*n/8).
  • A248380 (program): a(n) = 1 if first player in Sylver coinage game can force a win by choosing n as the first number, otherwise a(n) = 2.
  • A248422 (program): Even integers concatenated with themselves.
  • A248423 (program): Multiples of 4 with digits backwards.
  • A248427 (program): Circumference of the (n,n)-knight graph.
  • A248428 (program): Number of length n+2 0..3 arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
  • A248429 (program): Number of length n+2 0..4 arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
  • A248434 (program): Number of length three 0..n arrays with the sum of two elements equal to twice the third.
  • A248462 (program): Number of length 1+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.
  • A248474 (program): Numbers congruent to 13 or 17 mod 30.
  • A248514 (program): Fractal sequence of the dispersion of the “odious numbers”.
  • A248515 (program): Least number k such that 1 - k*sin(1/k) < 1/n^2.
  • A248516 (program): n^2+1 divided by its largest prime factor.
  • A248517 (program): Number of odd divisors > 1 in the numbers 1 through n, counted with multiplicity.
  • A248522 (program): Beatty sequence for 1/(1-exp(-1/3)): a(n) = floor(n/(1-exp(-1/3))).
  • A248533 (program): Number of length n+3 0..4 arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth.
  • A248558 (program): Squares of the digits of the decimal expansion of e.
  • A248567 (program): Numbers k such that A248565(k+1) = A248565(k) + 2.
  • A248572 (program): a(n) = 29*n + 1.
  • A248575 (program): Rounded sums of the non-integer cube roots of n, as partitioned by the integer roots: round[sum(j from n^3+1 to (n+1)^3-1, j^(1/3))].
  • A248577 (program): Product of the number of divisors of n and the number of distinct prime divisors of n; i.e., tau(n) * omega(n).
  • A248583 (program): The least number m == 1 (mod 6) that is divisible by prime(n).
  • A248598 (program): a(n) = (2n+23)n(n-1), a coefficient appearing in the formula a(n)Pi/324+n+1 giving the average number of regions into which n random planes divide the cube.
  • A248604 (program): Numbers a(n) which are the minimum number of moves needed in a variation of the tower of Hanoi with 4 towers and n disks.
  • A248619 (program): a(n) = (n*(n+1))^4.
  • A248621 (program): Floor of sums of the squares of the non-integer cube roots of n, as partitioned by the integer roots: floor[sum(j from n^3+1 to (n+1)^3-1, j^(2/3))].
  • A248646 (program): Expansion of x(5+x+x^2)/(1-2x).
  • A248666 (program): Greatest common divisor of the coefficients of the polynomial p(n,x) defined in Comments.
  • A248668 (program): Sum of the numbers in the n-th row of the array at A248664.
  • A248671 (program): Number of subgroups of the dihedral group Dn that are intersections of some maximal subgroups.
  • A248698 (program): Floor of sums of the non-integer fourth roots of n, as partitioned by the integer roots: floor[sum(j from n^4+1 to (n+1)^4-1, j^(1/4))].
  • A248707 (program): f(3n)/(f(n-1)f(n)f(n+1)), where f(k) = k!.
  • A248720 (program): a(n) = (n*(n+1))^5.
  • A248739 (program): a(n) = 29*n + ceiling(n/29).
  • A248740 (program): a(n) = Fibonacci(n) mod 1000.
  • A248800 (program): n^2 + 3/2 + (1/2)*(-1)^n.
  • A248803 (program): Decimal expansion of the square root of 101.
  • A248812 (program): Repeated terms of (2n)! (A010050).
  • A248825 (program): n^2 + 1 - (-1)^n.
  • A248833 (program): The curvature of touching circles inscribed in a special way in the larger segment of circle of radius 1/6 divided by a chord of length sqrt(8/75).
  • A248835 (program): a(n) = n + A033677(n), where A033677(n) is the smallest divisor of n >= sqrt(n).
  • A248851 (program): a(n) = ( 2n(2n^2 + 9n + 14) + (-1)^n - 1 )/16.
  • A248866 (program): Discrete Heilbronn Triangle Problem: a(n) is twice the maximal area of the smallest triangle defined by three vertices that are a subset of n points on an n X n square lattice.
  • A248877 (program): a(1) = 23, a(2) = 71, a(n) = 3a(n-1) - 2a(n-2) for n>2.
  • A248897 (program): Decimal expansion of Sum_ i >= 0 (i!)^2/(2*i+1)!.
  • A248917 (program): a(n) = 2^n * n^2 + 1.
  • A248928 (program): Interleave (2n+2)^2 with (2n+3)^2, both listed n+1 times.
  • A248974 (program): Floor( 1/(nsinh(1/n) + nsin(1/n) - 2) ).
  • A249013 (program): a(n) = floor( (n-1) * (n+4) / 10 ).
  • A249020 (program): a(n) = floor( n * (n+5) / 10) + 1.
  • A249031 (program): The non-anti-Fibonacci numbers: numbers not in A075326.
  • A249032 (program): First differences of A075326.
  • A249036 (program): a(1)=1, a(2)=2; thereafter a(n) = a(n-1-(number of even terms so far)) + a(n-1-(number of odd terms so far)).
  • A249037 (program): Number of even terms in first n terms of A249036.
  • A249038 (program): Number of odd terms in first n terms of A249036.
  • A249059 (program): Row sums of the triangular array at A249057.
  • A249060 (program): Column 1 of the triangular array at A249057.
  • A249075 (program): Sum of the numbers in row n of the array at A249074.
  • A249076 (program): a(n) = (n*(n+1))^6.
  • A249079 (program): a(n) = 29*n + floor( n/29 ) + 0^( 1-floor( (14+(n mod 29))/29 ) ).
  • A249098 (program): Position of n^6 in the ordered union of h^6, h >=1 and 3*k^6, k >=1 .
  • A249099 (program): Position of 3n^6 in the ordered union of h^6, h >=1 and 3k^6, k >=1 .
  • A249115 (program): Floor(r*n), where r = (5 - sqrt(5))/2; the Beatty complement of A003231.
  • A249118 (program): Position of 32n^6 in the ordered union of h^6, h >=1 and 32*k^6, k >=1 .
  • A249122 (program): a(n) = floor(n / lpf(n^2 + 1)) where lpf(n^2 + 1) is the smallest prime divisor of n^2 + 1.
  • A249127 (program): a(n) = n * floor(3*n/2).
  • A249140 (program): To obtain a(n), write the n-th composite number as a product of primes, subtract 1 from each prime and multiply.
  • A249152 (program): Exponent of 2 in the hyperfactorials: a(n) = A007814(A002109(n)).
  • A249153 (program): Exponent of 2 in the hyperfactorial of 2n: a(n) = A007814(A002109(2n)).
  • A249154 (program): (n+1) times the number of 1’s in the binary expansion of n.
  • A249166 (program): Odd integers concatenated with themselves.
  • A249181 (program): a(n) = A057137(n)^2 where A057137 = 0,1,12,123,…,123…90,…
  • A249222 (program): Expansion of x(1+5x-5x^3)/(1-6x^2+5*x^4).
  • A249227 (program): Number of length n+5 0..2 arrays with no six consecutive terms having two times the sum of any two elements equal to the sum of the remaining four
  • A249332 (program): a(n) = Sum_ k=0..2n binomial(2n, k)^4.
  • A249333 (program): Number of regions formed by extending the sides of a regular n-gon.
  • A249348 (program): a(n) = (A001147(n+1)^2-1)/8, where A001147(n+1) = 35…*(2n+1).
  • A249349 (program): (A001147(n+1)-1)/2, equals the index of A249348(n) within the triangular numbers A000217.
  • A249354 (program): a(n) = n(3n^2 + 3*n + 1).
  • A249356 (program): 8*A200975(n)-7 where A200975 are the numbers on the diagonals in Ulam’s spiral.
  • A249407 (program): Numbers not in A249406.
  • A249450 (program): Alternate Fibonacci numbers - 2.
  • A249452 (program): Numbers n such that A249441(n) = 3.
  • A249453 (program): a(0) = 4; for n>0, a(n) = a(n-1) + 2^n - 3.
  • A249455 (program): Decimal expansion of 2/sqrt(e), a constant appearing in the expression of the asymptotic expected volume V(d) of the convex hull of randomly selected n(d) vertices (with replacement) of a d-dimensional unit cube.
  • A249459 (program): Sum_ k=1..n k^(2*n).
  • A249547 (program): a(n) = (10n^2+8n-1+(-1)^n)/8.
  • A249572 (program): Least positive integer whose decimal digits divide the plane into n+1 regions. Equivalently, least positive integer with n holes in its decimal digits.
  • A249586 (program): Sum of the first n^3 cubes.
  • A249600 (program): Decimal expansion of 1/phi + 1/phi^3 + 1/phi^5, where phi is the Golden Ratio.
  • A249605 (program): Dissectible numbers in the sense of Gunjikar and Kaprekar.
  • A249674 (program): a(n) = 30*n.
  • A249708 (program): Number of length 2+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.
  • A249728 (program): After a(1) = 1 each n appears A000720(n) times.
  • A249734 (program): Even bisection of A003961: Replace in 2n each prime factor p(k) with prime p(k+1).
  • A249735 (program): Odd bisection of A003961: Replace in 2n-1 each prime factor p(k) with prime p(k+1).
  • A249736 (program): Triangular numbers modulo 30.
  • A249739 (program): The smallest prime whose square divides n, 1 if n is squarefree.
  • A249740 (program): The largest prime whose square divides n, 1 if n is squarefree.
  • A249745 (program): Permutation of natural numbers: a(n) = (1 + A064989(A007310(n))) / 2.
  • A249746 (program): Permutation of natural numbers: a(n) = A126760(A249735(n)) = A249824(A064216(n)).
  • A249769 (program): Sequence of distinct least positive numbers such that the average of the first n terms is a factorial.
  • A249824 (program): Permutation of natural numbers: a(n) = A078898(A003961(A003961(2*n))).
  • A249827 (program): Row 3 of A246278: replace in 2n each prime factor p(k) with prime p(k+2).
  • A249845 (program): Number of length 1+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.
  • A249852 (program): a(n) is the total number of pentagons on the left or the right of the vertical symmetry axis of a pentagon expansion (vertex to vertex) after n iterations.
  • A249910 (program): Digital root of A003500(n).
  • A249911 (program): 60-gonal (hexacontagonal) numbers: a(n) = n(29n - 28).
  • A249916 (program): a(n) = 4*(n - 1) - a(n-3), n >= 3, a(0) = a(1) = 1, a(2) = 5.
  • A249919 (program): Number of LCD (liquid-crystal display) segments needed to display n in binary.
  • A249945 (program): n! + 3^n.
  • A249947 (program): Number of available orbitals at increasing subshells in multi-electron atoms.
  • A249961 (program): Number of length 1+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.
  • A249983 (program): Number of length 3+1 0..2n arrays with the sum of the absolute values of adjacent differences equal to 3n.
  • A249992 (program): Expansion of 1/((1+x)(1+2x)(1-3x)).
  • A249993 (program): Expansion of 1/((1+x)(1+2x)(1-4x)).
  • A249997 (program): Expansion of 1/((1-x)(1+3x)(1-4x)).