# Programs for A300000-A349999

List of integer sequences with links to LODA programs.

- A300048 (program): G.f. A(x) satisfies: A(x)^3 = 1 + x*A(x) + x*A(x)^2 + x*A(x)^6.
- A300067 (program): Period 6: repeat [0, 0, 0, 1, 2, 2].
- A300068 (program): A sequence based on the period 6 sequence A300067.
- A300069 (program): Period 6: repeat [0, 0, 0, 1, 2, 1].
- A300070 (program): Decimal expansion of the positive member y of a triple (x, y, z) solving a certain historical system of three equations.
- A300071 (program): Decimal expansion of the member z of a triple (x, y, z) solving a certain historical system of three equations with positive y.
- A300072 (program): Decimal expansion of the positive member -y of a triple (x, y, z) solving a certain historical system of three equations.
- A300073 (program): Decimal expansion of the member z of a triple (x, y, z) satisfying a certain historical system of three equations with negative y.
- A300075 (program): Period 6: repeat [0, 1, 1, 2, 2, 2].
- A300076 (program): A sequence based on the period 6 sequence A300075.
- A300077 (program): Decimal expansion of Pi/2 truncated to n places.
- A300159 (program): Number of ways of converting one set of lists containing n elements to another set of lists containing n elements by removing the last element from one of the lists and either appending it to an existing list or treating it as a new list.
- A300177 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
- A300222 (program): In ternary (base-3) representation of n, replace 1’s with 0’s.
- A300254 (program): a(n) = 25*(n + 1)*(4*n + 3)*(5*n + 4)/3.
- A300270 (program): a(n) = Sum_{1 <= i <= j <= n} mu(i*j)*floor((n/i)/j)).
- A300287 (program): a(n) = floor((1/n) * Sum_{k=1..n} sqrt(k)).
- A300290 (program): Period 6: repeat [0, 1, 2, 2, 3, 3].
- A300291 (program): Triangle T read by rows: T is used to obtain the denominators of all fractional values for x = cos(phi) and y = sin(phi) with (x, y) on the unit circle for 0 < phi < Pi/2.
- A300293 (program): A sequence based on the period 6 sequence A151899.
- A300294 (program): Irregular triangle giving the GCD characteristic: t(n, m) = 1 if gcd(n, m) = 1 and zero otherwise, with t(1, 1) = 1 and t(n, m) for n >= 2 and m = 1..(n-1).
- A300295 (program): Denominator of (1/3)*n*(n + 2)/((1 + 2*n)*(3 + 2*n)).
- A300296 (program): Numerators of n*(5 + 3*n)/(8*(1 + 3*n)*(4 + 3*n)), n >= 0.
- A300326 (program): Sum of the largest possible permutations that can be written without repetition of digits in each base from binary to n+1.
- A300402 (program): Smallest integer i such that TREE(i) >= n.
- A300403 (program): Smallest integer i such that SSCG(i) >= n.
- A300404 (program): Smallest integer k such that the largest term in the Goodstein sequence starting at k is > n.
- A300409 (program): Number of centered triangular numbers dividing n.
- A300410 (program): Number of centered square numbers dividing n.
- A300438 (program): Expansion of (1+x)^3/(1-x-2*x^2-x^3+x^4).
- A300451 (program): a(n) = (3*n^2 - 3*n + 8)*2^(n - 3).
- A300484 (program): a(n) = 2 * Integral_{t>=0} T_n(t/2+1) * exp(-t) * dt, n>=0, where T_n(x) is n-th Chebyshev polynomial of first kind.
- A300489 (program): a(n) = n! * [x^n] -log(1 - x)/(1 - n*x).
- A300490 (program): Expansion of e.g.f. -exp(-x)*log(1 - x)/(1 - x).
- A300518 (program): The greatest prime factor of the squarefree part of n, or 1 if n is square.
- A300519 (program): Convolution of n! and n^n.
- A300522 (program): a(n) = (5*n + 3)*(5*n + 4)*(5*n + 5)/6.
- A300523 (program): a(n) = (5*n + 5)*(5*n + 6)*(5*n + 7)/6.
- A300559 (program): a(n) = n*(n+1)!/2 + 1.
- A300570 (program): a(n) is the concatenation n in base 2, n-1 in base 2, …, 1 in base 2.
- A300571 (program): a(n) is the concatenation n in base 2, n-1 in base 2, …, 0 in base 2.
- A300576 (program): Number of nights required in the worst case to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
- A300613 (program): Number of partitions of the n-dimensional hypercube resulting from a sequence of n n-sections, each of which divides any part perpendicular to any of the axes.
- A300622 (program): Denominators of sequence whose exponential self-convolution yields sequence 1, 2, 3, 5, 7, 11, 13, … (1 with primes).
- A300624 (program): Figurate numbers based on the 11-dimensional regular convex polytope called the 11-dimensional cross-polytope, or 11-dimensional hyperoctahedron.
- A300656 (program): Triangle read by rows: T(n,k) = 30*k^2*(n-k)^2 + 1; n >= 0, 0 <= k <= n.
- A300659 (program): Product of digits of n!.
- A300717 (program): Möbius transform of A003557, n divided by its largest squarefree divisor.
- A300758 (program): a(n) = 2n*(n+1)*(2n+1).
- A300763 (program): a(n) = ceiling(n/g^3), where g = (1+sqrt(5))/2 is the golden ratio.
- A300799 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A300828 (program): Multiplicative with a(p^2) = 1, a(p^3) = -2 and a(p^e) = 0 when e = 1 or e > 3.
- A300838 (program): Permutation of nonnegative integers: a(n) = A057300(A003188(n)).
- A300839 (program): Permutation of nonnegative integers: a(n) = A006068(A057300(n)).
- A300846 (program): a(n) = 3*(n - 1)^2*n^3.
- A300847 (program): a(n) = 12*binomial(n, 5).
- A300850 (program): Number of 6-cycles in the n-odd graph.
- A300853 (program): L.g.f.: log(Product_{k>=1} (1 + x^(k^2))) = Sum_{n>=1} a(n)*x^n/n.
- A300950 (program): Fixed points of A300948.
- A300951 (program): a(n) = Product_{j=1..floor(n/2)} p(j) where p(j) = j if j is prime else 1.
- A301270 (program): Number of labeled trees on n vertices containing two fixed non-adjacent edges.
- A301271 (program): Expansion of (1-16*x)^(1/8).
- A301291 (program): Expansion of (x^4+3*x^3+x^2+3*x+1) / ((x^2+1)*(x-1)^2).
- A301292 (program): Partial sums of A301291.
- A301293 (program): Expansion of (x^2+x+1)^2 / ((x^2+1)*(x-1)^2).
- A301294 (program): Partial sums of A301293.
- A301298 (program): Expansion of (1 + 4*x + 4*x^2 + 4*x^3 + x^4)/((1 - x)*(1 - x^3)).
- A301316 (program): a(n) = ((n-1)! + 1) mod n^2.
- A301317 (program): a(n) = (n-1)! + 1 mod n^3.
- A301336 (program): a(n) = total number of 1’s minus total number of 0’s in binary expansions of 0, …, n.
- A301337 (program): Number of steps required in the worst case for two knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
- A301347 (program): a(n) = n^(n-1) + (n-1)!.
- A301383 (program): Expansion of (1 + 3*x - 2*x^2)/(1 - 7*x + 7*x^2 - x^3).
- A301402 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A301426 (program): Number of steps required in the worst case for three knights to find the princess in a castle with n rooms arranged in a line (Castle and princess puzzle).
- A301451 (program): Numbers congruent to {1, 7} mod 9.
- A301454 (program): Number of strictly log-concave permutations of {1,…,n}.
- A301461 (program): Number of integers less than or equal to n whose largest prime factor is 3.
- A301483 (program): a(n) = floor(a(n-1)/(2^(1/3)-1) with a(1)=1.
- A301484 (program): Decimal expansion of J_0(2)/J_1(2) = 1 - 1/(2 - 1/(3 - 1/(4 - …))).
- A301516 (program): Numbers n with decimal expansion (d_1, …, d_k) such that the convex hull of the set of points { (i, d_i), i = 1..k } has positive area.
- A301560 (program): Matching number of the n-odd graph.
- A301571 (program): Number of vertices at distance 2 from a given vertex in the n-Keller graph.
- A301587 (program): Positive integers m such that whenever n is in the range of the Euler totient function, so is m*n.
- A301600 (program): a(n) = Primorial(n) / Product_{k prime<n} k.
- A301601 (program): Numbers k such that k^6 can be written as a sum of 11 positive 6th powers.
- A301616 (program): a(n) = Product_{k=1..n} (k^2+(n-k+1)^2).
- A301617 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 1.
- A301619 (program): Primes congruent to 65 (mod 192).
- A301621 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 2.
- A301622 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 4.
- A301623 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5.
- A301628 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 7.
- A301631 (program): Numerator of population variance of n-th row of Pascal’s triangle.
- A301647 (program): a(n) = n^3 - (n mod 2).
- A301653 (program): Expansion of x*(1 + 2*x)/((1 - x)*(1 + x)*(1 - x - x^2)).
- A301654 (program): Circumference of the n-triangular honeycomb acute knight graph.
- A301657 (program): Number of nX3 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.
- A301658 (program): Number of nX4 0..1 arrays with every element equal to 0, 1 or 4 horizontally or vertically adjacent elements, with upper left element zero.
- A301672 (program): Coordination sequence for node of type V2 in “krr” 2-D tiling (or net).
- A301673 (program): Partial sums of A301672.
- A301676 (program): Coordination sequence for node of type V2 in “krs” 2-D tiling (or net).
- A301677 (program): Partial sums of A301676.
- A301682 (program): Coordination sequence for node of type V1 in “krg” 2-D tiling (or net).
- A301683 (program): Partial sums of A301682.
- A301684 (program): Coordination sequence for node of type V2 in “krg” 2-D tiling (or net).
- A301685 (program): Partial sums of A301684.
- A301686 (program): Coordination sequence for node of type V1 in “krh” 2-D tiling (or net).
- A301687 (program): Partial sums of A301686.
- A301688 (program): Coordination sequence for node of type V2 in “krh” 2-D tiling (or net).
- A301689 (program): Partial sums of A301688.
- A301694 (program): Expansion of (1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)*(1 - x^3)).
- A301695 (program): Expansion of (1 + 5*x + 4*x^2 + 5*x^3 + x^4)/((1 - x)^2*(1 - x^3)).
- A301696 (program): Partial sums of A219529.
- A301697 (program): Coordination sequence for node of type V2 in “krj” 2-D tiling (or net).
- A301698 (program): Partial sums of A301697.
- A301699 (program): Generating function = g(g(x)), where g(x) = g.f. of Jacobsthal numbers A001045.
- A301707 (program): a(n) = n * Sum_{k prime<=n} k.
- A301708 (program): Coordination sequence for node of type V1 in “krc” 2-D tiling (or net).
- A301709 (program): Partial sums of A301708.
- A301710 (program): Coordination sequence for node of type V2 in “krc” 2-D tiling (or net).
- A301711 (program): Partial sums of A301710.
- A301716 (program): Coordination sequence for node of type V1 in “kre” 2-D tiling (or net).
- A301717 (program): Partial sums of A301716.
- A301718 (program): Coordination sequence for node of type V2 in “kre” 2-D tiling (or net).
- A301719 (program): Partial sums of A301718.
- A301720 (program): Coordination sequence for node of type V1 in “krb” 2-D tiling (or net).
- A301721 (program): Partial sums of A301720.
- A301722 (program): Coordination sequence for node of type V2 in “krb” 2-D tiling (or net).
- A301723 (program): Partial sums of A301722.
- A301724 (program): Coordination sequence for node of type V1 in “kra” 2-D tiling (or net).
- A301725 (program): Partial sums of A301724.
- A301726 (program): Coordination sequence for node of type V2 in “kra” 2-D tiling (or net).
- A301727 (program): Partial sums of A301726.
- A301729 (program): a(0)=1; thereafter positive numbers that are congruent to {0, 1, 3, 5} mod 6.
- A301730 (program): Expansion of (x^8-x^7+x^6+5*x^5+4*x^4+3*x^3+5*x^2+5*x+1)/(x^6-x^5-x+1).
- A301741 (program): a(n) = n! * [x^n] exp((n + 1)*x + x^2/2).
- A301752 (program): Clique covering number of the n-triangular grid graph.
- A301755 (program): Decimal expansion of 3/8.
- A301758 (program): Clique covering number of the n X n fiveleaper graph.
- A301773 (program): Number of odd chordless cycles in the 2n-Moebius ladder graph.
- A301774 (program): Number of chordless cycles in the (2n+1)-prism graph.
- A301775 (program): Number of odd chordless cycles in the (2n+1)-web graph.
- A301779 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2 or 3 horizontally or vertically adjacent elements, with upper left element zero.
- A301786 (program): Number of nX4 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301787 (program): Number of nX5 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301791 (program): Number of 2Xn 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301792 (program): Number of 3Xn 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301797 (program): a(n) = (4^prime(n) - 1)/3.
- A301809 (program): Group the natural numbers such that the first group is (1) then (2),(3),(4,5),(6,7,8),… with the n-th group containing F(n) sequential terms where F(n) is the n-th Fibonacci number (A000045(n)). Sequence gives the sum of terms in the n-th group.
- A301812 (program): Numbers of the form p^2 - 1 where p is a prime of the form 3*k-1 (A003627).
- A301819 (program): Number of nX4 0..1 arrays with every element equal to 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301836 (program): Number of n X 3 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301848 (program): Number of states generated by morphism during inflation stage of paper-folding sequence.
- A301862 (program): Decimal expansion of the probability of intersection of 2 random chords in a circle, where each chord is selected by a random point within the circle and a random direction.
- A301879 (program): Number of nX3 0..1 arrays with every element equal to 0, 1 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301895 (program): a(n) = (number of 1’s in binary expansion of n)^(number of 0’s in binary expansion of n).
- A301898 (program): a(n) is (2n + 1)! if n is even, 2*(2n-1)! if n is odd.
- A301902 (program): Number of n X 3 0..1 arrays with every element equal to 0, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301926 (program): a(n+3) = a(n) + 24*n + 32, a(0)=0, a(1)=3, a(2)=13.
- A301946 (program): Number of nX3 0..1 arrays with every element equal to 1, 2 or 3 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301959 (program): Number of nX3 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301960 (program): Number of nX4 0..1 arrays with every element equal to 0, 1 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301972 (program): a(n) = n*(n^2 - 2*n + 4)*binomial(2*n,n)/((n + 1)*(n + 2)).
- A301973 (program): a(n) = (n^2 - 3*n + 6)*binomial(n+2,3)/4.
- A301977 (program): a(n) is the number of distinct positive numbers whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.
- A301985 (program): a(n) = n^2 + 2329n + 1697.
- A301990 (program): a(n) = 8*(n-1)*a(n-1) + Product_{k=0..n-2} (2*k-1) with a(1) = 1.
- A301994 (program): Number of nX3 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A301995 (program): Number of nX4 0..1 arrays with every element equal to 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A302048 (program): a(n) = 1 if n = p^2 for some prime p, otherwise 0. Characteristic function of squares of primes (A001248).
- A302058 (program): Numbers that are not square pyramidal numbers.
- A302064 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A302076 (program): Number of nX3 0..1 arrays with every element equal to 0, 1, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A302117 (program): a(n) = 4*(n-1)*a(n-1) - (1/3)*Product_{k=0..n-1} (2*k-3), with a(0) = 0.
- A302126 (program): Interleaved Fibonacci and Lucas numbers.
- A302141 (program): Multiplicative order of 16 mod 2n+1.
- A302146 (program): Number of nX3 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero.
- A302156 (program): a(n) = Product_{k=1..n} prime(k+1)^(n-k+1).
- A302181 (program): Number of 3D walks of type abb.
- A302183 (program): Number of 3D walks of type abd.
- A302190 (program): Hurwitz logarithm of natural numbers 1,2,3,4,5,…
- A302245 (program): Maximum remainder of p*q divided by p+q with 0 < p <= q <= n.
- A302254 (program): Exponent of the group of the Gaussian integers in a reduced system modulo (1+i)^n.
- A302255 (program): Total domination number of the n-antiprism graph.
- A302279 (program): Number of 2 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
- A302286 (program): a(n) = [x^n] 1/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - …))))), a continued fraction.
- A302298 (program): Wiener index of the graph of nodes (i,j) of the square lattice such that abs(i) + abs(j) <= n.
- A302302 (program): Number of triples (i,j,k) such that i+j+k > 0 with -n <= i,j,k <= n.
- A302323 (program): Number of 2Xn 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
- A302329 (program): a(0)=1, a(1)=61; for n>1, a(n) = 62*a(n-1) - a(n-2).
- A302330 (program): a(0)=1, a(1)=97; for n>1, a(n) = 98*a(n-1) - a(n-2).
- A302331 (program): a(0)=1, a(1)=141; for n>1, a(n) = 142*a(n-1) - a(n-2).
- A302332 (program): a(0)=1, a(1)=193; for n>1, a(n) = 194*a(n-1) - a(n-2).
- A302338 (program): a(n) = 3*n + 2^v(n) where v(n) denotes the 2-adic valuation of n.
- A302339 (program): Triangle read by rows: T(n,k) = number of linear operators T on an n-dimensional vector space over GF(2) such that U is invariant under T for some given k-dimensional subspace U.
- A302342 (program): Cumulative sums of the bits in the binary representation of Pi.
- A302352 (program): a(n) = Sum_{k=0..n} k^4*binomial(2*n-k,n).
- A302353 (program): a(n) = Sum_{k=0..n} k^n*binomial(2*n-k,n).
- A302368 (program): Number of 2Xn 0..1 arrays with every element equal to 0, 2, 3 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
- A302390 (program): Triameter of the n-cube-connected cycle graph.
- A302392 (program): Number of odd parts in the partitions of 3n into 3 parts.
- A302393 (program): Number of even parts in the partitions of 3n into 3 parts.
- A302397 (program): Expansion of e.g.f. 1/(1 + x*exp(x)).
- A302398 (program): a(n) = n! * [x^n] 1/(1 + x*exp(n*x)).
- A302402 (program): Total domination number of the n-ladder graph.
- A302404 (program): Total domination number of the n-Moebius ladder.
- A302405 (program): Total domination number of the n-prism graph.
- A302406 (program): Total domination number of the n X n torus grid graph.
- A302436 (program): a(n) is the number of ways of writing the binary expansion of n as a concatenation of nonempty substrings with Hamming weight at most 1.
- A302451 (program): a(n) = [x^n] Product_{k>=0} (1 + n*x^(2^k)).
- A302488 (program): Total domination number of the n X n grid graph.
- A302491 (program): Prime numbers of squarefree index.
- A302493 (program): Prime numbers of prime-power index.
- A302506 (program): Number of total dominating sets in the n-pan graph.
- A302507 (program): a(n) = 4*(3^n-1).
- A302537 (program): a(n) = (n^2 + 13*n + 2)/2.
- A302546 (program): a(n) = Sum_{k = 1…n} 2^binomial(n, k).
- A302553 (program): Hyper-4 powers that are not hyper-5 powers.
- A302560 (program): Partial sums of icosahedral numbers (A006564).
- A302562 (program): Partial sums of A092181.
- A302563 (program): Numbers whose digital root is equal to their number of digits.
- A302576 (program): Numbers k such that k/10 + 1 is a square.
- A302581 (program): a(n) = n! * [x^n] -exp(-n*x)*log(1 - x).
- A302583 (program): a(n) = ((n + 1)^n - (n - 1)^n)/2.
- A302588 (program): a(n) = a(n-3) + 7*(n-2), a(0)=1, a(1)=2, a(2)=4.
- A302603 (program): Number of total dominating sets in the wheel graph on n nodes.
- A302604 (program): Number of partitions of n into two parts such that the positive difference of the parts is squarefree.
- A302612 (program): a(n) = (n+1)*(n^4-4*n^3+11*n^2-8*n+12)/12.
- A302642 (program): Number of partitions of n into two parts such that the positive difference of the parts is semiprime.
- A302643 (program): Number of partitions of n into two parts such that the positive difference of the parts is a squarefree semiprime.
- A302647 (program): a(n) = (2*n^2*(n^2 - 3) - (2*n^2 + 1)*(-1)^n + 1)/64.
- A302650 (program): Number of minimal total dominating sets in the n-barbell graph.
- A302660 (program): a(n) = (prime(n) mod 9) + (prime(n) mod 10).
- A302689 (program): a(n) = 4 + 2^n - 4*n.
- A302707 (program): Number of factors of Chebyshev polynomial S(2*n+1, x) (A049310) over the integers. Factorization is into the minimal integer polynomials C (A187360).
- A302709 (program): a(n) = Trinomial(2*n+1, 4) = (1/6)*n*(2*n + 1)*(2*n^2 + 9*n + 1), n >= 0.
- A302710 (program): a(n) = trinomial(2*n, 4) = (1/6)*n*(2*n - 1)*(2*n^2 + 7*n - 3).
- A302734 (program): Number of paths in the n-path complement graph.
- A302748 (program): Half thrice the previous number, rounded down, plus 1, starting with 6.
- A302757 (program): a(n) is the smallest number whose greedy representation as a sum of terms of A126684 uses n terms.
- A302758 (program): a(n) = n^2*(n*(4*n + 3) + 3*n*(-1)^n - 4)/96.
- A302761 (program): Number of total dominating sets in the n-barbell graph.
- A302764 (program): Pascal-like triangle with A000012 as the left border and A080956 as the right border.
- A302766 (program): a(n) = n*((4*n + 1)*(7*n - 4) + 15*n*(-1)^n)/48.
- A302769 (program): a(n) = 2*((2*n-1)*a(n-1) - (n-2)!), with a(1) = 4, n > 1.
- A302773 (program): Numerators of (3*n + 2)/12.
- A302774 (program): a(n) is the position of the first term in A303762 that has prime(n) as one of its prime factors.
- A302777 (program): a(n) = 1 if n is of the form p^(2^k) where p is prime and k >= 0, otherwise 0.
- A302778 (program): Number of “Fermi-Dirac primes” (A050376) <= n.
- A302906 (program): a(0) = 0; for n > 0, a(n) = a(n-1) + 5*n + 4.
- A302909 (program): Determinant of n X n matrix whose main diagonal consists of the first n 5-gonal numbers and all other elements are 1’s.
- A302910 (program): Determinant of n X n matrix whose main diagonal consists of the first n 6-gonal numbers and all other elements are 1’s.
- A302911 (program): Determinant of n X n matrix whose main diagonal consists of the first n 7-gonal numbers and all other elements are 1’s.
- A302912 (program): Determinant of n X n matrix whose main diagonal consists of the first n 8-gonal numbers and all other elements are 1’s.
- A302913 (program): Determinant of n X n matrix whose main diagonal consists of the first n 9-gonal numbers and all other elements are 1’s.
- A302914 (program): Determinant of n X n matrix whose main diagonal consists of the first n 10-gonal numbers and all other elements are 1’s.
- A302930 (program): Maximum number of 6’s possible in an infinite Minesweeper grid with n mines.
- A302941 (program): Number of total dominating sets in the 2n-crossed prism graph.
- A302942 (program): a(n) = (2^n-1)^2*(2^n + 2).
- A302946 (program): Number of minimal (and minimum) total dominating sets in the 2n-crossed prism graph.
- A302980 (program): Size of the smallest square Minesweeper grid that allows each number from 0 to 8 to appear exactly n times.
- A302989 (program): a(n) = n^n + n*n + n.
- A302999 (program): a(n) = Product_{k=1..n} (Fibonacci(k+2) - 1).
- A303005 (program): Number of dominating sets in the n-pan graph.
- A303054 (program): Number of minimum total dominating sets in the n-ladder graph.
- A303108 (program): a(n) = (2*n-1)*a(n-1) - (n-2)!, with a(1) = 2, n > 1.
- A303120 (program): Total area of all rectangles of size p X q such that p + q = n^2 and p <= q.
- A303211 (program): Number of minimum total dominating sets in the n X n rook graph.
- A303212 (program): Number of minimum total dominating sets in the n X n rook complement graph.
- A303223 (program): Sum of the perimeters of the family of rectangles with dimensions p and q such that |q - p| is prime, n = p + q and p < q.
- A303224 (program): a(0)=0, a(1)=1; for n>1, a(n) = n*a(n-1) - 3*a(n-2).
- A303226 (program): Number of minimal total dominating sets in the n-gear graph.
- A303260 (program): Determinant of n X n matrix A[i,j] = (j - i - 1 mod n) + [i=j], i.e., the circulant having (n, 0, 1, …, n-2) as first row.
- A303269 (program): Sum of squares of odd digits minus sum of squares of even digits of n.
- A303272 (program): Multiples of 1852.
- A303273 (program): Array T(n,k) = binomial(n, 2) + k*n + 1 read by antidiagonals.
- A303277 (program): If n = Product (p_j^k_j) then a(n) = (Sum (k_j))^(Sum (p_j)).
- A303279 (program): Expansion of (1/(1 - x)^2) * Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)).
- A303281 (program): Expansion of (x/(1 - x)) * (d/dx) Sum_{p prime, k>=1} x^(p^k)/(1 - x^(p^k)).
- A303295 (program): a(n) is the maximum water retention of a height-3 length-n number parallelogram with maximum water area.
- A303296 (program): Digital roots of fourth powers A000583.
- A303298 (program): Generalized 21-gonal (or icosihenagonal) numbers: m*(19*m - 17)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A303299 (program): Generalized 22-gonal (or icosidigonal) numbers: m*(10*m - 9) with m = 0, +1, -1, +2, -2, +3, -3, …
- A303302 (program): a(n) = 34*n^2.
- A303303 (program): Generalized 23-gonal (or icositrigonal) numbers: m*(21*m - 19)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A303304 (program): Generalized 25-gonal (or icosipentagonal) numbers: m*(23*m - 21)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A303305 (program): Generalized 17-gonal (or heptadecagonal) numbers: m*(15*m - 13)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A303331 (program): a(n) is the minimum size of a square integer grid allowing all triples of n points to form triangles of different areas.
- A303383 (program): Total volume of all cubes with side length q such that n = p + q and p <= q.
- A303384 (program): Total area of all rectangles with dimensions s and t where s | t, n = s + t and s <= t.
- A303416 (program): Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
- A303427 (program): Interleaved Lucas and Fibonacci numbers.
- A303449 (program): Denominator of (2*n+1)/(2^(2*n+1)-1).
- A303486 (program): a(n) = n! * [x^n] 1/(1 - 3*x)^(n/3).
- A303487 (program): a(n) = n! * [x^n] 1/(1 - 4*x)^(n/4).
- A303488 (program): a(n) = n! * [x^n] 1/(1 - 5*x)^(n/5).
- A303502 (program): Integers k such that the digits of k together with a single supplementary digit could be reordered to form a base-10 palindrome number.
- A303534 (program): Amount by which n exceeds the largest binary palindrome less than or equal to n.
- A303536 (program): Number of terms in greedy partition of n into binary palindromes.
- A303537 (program): Expansion of ((1 + 4*x)/(1 - 4*x))^(1/4).
- A303538 (program): Expansion of ((1 + 8*x)/(1 - 8*x))^(1/8).
- A303557 (program): a(0) = 1; a(n) = 2^(n-1)*prime(n)#, where prime(n)# is the product of first n primes.
- A303581 (program): Add i (>= 0) to the i-th block of terms in the Thue-Morse sequence A010060.
- A303589 (program): Floor(n*alpha)-1, where alpha is the number with continued fraction expansion [1;1,2,3,4,5,…] (A247844).
- A303590 (program): Floor(n*beta)-1, where 1/alpha+1/beta=1, alpha being the number with continued fraction expansion [1;1,2,3,4,5,…] (A247844).
- A303602 (program): a(n) = Sum_{k = 0..n} k*binomial(2*n+1, k).
- A303609 (program): a(n) = 2*n^3 + 9*n^2 + 9*n.
- A303611 (program): a(n) = (-1 - (-2)^(n-2)) mod 2^n.
- A303617 (program): Decimal expansion of Sum_{k >= 0} 2^(2*k+1)/Product_{i = 0..k} (2*i+1).
- A303647 (program): a(n) = ceiling(a(n-1)/(2^(1/3)-1)+1), a(1)=1.
- A303649 (program): Number of involutions of [n] having exactly one peak.
- A303658 (program): Decimal expansion of the alternating sum of the reciprocals of the triangular numbers.
- A303692 (program): a(n) = n^2*(2*n - 3 - (-1)^n)/4.
- A303699 (program): Triangle read by rows in which row n gives coefficients of polynomial f_n(x) of degree less than n that satisfies Integral_{x=0..1} g(t - x) * f_n(x) dx = g(t) for any polynomial g(x) of degree less than n.
- A303700 (program): Triangle read by rows in which row n gives coefficients of polynomial f_n(x)/(n+1) of degree less than n that satisfies Integral_{x=0..1} g(t - x) * f_n(x) dx = g(t) for any polynomial g(x) of degree less than n.
- A303714 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.
- A303735 (program): a(n) is the metric dimension of the n-dimensional hypercube.
- A303739 (program): Numbers k such that 9*k^2 + 3*k + 1 (A082040) is prime.
- A303740 (program): Primes of the form 9*k^2 + 3*k + 1 (A082040).
- A303749 (program): First differences of A302774; Number of terms in A303762 that have prime(n) as their largest prime factor (A006530).
- A303768 (program): Inverse permutation to A303767.
- A303781 (program): a(2) = 1; for n <> 2, a(n) = gcd(n, A000005(n)), where A000005(n) = number of divisors of n.
- A303788 (program): a(n) = Sum_{i=0..m} d(i)*5^i, where Sum_{i=0..m} d(i)*6^i is the base-6 representation of n.
- A303802 (program): Number of n X 2 0..1 arrays with every element unequal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero.
- A303812 (program): Generalized 28-gonal (or icosioctagonal) numbers: m*(13*m - 12) with m = 0, +1, -1, +2, -2, +3, -3, …
- A303813 (program): Generalized 19-gonal (or enneadecagonal) numbers: m*(17*m - 15)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A303814 (program): Generalized 24-gonal (or icositetragonal) numbers: m*(11*m - 10) with m = 0, +1, -1, +2, -2, +3, -3, …
- A303815 (program): Generalized 29-gonal (or icosienneagonal) numbers: m*(27*m - 25)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A303816 (program): Decimal expansion of 2700/17.
- A303817 (program): Decimal expansion of 360/17.
- A303846 (program): Total domination number of the n-halved cube graph.
- A303872 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = -T(n-1,k) + 2 T(n-1,k-1) for k = 0,1,…,n; T(n,k)=0 for n or k < 0.
- A303873 (program): Total area of the family of squares with side length n such that n = p + q, p divides q and p < q.
- A303901 (program): Triangle read by rows of coefficients in expansion of (3-2x)^n, where n is a nonnegative integer.
- A303915 (program): a(n) = lambda(n)*E(n), where lambda(n) = A008836(n) and E(n) = A005361(n).
- A303916 (program): Constant term in the expansion of (Sum_{k=0..n} k*(x^k + x^(-k)))^3.
- A303972 (program): Total volume of all cubes with side length n which can be split such that n = p + q, p divides q and p < q.
- A303977 (program): Number of inequivalent solutions to problem discussed in A286874.
- A303987 (program): Triangle read by rows: T(n, k) = (binomial(n,k)*binomial(n+k,k))^2 = A063007(n, k)^2, for n >= 0, k = 0..n.
- A303990 (program): Triangle, read by rows: n^k * k^n, for n >= 1 and k = 1..n.
- A303991 (program): Row sums of triangle A303990.
- A304004 (program): Number of n X 2 0..1 arrays with every element unequal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
- A304011 (program): Number of same-sized pairs of subsets of set of n numbers that might have the same sum.
- A304025 (program): a(n) is the largest integer that can be written with n digits in base 3/2.
- A304035 (program): a(n) is the number of lattice points inside a square bounded by the lines x=-n/sqrt(2), x=n/sqrt(2), y=-n/sqrt(2), y=n/sqrt(2).
- A304041 (program): Number of inequivalent solutions to problem in A054961.
- A304100 (program): a(n) = A003602(A048679(n)).
- A304157 (program): a(n) is the first Zagreb index of the linear phenylene G[n], defined pictorially in the Darafsheh reference.
- A304158 (program): a(n) is the second Zagreb index of the linear phenylene G[n], defined pictorially in the Darafsheh reference (Fig. 3).
- A304159 (program): a(n) = 2*n^3 - 4*n^2 + 6*n - 2 (n>=1).
- A304160 (program): a(n) = n^4 - 3*n^3 + 6*n^2 - 5*n + 2 (n >= 1).
- A304161 (program): a(n) = 2*n^3 - 4*n^2 + 10*n - 2 (n>=1).
- A304162 (program): a(n) = n^4 - 3*n^3 + 9*n^2 - 7*n + 5 (n>=1).
- A304163 (program): a(n) = 9*n^2 - 3*n + 1 with n>0.
- A304164 (program): a(n) = 27*n^2 - 21*n + 6 (n>=1).
- A304165 (program): a(n) = 324*n^2 - 336*n + 102 (n >= 1).
- A304166 (program): a(n) = 972*n^2 - 1224*n + 414 with n > 0.
- A304167 (program): a(n) = 3^n - 2^(n-1) + 2 (n>=1).
- A304168 (program): a(n) = 2*3^n - 2^(n-1) (n>=1).
- A304169 (program): a(n) = 16*3^n + 2^(n+1) - 26 (n>=1).
- A304170 (program): a(n) = 32*3^n + 18*2^n - 116 (n>=1).
- A304171 (program): a(n) = 87*2^n - 38 (n>=0).
- A304172 (program): a(n) = 99*2^n - 45 (n>=0).
- A304182 (program): Number of primitive inequivalent mirror-symmetric sublattices of rectangular lattice of index n.
- A304205 (program): Numbers k such that 24*k + 6 is congruent to 0 (mod 49).
- A304207 (program): a(1)=17; for n>1, a(n) = (a(n-1)^2 - 1)/2 if n is even, a(n-1) + 1 if n is odd.
- A304214 (program): Smallest k > 0 such that 2^(p-1) (mod p^2) < k*p for p = prime(n).
- A304236 (program): Triangle T(n,k) = T(n-1,k) + 3*T(n-2,k-1) for k = 0..floor(n/2), with T(0,0) = 1, T(n,k) = 0 for n or k < 0, read by rows.
- A304252 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 6*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
- A304265 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 5 or 8 king-move adjacent elements, with upper left element zero.
- A304273 (program): The concatenation of the first n terms is the smallest positive even number with n digits when written in base 3/2 (cf. A024629).
- A304274 (program): The concatenation of the first n elements is the largest positive even number with n digits when written in base 3/2.
- A304275 (program): Sum_{k=1..n} gcd(k,n) / cos(Pi*k/n)^2 for odd n.
- A304293 (program): Number of points of a Koblitz curve E: y^2 + x*y = x^3 + a*x^2 + 1 over a field with 2^n elements.
- A304335 (program): Sum of digits of (2*n-1)!!.
- A304349 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
- A304370 (program): Number of function calls of the first kind required to compute ack(3,n), where ack denotes the Ackermann function.
- A304371 (program): Number of function calls of the second kind required to compute ack(3,n), where ack denotes the Ackermann function.
- A304373 (program): Numbers n with additive persistence = 4.
- A304374 (program): a(n) = 9*n^2 + 21*n - 6 (n>=1).
- A304375 (program): a(n) = 27*n^2/2 + 45*n/2 - 12 (n>=1).
- A304376 (program): a(n) = 60*2^n - 48 (n>=1).
- A304377 (program): a(n) = 102*2^n - 96 (n>=1).
- A304378 (program): a(n) = 4*(n - 1)*(16*n - 23) for n >= 1.
- A304379 (program): a(n) = 256n^2 - 828n + 656 (n>=1).
- A304380 (program): a(n) = 36*n^2 - 4*n (n>=1).
- A304381 (program): a(n) = 54*n^2 - 26*n + 4 (n>=1).
- A304383 (program): a(n) = 36*2^n - 5 (n>=1).
- A304384 (program): a(n) = 168*2^n - 26 (n>=1).
- A304385 (program): a(n) = 192*2^n - 31 (n>=1).
- A304387 (program): a(n) = 27*2^n - 5.
- A304388 (program): a(n) = 144*2^n - 20 (n>=1).
- A304389 (program): a(n) = 126*2^n - 22 (n>=1).
- A304404 (program): If n = Product (p_j^k_j) then a(n) = Product (n/p_j^k_j).
- A304407 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)*k_j).
- A304408 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j - 1)*(k_j + 1)).
- A304409 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j*(k_j + 1)).
- A304411 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)*k_j).
- A304412 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)*(k_j + 1)).
- A304421 (program): Number of nX2 0..1 arrays with every element unequal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
- A304438 (program): Coefficient of s(y) in p(|y|), where s is Schur functions, p is power-sum symmetric functions, y is the integer partition with Heinz number n, and |y| = Sum y_i.
- A304439 (program): Add to n the sum of its odd digits minus the sum of its even digits.
- A304453 (program): An expanded binary notation for n: the normal binary expansion for n is expanded by mapping each 1 to 10 and retaining the existing 0’s.
- A304487 (program): a(n) = (3 + 2*n - 3*n^2 + 4*n^3 - 3*((-1 + n) mod 2))/6.
- A304491 (program): Last or deepest exponent in the power-tower for n.
- A304498 (program): Solution (b(n)) of the system of complementary equations defined in Comments.
- A304503 (program): a(n) = 3*(n+1)*(9*n+4).
- A304504 (program): a(n) = 3*(3*n+1)*(9*n+8)/2.
- A304505 (program): a(n) = 4*(n+1)*(9*n+4).
- A304506 (program): a(n) = 2*(3*n+1)*(9*n+8).
- A304507 (program): a(n) = 5*(n+1)*(9*n+4).
- A304508 (program): a(n) = 5*(3*n+1)*(9*n+8)/2 (n>=0).
- A304509 (program): a(n) = 63*2^n - 39 (n>=1).
- A304510 (program): a(n) = 69*2^n - 42 (n>=1).
- A304511 (program): a(n) = 318*2^n - 186 (n>=1).
- A304512 (program): a(n) = 366*2^n - 204 (n >= 1).
- A304513 (program): a(n) = 57*2^(n-1) - 38 (n >= 1).
- A304514 (program): a(n) = 33*2^n - 45 (n>=1).
- A304515 (program): a(n) = 159*2^n - 222 (n>=1).
- A304516 (program): a(n) = 192*2^n - 273 (n>=1).
- A304517 (program): a(n) = 16*2^n - 11 (n>=1).
- A304518 (program): a(n) = 68*2^n - 50 (n>=1).
- A304519 (program): a(n) = 72*2^n -56 (n>=1).
- A304569 (program): Triangle read by rows: T(n,k) = 1 if k | n^e with e >= 0, otherwise T(n,k) = 0 (1 <= k <= n).
- A304577 (program): Period 21: repeat (0,0,0,0,1,1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,1).
- A304579 (program): a(n) = (n^2 + 1)*(n^2 + 2).
- A304583 (program): Period length 18: repeat 1,8,3,6,5,4,7,2,9,0,9,2,7,4,5,6,3,8.
- A304584 (program): A linear mapping a(n) = x + d*n of pairs of nonnegative integers (x,d), where the pairs are enumerated by antidiagonals.
- A304588 (program): Length of shortest prefix of the Thue-Morse word (A010060) such that some length-n block appears twice.
- A304605 (program): a(n) = 48*2^n + 26 (n>=1).
- A304606 (program): a(n) = 54*2^n + 28 (n >= 1).
- A304607 (program): a(n) = 252*2^n + 140 (n>=1).
- A304608 (program): a(n) = 288*2^n + 178 (n >= 1).
- A304609 (program): a(n) = 114*n - 20.
- A304610 (program): a(n) = 157*n - 40 (n>=1).
- A304611 (program): a(n) = 155*n - 38.
- A304612 (program): a(n) = 75*2^n - 38.
- A304613 (program): a(n) = 87*2^n - 45.
- A304614 (program): a(n) = 420*2^n - 222.
- A304615 (program): a(n) = 507*2^n - 273.
- A304616 (program): a(n) = 81*n^2 - 69*n + 24.
- A304617 (program): a(n) = 324*n^2 - 564*n + 321 (n>=1).
- A304618 (program): a(n) = 108*n^2 - 228*n + 114 (n>=2).
- A304619 (program): a(n) = 324*n^2 - 804*n + 468 (n>=2).
- A304651 (program): Number of coprime pairs (x,y) with x^2 + y^2 <= n.
- A304656 (program): Decimal expansion of Pi*sqrt(3).
- A304659 (program): a(n) = n*(n + 1)*(16*n - 1)/6.
- A304685 (program): a(n) = A000699(n) (mod 3).
- A304723 (program): a(n) = 5^(n-1)*(3^n - 1)/2.
- A304725 (program): a(n) = n^4 + 8*n^3 + 20*n^2 + 16*n + 2.
- A304726 (program): a(n) = n^4 + 4*n^2 + 3.
- A304727 (program): a(0) = 0, a(1) = 1, a(n) = n! * a(n-1) + a(n-2).
- A304759 (program): Binary encoding of 1-digits in ternary representation of A048673(n).
- A304809 (program): Solution (a(n)) of the complementary equation a(n) = b(2n) + b(4n) ; see Comments.
- A304826 (program): a(n) = 32*7^n/21 - 8/3, n>=1.
- A304827 (program): a(n) = 52*7^n/21 - 16/3 (n>=1).
- A304828 (program): a(n) = 344*7^n/21 - 128/3 (n>=1).
- A304829 (program): a(n) = 4024*7^n/147 - 256/3 (n >= 2).
- A304830 (program): a(n) = 102*2^n - 108 (n>=1).
- A304831 (program): a(n) = 123*2^n - 135.
- A304832 (program): a(n) = n^2 + 25*n - 34 (n >=2).
- A304833 (program): a(n) = 3*n^2 + 38*n - 76 (n>=2).
- A304834 (program): a(n) = 36*n^2 - 8*n - 2 (n >=1).
- A304835 (program): a(n) = 108*n^2 - 104*n + 20 (n>=1).
- A304836 (program): a(n) = 27*n^2 - 51*n + 24, n>=1.
- A304837 (program): a(n) = 6*(n - 1)*(81*n - 104) for n >= 1.
- A304838 (program): a(n) = 1944*n^2 - 5016*n + 3138 (n >= 1).
- A304839 (program): a(n) = 61*n - 38 (n>=1).
- A304840 (program): a(n) = 52*n - 2 (n>=1).
- A304841 (program): a(n) = 67*n - 10 (n>=1).
- A304887 (program): Number of non-isomorphic blobs of weight n.
- A304902 (program): Let (P,<) be the strict partial order on the subsets of {1,2,…,n} ordered by their cardinality. Then a(n) is the number of paths of any length from {} to {1,2,…,n}.
- A304909 (program): Expansion of x * (d/dx) Product_{k>=0} 1/(1 - x^(2^k)).
- A304915 (program): Expansion of ((1 + 16*x)/(1 - 16*x))^(1/16).
- A304933 (program): a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 16*a(n-2) for n > 1.
- A304934 (program): a(0) = 0, a(1) = 1 and a(n) = 2*a(n-1)/(n-1) + 64*a(n-2) for n > 1.
- A304940 (program): Expansion of ((1 + 4*x)/(1 - 4*x))^(1/2).
- A304941 (program): Expansion of ((1 + 4*x)/(1 - 4*x))^(3/4).
- A304944 (program): a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 16*a(n-2) for n > 1.
- A304960 (program): Number of business cards required to build an origami level n Mosely snowflake sponge.
- A304973 (program): Number of achiral color patterns (set partitions) for a row or loop of length n using exactly 3 colors (sets).
- A304974 (program): Number of achiral color patterns (set partitions) for a row or loop of length n using exactly 4 colors (sets).
- A304993 (program): a(n) = n*(n + 1)*(7*n + 5)/6.
- A304995 (program): Expansion of (1 + 6*x + 6*x^2 + 6*x^3 + x^4 + 6*x^5)/((1 - x)*(1 + x^4)).
- A305006 (program): Numerators of coefficients in expansion of Sum_{k>=1} x^k/(k*(1 + x^k)).
- A305007 (program): Denominators of coefficients in expansion of Sum_{k>=1} x^k/(k*(1 + x^k)).
- A305029 (program): Period 10 sequence [ 0, 2, 2, 2, 2, 0, -2, -2, -2, -2, …] except a(0) = 1.
- A305031 (program): Expansion of ((1 + 2*x)/(1 - 2*x))^(3/2).
- A305032 (program): a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 4*a(n-2) for n > 1.
- A305060 (program): a(n) = 18*2^n + 10.
- A305061 (program): a(n) = 20*2^n + 14.
- A305062 (program): a(n) = 96*2^n + 80.
- A305063 (program): a(n) = 110*2^n + 118.
- A305064 (program): a(n) = 42*2^n - 20.
- A305065 (program): a(n) = 48*2^n - 24.
- A305066 (program): a(n) = 234*2^n - 120.
- A305067 (program): a(n) = 282*2^n - 150.
- A305068 (program): a(n) = 54*n - 18 (n>=1).
- A305069 (program): a(n) = 117*n - 72 (n>=1).
- A305070 (program): a(n) = 378*n^2 - 54*n (n>=1).
- A305071 (program): a(n) = 972*n^2 - 270*n (n>=1).
- A305072 (program): a(n) = 144*n^2 - 24*n (n>=1).
- A305073 (program): a(n) = 288*n^2 - 96*n (n>=1).
- A305074 (program): a(n) = 20*n - 8 (n>=1).
- A305075 (program): a(n) = 32*n - 24 (n>=1).
- A305117 (program): a(n) = A304651(n)/4.
- A305153 (program): a(n) = 30*2^n + 12.
- A305154 (program): a(n) = 36*2^n + 9.
- A305155 (program): a(n) = 28*2^n - 15.
- A305156 (program): a(n) = 136*2^n - 78 (n>=0).
- A305157 (program): a(n) = 164*2^n - 99.
- A305158 (program): a(n) = 21*2^n - 15.
- A305159 (program): a(n) = 102*2^n - 78.
- A305160 (program): a(n) = 123*2^n - 99.
- A305163 (program): a(n) = 24*2^n - 18.
- A305164 (program): a(n) = 28*2^n - 22.
- A305165 (program): a(n) = 136*2^n - 112.
- A305166 (program): a(n) = 164*2^n - 140.
- A305185 (program): a(n) minimizes the maximum norm of elements in a complete residue system of Eisenstein integers modulo n.
- A305189 (program): a(n) = 1*2 + 3 + 4*5 + 6 + 7*8 + 9 + 10*11 + 12 + … + (up to n).
- A305215 (program): a(n) is the number of numbers whose largest prime power factor equals A000961(n).
- A305258 (program): List of y-coordinates of a point moving in a smooth counterclockwise spiral rotated by Pi/4.
- A305261 (program): a(n) = 120*2^n - 108.
- A305262 (program): a(n) = 140*2^n - 127.
- A305263 (program): a(n) = 680*2^n - 622.
- A305264 (program): a(n) = 836*2^n - 771.
- A305265 (program): a(n) = 12*2^n + 62.
- A305266 (program): a(n) = 14*2^n + 73.
- A305267 (program): a(n) = 68*2^n + 358.
- A305268 (program): a(n) = 82*2^n + 440.
- A305269 (program): a(n) = 120*2^n - 95.
- A305270 (program): a(n) = 140*2^n - 112.
- A305271 (program): a(n) = 680*2^n - 548.
- A305272 (program): a(n) = 836*2^n - 676.
- A305276 (program): Expansion of e.g.f. 1/(1 + LambertW(-x/(1 - x))).
- A305290 (program): Numbers k such that 4*k + 1 is a perfect cube, sorted by absolute values.
- A305291 (program): Numbers k such that 4*k + 3 is a perfect cube, sorted by absolute values.
- A305292 (program): Numbers k such that k-1 is a square and k+1 is a triangular number.
- A305304 (program): Expansion of e.g.f. 1/(1 + LambertW(-x/(1 + x))).
- A305315 (program): a(n) = sqrt(5*b(n)^2 - 4), with b(n) = A134493(n) = Fibonacci(6*n+1), n >= 0.
- A305316 (program): a(n) = sqrt(5*b(n)^2 - 4) with b(n) = Fibonacci(6*n+5) = A134497(n).
- A305324 (program): Number of n-celled one-sided ‘divisible’ polyominoes, where a ‘divisible’ polyomino is either a monomino (square) or a polyomino which can be separated into two identical ‘divisible’ polyominoes.
- A305326 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 1.
- A305327 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+2) = 1.
- A305328 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 1 (negated).
- A305395 (program): Records in A073053.
- A305396 (program): Records in A171797.
- A305397 (program): Largest diameter of a lattice polygon.
- A305412 (program): a(n) = F(n)*F(n+1) + F(n+2), where F = A000045 (Fibonacci numbers).
- A305413 (program): a(n) = Fibonacci(11*n)/89.
- A305426 (program): Number of proper divisors of n of the form 2^k - 1 for k >= 1.
- A305435 (program): Number of proper divisors of n of the form 2^k + 1 for k >= 0.
- A305436 (program): Number of divisors of n of the form 2^k + 1 for k >= 0.
- A305444 (program): a(n) = Product_{p is odd and prime and divisor of n} (p - 2).
- A305459 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) + a(n-2).
- A305460 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) + 2*a(n-2).
- A305461 (program): The number of one-digit numbers, k, in base n such that k^2 and k^3 end in the same digit.
- A305471 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - a(n-2).
- A305472 (program): a(0) = 1, a(1) = 3, a(n) = 3*n*a(n-1) - 2*a(n-2).
- A305491 (program): a(n) = numerator(r(n)) where r(n) = (((1/2)*(sqrt(3) + 1))^n - ((1/2)*(sqrt(3) - 1))^n * cos(Pi*n))/sqrt(3).
- A305492 (program): a(n) = ((1 + y)^n - (1 - y)^n)/y with y = sqrt(8).
- A305497 (program): The largest positive even integer that can be represented with n digits in base 3/2.
- A305498 (program): The smallest positive even integer that can be represented with n digits in base 3/2.
- A305503 (program): Largest cardinality of subsets A of {0,1,…,n-1} with |A + A| > |A - A|.
- A305539 (program): a(n) is a generalized pentagonal number such that 2*a(n) is also a generalized pentagonal number.
- A305548 (program): a(n) = 27*n.
- A305549 (program): Crystal ball sequence for the lattice C_6.
- A305559 (program): [0, -1, -1] together with A000290.
- A305573 (program): Number of (1,1) pairs occurring at depth 3n of the Fibonacci tree.
- A305574 (program): Number of primitive (1,1) pairs in the Fibonacci tree at depth 3n.
- A305608 (program): Expansion of 1/2 * (((1 + 4*x)/(1 - 4*x))^(1/4) - 1).
- A305609 (program): Expansion of 1/2 * (((1 + 8*x)/(1 - 8*x))^(1/8) - 1).
- A305612 (program): Expansion of 1/2 * (((1 + 2*x)/(1 - 2*x))^(3/2) - 1).
- A305615 (program): Next term is the largest earlier term that would not create a repetition of an earlier subsequence of length 2, if such a number exists; otherwise it is the smallest nonnegative number not yet in the sequence.
- A305623 (program): Number of chiral pairs of rows of n colors with exactly 3 different colors.
- A305624 (program): Number of chiral pairs of rows of n colors with exactly 4 different colors.
- A305627 (program): a(n) = (2^n / n!) * (2^1 - 1) * (2^2 - 1) * … * (2^n - 1).
- A305650 (program): a(n) = -1/3 * (u^n-1)*(v^n-1) with u = 1+sqrt(3), v = 1-sqrt(3).
- A305658 (program): Powers of 3 in base 3/2.
- A305659 (program): Powers of 2 in base 3/2.
- A305714 (program): Number of finite sequences of positive integers of length n that are polydivisible and strictly pandigital.
- A305716 (program): Order of rowmotion on the divisor lattice for n.
- A305721 (program): Crystal ball sequence for the lattice C_7.
- A305722 (program): Crystal ball sequence for the lattice C_8.
- A305723 (program): Crystal ball sequence for the lattice C_9.
- A305724 (program): Crystal ball sequence for the lattice C_10.
- A305728 (program): Numbers of the form 216*p^3, where p is a Pythagorean prime (A002144).
- A305730 (program): a(n) is the total displacement of all letters in all permutations of n letters with no fixed points.
- A305739 (program): a(n) = n!*T(n) - 1, where T(n) is the n-th triangular number.
- A305747 (program): Let c be the n-th composite number; then a(n) is the smallest divisor of c such that a(n) >= sqrt(c).
- A305748 (program): Distance of a prime number from the average of the next two consecutive prime numbers.
- A305750 (program): Number of achiral color patterns (set partitions) in a row or cycle of length n with 4 or fewer colors (subsets).
- A305753 (program): A base-3/2 sorted Fibonacci sequence that starts with a(0) = 0 and a(1) = 1. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the “digits” into increasing order, omitting all zeros.
- A305762 (program): a(0) = 24, a(n) = 2^(max(0, min(3, p - 1))) * 3^(max(0, min(1, q - 1))) where n = 2^p * 3^q * 5^r * … .
- A305800 (program): Filter sequence for a(prime) = constant sequences.
- A305801 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = 0 if n is an odd prime, with f(n) = n for all other n.
- A305834 (program): Triangle read by rows: T(0,0)= 1; T(n,k)= T(n-1,k) + 4*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
- A305838 (program): Triangle read by rows: T(0,0)= 1; T(n,k)= T(n-1,k) + 5*T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
- A305847 (program): Solution a() of the complementary equation a(n) + b(n) = 5*n, where a(1) = 1. See Comments.
- A305848 (program): Solution b() of the complementary equation a(n) + b(n) = 5n, where a(1) = 1. See Comments.
- A305849 (program): Positions of 2 in the difference sequence of A305847.
- A305859 (program): Numbers that are congruent to {1, 3, 11} mod 12.
- A305861 (program): a(n) = 32*3^n - 2^(n+5) + 5.
- A305877 (program): Numbers in base 3 reversed.
- A305878 (program): For any number n >= 0: apply the map 0 -> “0”, 1 -> “01”, 2 -> “011” to the ternary representation of n and interpret the result as a binary string.
- A305880 (program): A base 3/2 reverse sorted Fibonacci sequence that starts with terms 2211 and 2211. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the digits into decreasing order, omitting all zeros.
- A305889 (program): a(n) = 3*a(n-2) + a(n-4), a(0)=a(1)=0, a(2)=1, a(3)=2.
- A305989 (program): Numbers in binary reversed.
- A305990 (program): E.g.f.: (1+x) / (exp(-x) - x).
- A305991 (program): Expansion of (1-27*x)^(1/9).
- A305994 (program): a(n) = ((A000265(3*n + 1) + 1) mod 4)/2.
- A306006 (program): Number of non-isomorphic intersecting set-systems of weight n.
- A306007 (program): Number of non-isomorphic intersecting antichains of weight n.
- A306020 (program): a(n) is the number of set-systems using nonempty subsets of {1,…,n} in which all sets have the same size.
- A306069 (program): Partial sums of A286324: Sum_{k=1..n} bd(k) where bd(k) is the number of bi-unitary divisors of k.
- A306150 (program): Row sums of A306015.
- A306174 (program): a(n) = (prime(n)^6 - 1)/504.
- A306183 (program): The coefficients of x in the reduction of x^2 -> x + 1 for the polynomial p(n,x) = Product_{k=1..n} (x+k).
- A306184 (program): a(n) = (2n+1)!! mod (2n)!! where k!! = A006882(k).
- A306185 (program): a(n) = (2n+1)!! + (2n)!! where k!! = A006882(k).
- A306190 (program): a(n) = p^2 - p - 1 where p = prime(n), the n-th prime.
- A306192 (program): a(n) = (n - 1)*prime(n + 1).
- A306193 (program): a(n) = Product_{k=0..n} (1 + n!/k!).
- A306198 (program): Multiplicative with a(p^e) = p^(e-1)*(p^2 - p - 1).
- A306237 (program): a(n) = primorial prime(n)#/prime(n - 1).
- A306258 (program): a(n) = floor(n^2/4)*n!.
- A306262 (program): Difference between maximum and minimum sum of products of successive pairs in permutations of [n].
- A306266 (program): Number of reciprocally monophyletic coalescence sequences for 2n lineages, n each in 2 species.
- A306276 (program): a(0) = a(1) = a(2) = a(3) = 1; thereafter a(n) = a(n-2) + a(n-3) + a(n-4).
- A306277 (program): Numbers congruent to 1 or 8 mod 10.
- A306278 (program): Numbers congruent to 2 or 11 mod 14.
- A306279 (program): Numbers congruent to 3 or 18 mod 22.
- A306280 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(n^2+k,k).
- A306285 (program): Numbers congruent to 4 or 21 mod 26.
- A306289 (program): The smallest prime factor of numbers greater than 1 and coprime to 6.
- A306290 (program): a(n) = 1/(Integral_{x=0..1} (x^3 - x^4)^n dx).
- A306292 (program): Number of asymmetric Dyck paths of semilength n.
- A306295 (program): Maximal number of coalescent histories among non-matching pairs consisting of a caterpillar gene tree and a caterpillar species tree with n+2 leaves.
- A306312 (program): Number of terms of the set of divisors of n that are not the product of any other two distinct divisors.
- A306331 (program): Numbers congruent to 6 or 31 mod 38.
- A306354 (program): a(n) = gcd(n, A101337(n)).
- A306357 (program): Number of nonempty subsets of {1, …, n} containing no three cyclically successive elements.
- A306362 (program): Prime numbers in A317298.
- A306367 (program): a(n) = numerator of (n^2 + 2)/(n + 2).
- A306368 (program): a(n) = numerator of (n + 3)*(n + 4)/((n + 1)*(n + 2)).
- A306376 (program): Sum of the 2 X 2 minors in the n X n Pascal matrix.
- A306377 (program): a(n) = n^(n+1) - Sum_{k=1..n-1} k^(k+1).
- A306379 (program): Dirichlet convolution of psi(n) with itself.
- A306380 (program): Squares of the form 5*k^2 + 5.
- A306388 (program): a(n) is a decimal number k having a length n binary expansion which encodes, from left to right at digit j, the coprimality (0) or non-coprimality (1) of j to n, for 1 < j <= n, except for the first digit, which is always 1.
- A306390 (program): Size of one subtree in the unlabeled binary rooted tree shape of size n whose leaf-labeled trees have the largest number of coalescence sequences.
- A306408 (program): a(n) = Sum_{d|n} (-1)^omega(n/d) * d.
- A306409 (program): a(n) = -Sum_{0<=i<j<=n} (-1)^(i+j) * (i+j)!/(i!*j!).
- A306411 (program): a(n) = phi(n^6) = n^5*phi(n).
- A306412 (program): a(n) = phi(n^8) = n^7*phi(n).
- A306447 (program): Number of (undirected) Hamiltonian cycles in the n-antiprism graph.
- A306455 (program): Total number of covered falling diagonals in all n X n permutation matrices.
- A306472 (program): a(n) = 37*27^n.
- A306473 (program): a(n) is the maximum number of distinct palindromic not necessarily contiguous subwords over all binary words of length n.
- A306480 (program): Numbers k such that A054404(k) is not floor(k/e - 1/(2*e) + 1/2).
- A306486 (program): Number of squares in the interval [e^(n-1), e^n).
- A306495 (program): Expansion of e.g.f. (2-exp(-x))*exp(x)/(x-1)^2.
- A306496 (program): Number of (undirected) Hamiltonian cycles in the n-crown graph.
- A306519 (program): Expansion of 2/(1 + 2*x + sqrt(1 - 4*x*(1 + x))).
- A306535 (program): Number of permutations p of [2n] having no index i with |p(i)-i| = n.
- A306546 (program): Modified Collatz Map such that odd numbers are treated the same, but even numbers have all factors of 2 removed.
- A306556 (program): Integers that appear as (unreduced) numerators of segment endpoints when a ternary Cantor set is created.
- A306561 (program): Square numbers that are also central polygonal numbers (i.e., square numbers found in the Lazy Caterer’s sequence).
- A306577 (program): Last odd number reached by n before 1 through Collatz iteration, where a(n) = 1 when no other odd number is reached, or -1 if 1 is never reached.
- A306591 (program): a(n) is the denominator of 1/2 - 1/(prime(n)+1), where prime(n) is the n-th prime.
- A306609 (program): a(n) = Sum_{k=0..n} k*binomial(4*n+2,2*k)
- A306610 (program): a(n) = (2*cos(Pi/15))^(-n) + (2*cos(7*Pi/15))^(-n) + (2*cos(11*Pi/15))^(-n) + (2*cos(13*Pi/15))^(-n), for n >= 1.
- A306637 (program): a(n) = Fibonacci(n) * A128834(n).
- A306671 (program): a(n) = gcd(tau(n), pod(n)) where tau(k) = the number of the divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).
- A306672 (program): Partial sums of the even Lucas numbers (A014448).
- A306675 (program): Number of permutations p of [2n] having at least one index i with |p(i)-i| = n.
- A306682 (program): a(n) = gcd(sigma(n), pod(n)) where sigma(k) = the sum of the divisors of k (A000203) and pod(k) = the product of the divisors of k (A007955).
- A306683 (program): Integers k for which the base-phi representation of k does not include 1 or phi.
- A306694 (program): a(n) is the denominator of log(A014963(n))/log(n) if n > 1 and a(1) = 1.
- A306695 (program): a(n) = gcd(n, psi(n)).
- A306696 (program): Lexicographically earliest sequence of nonnegative terms such that for any n > 0 and k > 0, if a(n) >= a(n+k), then a(n+2*k) <> a(n+k).
- A306712 (program): Decimal expansion of 3*sqrt(3)/Pi.
- A306721 (program): a(n) = Sum_{k=0..n} binomial(k, 7*(n-k)).
- A306752 (program): a(n) = Sum_{k=0..n} binomial(k, 8*(n-k)).
- A306753 (program): a(n) = Sum_{k=0..n} binomial(k, 9*(n-k)).
- A306764 (program): a(n) is a sequence of period 12: repeat [1, 1, 6, 2, 1, 3, 2, 2, 3, 1, 2, 6].
- A306771 (program): Numbers m such that m = i + j = i * k and phi(m) = phi(i) + phi(j) = phi(i) * phi(k) for some i, j, k, where phi is the Euler totient function A000010.
- A306775 (program): Partial sums of A060648: sum of the inverse Moebius transform of the Dedekind psi function from 1 to n.
- A306789 (program): a(n) = Product_{k=0..n} binomial(n + k, n).
- A306807 (program): An irregular fractal sequence: underline a(n) iff the absolute difference |a(n-1) - a(n)| is prime; all underlined terms rebuild the starting sequence.
- A306811 (program): Decimal expansion of Pi/(Pi - 1) = 1 + 1/Pi + 1/Pi^2 + … .
- A306843 (program): a(n) = Sum_{d|n} binomial(n,d)^3.
- A306847 (program): a(n) = Sum_{k=0..floor(n/6)} binomial(n,6*k).
- A306848 (program): Product of first n odd nonprimes, a(n) = Product_{k=1..n) A071904(k).
- A306852 (program): a(n) = Sum_{k=0..floor(n/7)} binomial(n,7*k).
- A306858 (program): Decimal expansion of 1 - 1/(1*3) + 1/(1*3*5) - 1/(1*3*5*7) + …
- A306859 (program): a(n) = Sum_{k=0..floor(n/8)} binomial(n,8*k).
- A306860 (program): a(n) = Sum_{k=0..floor(n/9)} binomial(n,9*k).
- A306863 (program): a(n) is the number of primes between the n-th and (n+1)-st odd composite numbers.
- A306921 (program): Number of ways of breaking the binary expansion of n into consecutive blocks with no leading zeros.
- A306927 (program): a(n) = A001615(n) - n.
- A306948 (program): Expansion of e.g.f. (1 + x)*log(1 + x)*exp(x).
- A306957 (program): a(n) = n!*binomial(10,n).
- A306966 (program): Decimal expansion of t+t^2, where t is the tribonacci constant, the real root of x^3 - x^2 - x - 1.
- A307005 (program): Expansion of e.g.f. (2*exp(x)-2*x-x^2)/(2-2*x-x^2).
- A307006 (program): Expansion of e.g.f. (2*exp(x)-1-2*x-x^2)/(1-x-x^2).
- A307018 (program): Total number of parts of size 3 in the partitions of n into parts of size 2 and 3.
- A307035 (program): a(n) is the unique integer k such that A108951(k) = n!.
- A307037 (program): The unitary analog of the alternating sum-of-divisors function (A206369).
- A307040 (program): a(n) = Sum_{k=0..floor(n/6)} (-1)^k*binomial(n,6*k).
- A307041 (program): a(n) = Sum_{k=0..floor(n/7)} (-1)^k*binomial(n,7*k).
- A307044 (program): a(n) = Sum_{k=0..floor(n/8)} (-1)^k*binomial(n,8*k).
- A307086 (program): Decimal expansion of 4*(5 - sqrt(5)*log(phi))/25, where phi is the golden ratio (A001622).
- A307089 (program): Expansion of (1 - x)^4/((1 - x)^6 + x^6).
- A307093 (program): a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k^2).
- A307094 (program): a(n) = Sum_{k=0..n} (-1)^k * binomial(n^2,k^2).
- A307096 (program): Positive integers m such that for any positive integer k the last k bits of the binary expansion of m is not a multiple of 3.
- A307118 (program): a(1) = 0; for n>1, a(n) = dr(n-1) + dr(n) + dr(n+1), where dr(n) is the number of nontrivial divisors of n (A070824).
- A307119 (program): a(1) = 1, for n>1, a(n) = dp(n-1) + dp(n) + dp(n+1), where dp(n) is the number of divisors of n less than n (A032741).
- A307120 (program): a(1) = 3, for n>1, a(n) = A000005(n-1) + A000005(n) + A000005(n+1).
- A307124 (program): a(n) is twice the square of the product of the first n primes each decreased by one.
- A307136 (program): a(n) = ceiling(2*sqrt(A000037(n))), n >= 1.
- A307138 (program): State complexity profile of R-Lambda_24 version of Leech lattice.
- A307152 (program): a(n) = floor((A002144(n)+19)/24).
- A307158 (program): a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n,3*k)^2.
- A307163 (program): Minimum number of intercalates in a diagonal Latin square of order n.
- A307168 (program): First class of all proper positive solutions x1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.
- A307169 (program): First class of all proper positive solutions y1(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.
- A307172 (program): Second class of all proper positive solutions x2(n) of the Pell equation x^2 - 7*y^2 = 9.
- A307173 (program): Second class of all proper positive solutions y2(n) = a(n) of the Pell equation x^2 - 7*y^2 = 9.
- A307178 (program): Decimal expansion of coth(1/2).
- A307182 (program): Crossing number of the n-crown graph (conjectured).
- A307229 (program): Decimal expansion of (3*exp(1/2) - 1)/2.
- A307233 (program): a(n) = Product_{k=1..n} (k^2 + k + 1) mod n.
- A307248 (program): a(n) is the number of n X n binary matrices (over the reals) with at least one row and column full of 1’s where the row index equals the column index.
- A307253 (program): Number of triangles larger than size=1 in a matchstick-made hexagon with side length n.
- A307268 (program): Partial sums of the Lucas numbers of the form L(3n+2) (A163063).
- A307294 (program): If n is even, a(n) = A000201(n/2+1), otherwise a(n) = A000201((n-1)/2+1) + 1.
- A307295 (program): If n is even, a(n) = A001950(n/2+1), otherwise a(n) = A001950((n-1)/2+1) + 1.
- A307304 (program): Number of inequivalent ways of placing 2 nonattacking rooks on n X n board up to rotations and reflections of the board.
- A307313 (program): a(n) is the denominator of n/2^(length of the binary representation of n).
- A307349 (program): a(n) = Sum_{i=1..n} Sum_{j=1..n} (-1)^(i+j) * (i+j)!/(2!*i!*j!).
- A307354 (program): a(n) = Sum_{0<=i<=j<=n} (-1)^(i+j) * (i+j)!/(i!*j!).
- A307368 (program): a(n) is the minimal positive integer such that 2*a(n)*prime(n)-1 equals another prime.
- A307371 (program): Numbers k such that the digits of sqrt(k) begin with k.
- A307374 (program): G.f. A(x) satisfies: A(x) = 1 + x - x^2*A(x)^2.
- A307395 (program): Expansion of 1/((1 - x) * ((1 - x)^3 + x^3)).
- A307408 (program): a(n) = (A001222(n) - 1)*A001221(n) + 2.
- A307409 (program): a(n) = (A001222(n) - 1)*A001221(n).
- A307413 (program): G.f. A(x) satisfies: A(x) = 1 + x*A(x)/(1 - x*A(x) - 2*x^2*A(x)^2).
- A307420 (program): Dirichlet g.f.: zeta(2*s) * zeta(3*s) / zeta(s).
- A307421 (program): Dirichlet g.f.: zeta(s) * zeta(3*s) / zeta(2*s).
- A307423 (program): Dirichlet g.f.: zeta(2*s) / zeta(3*s).
- A307424 (program): Dirichlet g.f.: zeta(3*s) / zeta(2*s).
- A307430 (program): Dirichlet g.f.: zeta(s) / zeta(4*s).
- A307445 (program): Dirichlet g.f.: 1 / (zeta(s) * zeta(2*s)).
- A307464 (program): Number of Catalan words of length n avoiding the pattern 000.
- A307465 (program): Number of Catalan words of length n avoiding the pattern 110.
- A307467 (program): The number of points, corresponding to the first n primes, and placed on the unit circle according to an algorithm using the data from A077218 (in the spirit of Ulam’s spiral, and described in the COMMENTS section below), which lie on the closed arc of the unit circle from 0 to 45 degrees.
- A307469 (program): a(n) = 2*a(n-1) + 6*a(n-2) for n >= 2, a(0) = 1, a(1) = 5.
- A307485 (program): A permutation of the nonnegative integers: one odd, two even, four odd, eight even, etc.; extended to nonnegative integer with a(0) = 0.
- A307513 (program): Beatty sequence for 1/log(2).
- A307539 (program): Heinz numbers of square integer partitions, where the Heinz number of an integer partition (y_1,…,y_k) is prime(y_1)*…*prime(y_k).
- A307559 (program): a(n) = floor(n/3)*(n - floor(n/3))*(n - floor(n/3) - 1).
- A307612 (program): Partial sums of the permutation A307485: one odd, two even, four odd, eight even, etc.
- A307613 (program): Inverse of the permutation A307485: one odd, two even, four odd, eight even, etc; extended with a(0) = 0.
- A307618 (program): A Calabi-Yau period integral: a(n) = C(4*n,2*n)*C(2*n,n)^3.
- A307621 (program): Number of cycles in the n-dipyramidal graph.
- A307642 (program): a(n) = n!*Sum_{i=1..n} (Sum_{j=1..i} (i/j)).
- A307654 (program): a(n) = Product_{p|n, p prime} (1 - p^p).
- A307662 (program): Triangle T(i,j=1..i) read by rows which contain the naturally ordered divisors-or-ones of the row number i.
- A307673 (program): Partial sums of A108754.
- A307677 (program): a(0) = a(1) = a(2) = a(3) = 1; thereafter a(n) = a(n-1) + a(n-2) + a(n-4).
- A307678 (program): G.f. A(x) satisfies: A(x) = 1 + x*A(x)^3/(1 - x).
- A307681 (program): Difference between the number of diagonals and the number of sides for a convex n-gon.
- A307688 (program): a(n) = 2*a(n-1)-2*a(n-2)+a(n-3)+2*a(n-4) with a(0)=a(1)=0, a(2)=2, a(3)=3.
- A307692 (program): g values of Triphosian primes.
- A307695 (program): Expansion of 1/(sqrt(1-4*x)*sqrt(1-16*x)).
- A307702 (program): Clique covering number of the n-Sierpinski tetrahedron graph.
- A307707 (program): Lexicographically earliest sequence starting with a(1) = 0 such that a(n) is the number of pairs of contiguous terms whose sum is a(n).
- A307753 (program): Number of palindromic pentagonal numbers of length n whose index is also palindromic.
- A307766 (program): Number of palindromic hexagonal numbers of length n whose index is also palindromic.
- A307768 (program): Number of n-step random walks on a line starting from the origin and returning to it at least once.
- A307789 (program): Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 1243.
- A307791 (program): Number of palindromic heptagonal numbers of length n whose index is also palindromic.
- A307802 (program): Number of palindromic octagonal numbers of length n whose index is also palindromic.
- A307808 (program): Number of palindromic nonagonal numbers of length n whose index is also palindromic.
- A307810 (program): Expansion of 1/AGM(1-64*x, sqrt((1-16*x)*(1-256*x))).
- A307811 (program): Expansion of 1/AGM(1-45*x, sqrt((1-25*x)*(1-81*x))).
- A307826 (program): The number of integers r such that all primes above a certain value have the form primorial(n)*q +- r.
- A307832 (program): Number of palindromic decagonal (10-gonal) numbers of length n whose index is also palindromic.
- A307844 (program): Constant term in the expansion of (n/x + 1 + n*x)^n.
- A307845 (program): Exponential unitary highly composite numbers: where the number of exponential unitary divisors (A278908) increases to a record.
- A307862 (program): Coefficient of x^n in (1 + x - n*x^2)^n.
- A307872 (program): Sum of the smallest parts in the partitions of n into 3 parts.
- A307885 (program): Coefficient of x^n in (1 - (n-1)*x - n*x^2)^n.
- A307893 (program): a(n) = lcm(sigma(n), pod(n)) / n, where sigma (k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).
- A307897 (program): Dimensions of space of harmonic polynomials of each degree invariant under the icosahedral rotation group.
- A307906 (program): Coefficient of x^n in 1/(n+1) * (1 + x + n*x^2)^(n+1).
- A307908 (program): a(n) is the least k such that p^k >= n for any prime factor p of n.
- A307911 (program): Coefficient of x^n in expansion of (1 - n*x - n*x^2)^n.
- A307912 (program): a(n) = n - 1 - pi(2*n-1) + pi(n), where pi is the prime counting function.
- A307921 (program): Number of (undirected) paths in the n-book graph.
- A307923 (program): Number of (undirected) Hamiltonian cycles in the n-cocktail party graph.
- A307935 (program): Number of (undirected) Hamiltonian paths in the n-cocktail party graph.
- A307939 (program): Number of (undirected) Hamiltonian paths in the n-dipyramidal graph.
- A307946 (program): Coefficient of x^n in 1/(n+1) * (1 - n*x - n*x^2)^(n+1).
- A307947 (program): Coefficient of x^n in 1/(n+1) * (1 + x - n*x^2)^(n+1).
- A307966 (program): Sum of the largest side lengths of all integer-sided triangles with perimeter n.
- A307969 (program): Coefficient of x^n in 1/(n+1) * (1 - 2*x - 2*x^2)^(n+1).
- A307985 (program): Number of integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c and b|n.
- A307989 (program): a(n) = n - pi(2*n) + pi(n-1), where pi is the prime counting function.
- A308025 (program): a(n) = n*(2*n - 3 - (-1)^n)*(5*n - 2 + (-1)^n)/16.
- A308026 (program): a(n) = n*(2*n - 3 - (-1)^n)*(11*n + (-1)^n)/24.
- A308036 (program): Coefficient of x^n in 1/(n+1) * (1 + x - 3*x^2)^(n+1).
- A308038 (program): a(n) = Sum_{i=1..floor((n-1)/2)} i * (n-i)^2.
- A308044 (program): a(n) = 2*prevprime(2*n-1) - 2*n, where prevprime(n) is the largest prime < n.
- A308046 (program): a(n) = 2*nextprime(n - 1) - 2*n, where nextprime(n) is the smallest prime > n.
- A308047 (program): Sum of subgroup indices of dihedral group, Sum_{H <= D(n)} [D(n):H].
- A308048 (program): a(n) = n - nextprime(ceiling(n/2) - 1), where nextprime(n) is the smallest prime > n.
- A308050 (program): a(n) = n - prevprime(n - 1), where prevprime(n) is the largest prime < n.
- A308052 (program): a(n) = nextprime(ceiling(n/2)-1), where nextprime(n) is the smallest prime > n.
- A308068 (program): Number of integer-sided triangles with perimeter n whose longest side length is even.
- A308084 (program): a(n) = n*(n-1)*d(n)/4, where d(n)=A000005(n) is the number of divisors of n.
- A308089 (program): Sum of the perimeters of all integer-sided triangles with perimeter n.
- A308090 (program): a(n) = gcd(2^n + n!, 3^n + n!, n+1).
- A308123 (program): Sum of the perimeters of all integer-sided isosceles triangles with perimeter n.
- A308124 (program): a(n) = (2 + 7*4^n)/3.
- A308135 (program): Sum of non-coreful divisors of n.
- A308136 (program): Number of (undirected) Hamiltonian paths in the 2n-crossed prism graph.
- A308137 (program): Number of (undirected) Hamiltonian paths on the n-prism graph.
- A308160 (program): Take all the integer-sided isosceles triangles with perimeter n and sides a, b, and c such that a <= b <= c. a(n) is the sum of all the b’s.
- A308167 (program): Number of integer-sided triangles with perimeter n and sides a, b, and c such that a <= b <= c and a|b.
- A308185 (program): Fixed point (beginning with a) of the morphism a -> abab, b -> b, over the alphabet {a,b} = {0,1}.
- A308186 (program): Fixed point (beginning with a) of the morphism a -> abab, b -> b, over the alphabet {a,b} = {1,2}.
- A308187 (program): Fixed point (beginning with a) of the morphism a -> aab, b -> b, over the alphabet {a,b} = {0,1}.
- A308188 (program): Fixed point (beginning with a) of the morphism a -> aab, b -> b, over the alphabet {a,b} = {1,2}.
- A308196 (program): Partial sums of A063808.
- A308215 (program): a(n) is the multiplicative inverse of A001844(n+1) modulo A001844(n); where A001844 is the sequence of centered square numbers.
- A308217 (program): a(n) is the multiplicative inverse of A001844(n) modulo A001844(n+1); where A001844 is the sequence of centered square numbers.
- A308265 (program): Sum of the largest parts in the partitions of n into 3 parts.
- A308266 (program): Sum of the middle parts in the partitions of n into 3 parts.
- A308287 (program): Length 20 arithmetic progression of primes (PAP-20).
- A308305 (program): a(n) = s(n,n) + s(n,n-1) + s(n,n-2), where s(n,k) are the unsigned Stirling numbers of the first kind (see A132393).
- A308320 (program): Decimal expansion of 2^(-7/4); exact length of the A4 paper size measured in meters according to the ISO 216 standard.
- A308321 (program): Decimal expansion of 2^(-9/4); exact width of the A4 paper size measured in meters according to the ISO 216 standard.
- A308329 (program): Even moments of the trace of elements of the binary icosahedral group.
- A308347 (program): n-th digit in the base-6 expansion of 1/n.
- A308357 (program): Smallest k such that k! can be represented as the sum of the n-th powers of two or more distinct primes; or -1 if no such k exists.
- A308358 (program): Beatty sequence for sqrt(3)/4.
- A308366 (program): Expansion of Sum_{k>=1} (-1)^(k+1)*k*x^k/(1 - k*x^k).
- A308367 (program): Expansion of Sum_{k>=1} x^k/(1 + k*x^k).
- A308375 (program): Digital sum of composite numbers.
- A308385 (program): a(n) is the last square visited by fers moves on a spirally numbered (2n-1) X (2n-1) board, moving to the lowest available unvisited square at each step.
- A308422 (program): a(n) = n^2 if n odd, 3*n^2/4 if n even.
- A308434 (program): n! + n!!.
- A308436 (program): Expansion of 1/((1-2*x)*(1-4*x)*(1-8*x)*(1-16*x)*(1-32*x)).
- A308469 (program): a(1) = 1, a(2)=2, a(n) = a(n-1) + gcd(a(n-2), n-2).
- A308473 (program): Sum of numbers < n which have common prime factors with n.
- A308474 (program): a(n) = Sum_{k=1..n^2, gcd(n,k) = 1} k.
- A308481 (program): a(n) = Sum_{k=1..n, gcd(n,k) = 1} k^n.
- A308495 (program): a(n) is the position of the first occurrence of prime(n) in A027748.
- A308506 (program): Expansion of e.g.f.: -1/(1-LambertW(-2*x)).
- A308523 (program): Number of essentially simple rooted toroidal triangulations with n vertices.
- A308546 (program): Number of double-closed subsets of {1..n}.
- A308567 (program): Consider the second least-significant bits of the first n prime numbers: a(n) equals the number of zeros minus the number of ones.
- A308570 (program): a(n) = sigma_{2*n}(n).
- A308572 (program): a(n) = Fibonacci(2*prime(n)).
- A308578 (program): Maximum number of non-overlapping circles of radius 1/n that can be placed inside a unit square.
- A308579 (program): a(n) = (9*2^n - 6*n - 10)/2.
- A308580 (program): a(n) = 3*2^n + n^2 - n.
- A308585 (program): a(n) = 2^(n + 3) - 10*n - 6.
- A308589 (program): Number of minimal edge covers in the (2n-1)-triangular snake graph.
- A308592 (program): Number of total dominating sets in the (2n-1)-triangular snake (for n > 1).
- A308593 (program): a(n) = Sum_{d|n} d^(n^2/d).
- A308594 (program): a(n) = Sum_{d|n} d^(d+n).
- A308596 (program): a(n) is the product of the prime(n) smallest primes other than prime(n).
- A308598 (program): The smaller term of the pair (a(n), a(n+1)) is always prime and in each pair there is a composite number; a(1) = 2 and the sequence is always extended with the smallest integer not yet present and not leading to a contradiction.
- A308599 (program): Number of (not necessarily maximum) cliques in the n-alternating group graph.
- A308600 (program): Number of (not necessarily maximum) cliques in the n X n antelope graph.
- A308602 (program): Number of (not necessarily maximum) cliques in the n-cycle graph.
- A308603 (program): Number of (not necessarily maximal) cliques in the n-dipyramidal graph.
- A308604 (program): Number of (not necessarily maximal) cliques in the n X n fiveleaper graph.
- A308606 (program): Number of (not necessarily maximum) cliques in the n-transposition graph.
- A308607 (program): Number of (not necessarily maximum) cliques in the wheel graph on n vertices.
- A308632 (program): Largest aggressor for the maximum number of peaceable coexisting queens as given in A250000.
- A308655 (program): Alternating partial sums of the prime gaps.
- A308663 (program): Partial sums of A097805.
- A308668 (program): a(n) = Sum_{d|n} d^(n/d+n).
- A308677 (program): Kuba-Panholzer Table 2 pattern 312, 213 for Stirling permutation k = 2.
- A308688 (program): a(n) = Sum_{d|n} d^(2*n/d - 1).
- A308689 (program): a(n) = Sum_{d|n} d^(3*n/d - 2).
- A308692 (program): a(n) = Sum_{d|n} d^(2*(n/d - 1)).
- A308693 (program): a(n) = Sum_{d|n} d^(3*(n/d - 1)).
- A308696 (program): a(n) = Sum_{d|n} d^(2*d).
- A308697 (program): a(n) = Sum_{d|n} d^(3*d).
- A308700 (program): a(n) = n * 2^(n - 2) * (2^(n - 1) - 1).
- A308707 (program): a(n) = gcd(n, phi(n) + sigma(n)), where phi is A000010 and sigma is A000203.
- A308709 (program): Start with 3, divide by 3, multiply by 2, multiply by 3, multiply by 2, repeat.
- A308710 (program): Primitive practical numbers of the form 2^i * prime(k).
- A308720 (program): The maximum value in the continued fraction of sqrt(n), or 0 if there is no fractional part.
- A308729 (program): a(n)/n! is the expected number of left-to-right maxima in the lexicographical or colexicographical ordering of all the 2-subsets of [n] under a random permutation of [n], when the 2-subsets hold the worst order of ranks.
- A308733 (program): Sum of the smallest parts of the partitions of n into 4 parts.
- A308741 (program): Decimal expansion of BesselI(1/4,1/2)/BesselI(-3/4,1/2).
- A308742 (program): Decimal expansion of BesselI(3/4,1/2)/BesselI(-1/4,1/2).
- A308747 (program): Number of achiral m-color cyclic compositions of n (that is, number of cyclic compositions of n with reflection symmetry where each part of size m can be colored with one of m colors).
- A308753 (program): a(n) = Sum_{d|n} d^(2*(d-1)).
- A308754 (program): a(0) = 0, a(n) = a(n-1) + 1 if 2*n + 3 is prime, otherwise a(n) = a(n-1).
- A308755 (program): a(n) = Sum_{d|n} d^(d-2).
- A308756 (program): a(n) = Sum_{d|n} d^(2*(d-2)).
- A308757 (program): a(n) = Sum_{d|n} d^(3*(d-2)).
- A308775 (program): Sum of all the parts in the partitions of n into 4 parts.
- A308807 (program): a(n) = 4*5^(n-1) + n.
- A308812 (program): a(n) = Sum_{k=1..n} binomial(n,k) * floor(n/k).
- A308814 (program): a(n) = Sum_{d|n} n^(d-1).
- A308820 (program): a(n) = Product_{k=1..n} ceiling(n/k)!.
- A308822 (program): Sum of all the parts in the partitions of n into 5 parts.
- A308823 (program): Sum of the smallest parts of the partitions of n into 5 parts.
- A308833 (program): Numbers r such that the r-th tetrahedral number A000292(r) divides r!.
- A308863 (program): Expansion of e.g.f. (1 + LambertW(-x))/(1 + 2*LambertW(-x)).
- A308865 (program): a(n) = Sum_{k>=0} k^(2*n+1)/2^(k+1).
- A308876 (program): Expansion of e.g.f. exp(x)*(1 - x)/(1 - 2*x).
- A308900 (program): An explicit example of an infinite sequence with a(1)=1 and, for n >= 2, a(n) and S(n) = Sum_{i=1..n} a(i) have no digit in common.
- A308901 (program): Lexicographically earliest overlap-free binary sequence.
- A308914 (program): Number of unordered pairs of non-intersecting non-selfintersecting paths with nodes that cover all vertices of a convex n-gon, n > 3.
- A308944 (program): a(n) = Product_{k=1..n} lcm(n,k) / (k * gcd(n,k)).
- A309000 (program): Number of strings of length n from a 3-symbol alphabet (A,B,C, say) containing at least one “A” and at least two “B”s.
- A309006 (program): Product minus sum of the two previous terms in the sequence, with a(1) = 2 and a(2) = 5.
- A309014 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling2(n,k) mod 2).
- A309025 (program): Expansion of x * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+3))).
- A309057 (program): a(0) = 1; a(2*n) = 3*a(n), a(2*n+1) = a(n).
- A309074 (program): a(0) = 1; a(2*n) = 4*a(n), a(2*n+1) = a(n).
- A309075 (program): Total number of black cells after n iterations of Langton’s ant with two ants on the grid placed side-by-side on neighboring squares and initially looking in the same direction.
- A309091 (program): Decimal expansion of 4/(Pi-2).
- A309093 (program): The analog of A309077(n), but allowing fractional powers.
- A309097 (program): Number of partitions of n avoiding the partition (4,2,1).
- A309099 (program): Number of partitions of n avoiding the partition (4,3,1).
- A309118 (program): Number of tiles added at iteration n when successively, layer by layer, building a symmetric patch of a rhombille tiling around a central star of six rhombs.
- A309124 (program): a(n) = n - 3 * floor(n/3) + 5 * floor(n/5) - 7 * floor(n/7) + …
- A309125 (program): a(n) = n + 2^2 * floor(n/2^2) + 3^2 * floor(n/3^2) + 4^2 * floor(n/4^2) + …
- A309126 (program): a(n) = n + 2^3 * floor(n/2^3) + 3^3 * floor(n/3^3) + 4^3 * floor(n/4^3) + …
- A309153 (program): a(n) = A000203(n)*A001227(n).
- A309176 (program): a(n) = n^2 * (n + 1)/2 - Sum_{k=1..n} sigma_2(k).
- A309192 (program): a(n) = Sum_{k=1..n} mu(k)^2 * k * floor(n/k).
- A309212 (program): Nearest integer to (4/3)^n.
- A309214 (program): a(0)=0; thereafter a(n) = a(n-1)+n if a(n-1) even, otherwise a(n) = a(n-1)-n.
- A309215 (program): a(0)=0; thereafter a(n) = a(n-1)+n if a(n-1) odd, otherwise a(n) = a(n-1)-n.
- A309231 (program): Column 3 of the array at A326662 see Comments.
- A309243 (program): Completely multiplicative with a(p) = p * a(p-1) for any prime number p.
- A309250 (program): a(n) is the index of the binary string of a Post’s Correspondence Problem Encoding with index n.
- A309255 (program): a(n) = n + 1 - Sum_{k=0..n} (Stirling1(n,k) mod 2).
- A309256 (program): a(n) = n + 1 - Sum_{k=0..n} (Stirling2(n,k) mod 2).
- A309269 (program): Numbers that are the sum of two successive prime powers.
- A309294 (program): (1/2) times the sum of the elements of all subsets of [n] whose sum is divisible by two.
- A309303 (program): Expansion of g.f. (sqrt(x+1) - sqrt(1-3*x))/(2*(x+1)^(3/2)).
- A309307 (program): Number of unitary divisors of n (excluding 1).
- A309315 (program): Number of 5-colorings of an n-wheel graph.
- A309322 (program): Expansion of Sum_{k>=1} phi(k) * x^k/(1 - x^k)^3, where phi = Euler totient function (A000010).
- A309324 (program): Expansion of Sum_{k>=1} psi(k) * x^k/(1 + x^k), where psi = Dedekind psi function (A001615).
- A309327 (program): a(n) = Product_{k=1..n-1} (4^k + 1).
- A309330 (program): Numbers k such that 10*k^2 + 40 is a square.
- A309332 (program): Number of ways the n-th triangular number T(n) = A000217(n) can be written as the sum of two positive triangular numbers.
- A309335 (program): a(n) = n^3 if n odd, 7*n^3/8 if n even.
- A309336 (program): a(n) = n^4 if n odd, 15*n^4/16 if n even.
- A309337 (program): a(n) = n^3 if n odd, 3*n^3/4 if n even.
- A309338 (program): a(n) = n^4 if n odd, 7*n^4/8 if n even.
- A309355 (program): Even numbers k such that k! is divisible by k*(k+1)/2.
- A309372 (program): a(n) = n^2 - n^3 + n^4.
- A309379 (program): Number of unordered pairs of 4-colorings of an n-wheel that differ in the coloring of exactly one vertex.
- A309391 (program): a(n) = gcd(n, A064169(n-2)) for n > 2.
- A309397 (program): a(n) = gcd(n^2, A001008(n-1)) for n > 1.
- A309398 (program): a(n) is the nearest integer to log(log(10^n)).
- A309419 (program): Decimal expansion of e/(e-2).
- A309462 (program): Limiting row sequence for Pascal-like triangle A140995 (Stepan’s triangle with index of asymmetry s = 3).
- A309472 (program): a(n) = n^n - n * n!.
- A309490 (program): Total number of adjacent node merge operations to turn a circular list of size n to a node.
- A309507 (program): Number of ways the n-th triangular number T(n) = A000217(n) can be written as the difference of two positive triangular numbers.
- A309511 (program): Number of odd parts in the partitions of n into 3 parts.
- A309555 (program): Triangle read by rows: T(n,k) = 3 + k*(n-k) for n >= 0, 0 <= k <= n.
- A309557 (program): Number triangle with T(n,k) = 2 + 3*n - 2*k + 2*k*(n-k) for n >= 0, 0 <= k <= n.
- A309559 (program): Triangle read by rows: T(n,k) = 1 + n + k^2/2 - k/2 + k*(n-k), n >= 0, 0 <= k <= n.
- A309574 (program): n-th prime minus its ternary (base 3) reversal.
- A309579 (program): Maximum principal ratio of a strongly connected digraph on n nodes.
- A309618 (program): a(n) = Sum_{k=0..floor(n/2)} k! * 2^k * (n - 2*k)!.
- A309619 (program): a(n) = Sum_{k=0..floor(n/2)} k! * (n - 2*k)!.
- A309649 (program): Sieved recursive primeth recurrence (see Comments for precise definition).
- A309665 (program): a(1)=1; for n > 1, a(n) = a(n-1)/gcd(a(n-1),n) + n + 1.
- A309674 (program): a(1) = 1, a(n) = hamming_weight(Sum_{k=1..n-1} a(k) ) for n>=2.
- A309675 (program): a(n) = 4^n^2 + n!.
- A309678 (program): G.f. A(x) satisfies: A(x) = A(x^4) / (1 - x)^2.
- A309683 (program): Number of odd parts appearing among the smallest parts of the partitions of n into 3 parts.
- A309684 (program): Sum of the odd parts appearing among the smallest parts of the partitions of n into 3 parts.
- A309685 (program): Number of even parts appearing among the smallest parts of the partitions of n into 3 parts.
- A309686 (program): Sum of the even parts appearing among the smallest parts of the partitions of n into 3 parts.
- A309687 (program): Number of odd parts appearing among the second largest parts of the partitions of n into 3 parts.
- A309689 (program): Number of even parts appearing among the second largest parts of the partitions of n into 3 parts.
- A309705 (program): a(n) = lcm(a(n-1), n) - gcd(a(n-1), n) where a(1) = 1.
- A309709 (program): Number of binary digits that change when n is multiplied by 4.
- A309714 (program): The smallest possible nonnegative difference between the sum of the first n positive integers (A000217) and the sum of any number of the directly following and consecutive integers.
- A309715 (program): Number of even parts appearing among the third largest parts of the partitions of n into 4 parts.
- A309725 (program): Number of set partitions of {1,2,…,3n} with sizes in {[n, n, n], [2n, n], [3n]}.
- A309726 (program): Numbers n such that n^2 - 12 is prime.
- A309729 (program): Expansion of Sum_{k>=1} x^k/(1 - x^k - 2*x^(2*k)).
- A309731 (program): Expansion of Sum_{k>=1} k * x^k/(1 - x^k)^3.
- A309732 (program): Expansion of Sum_{k>=1} k^2 * x^k/(1 - x^k)^3.
- A309758 (program): Numbers that are sums of consecutive powers of 3.
- A309759 (program): Numbers that are sums of consecutive powers of 4.
- A309761 (program): Numbers that are sums of consecutive powers of 10.
- A309773 (program): n directly precedes a(n) in Sharkovskii ordering.
- A309779 (program): Squares that can be expressed as the sum of two positive squares but not as the sum of three positive squares.
- A309790 (program): G.f. A(x) satisfies: A(x) = 2*x*(1 - x)*A(x^2) + x/(1 - x).
- A309805 (program): Maximum number of nonattacking kings placeable on a hexagonal board with edge-length n in Glinski’s hexagonal chess.
- A309809 (program): a(n) is the concatenation of n and 2n+1.
- A309816 (program): a(n) is the 2-adic valuation of A014664(n).
- A309827 (program): a(n) is the square of the number consisting of one 1 and n 6’s: (166…6)^2.
- A309831 (program): Number of even parts appearing among the smallest parts of the partitions of n into 5 parts.
- A309842 (program): a(n) is the total surface area of a hollow cubic block (defined as a block with a shell thickness of 1 cube) where n is the edge length of the removed volume.
- A309873 (program): Period-doubling turn sequence, +1 when the 2-adic valuation of n is even or -1 when odd.
- A309874 (program): a(n) = 2*n*Fibonacci(n-2) + (-1)^n + 1.
- A309878 (program): The real part of b(n) where b(n) = (n + b(n-1)) * (1 + i) with b(-1)=0; i = sqrt(-1).
- A309891 (program): a(n) is the total number of trailing zeros in the representations of n over all bases b >= 2.
- A309907 (program): a(n) is the square of the number consisting of one 1 and n 3’s: (133…3)^2.
- A309914 (program): Distance from n to closest triangular number that is different from n.
- A309945 (program): a(n) = floor(n - sqrt(2*n-1)).
- A309948 (program): Decimal expansion of the real part of the square root of 1 + i.
- A309949 (program): Decimal expansion of the imaginary part of the square root of 1 + i.
- A309952 (program): XOR contraction of binary representation of n.
- A309953 (program): Product of digits of (n written in base 3).
- A309954 (program): Product of digits of (n written in base 4).
- A309956 (program): Product of digits of (n written in base 5).
- A309957 (program): Product of digits of (n written in base 6).
- A309970 (program): Period 12: repeat [1, 1, 0, 0, -1, -1, -1, -1, 0, 0, 1, 1].
- A309983 (program): Numbers n resulting from adding the exponents of 2 associated with the “1” terms of their binary representation and subtracting the exponents of 2 associated with the “0” terms of their binary representation.
- A309991 (program): Balanced quinary (base 5) enumeration (or balanced quinary representation) of integers, write n in quinary, and then replace 3’s with (-2)’s and 4’s with (-1)’s.
- A309995 (program): Balanced septenary enumeration (or balanced septenary representation) of integers; write n in septenary and then replace 4’s with (-3),s, 5’s with (-2)’s, and 6’s with (-1)’s.
- A310238 (program): Coordination sequence Gal.4.7.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310341 (program): Coordination sequence Gal.6.527.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310342 (program): Coordination sequence Gal.5.253.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310367 (program): Coordination sequence Gal.6.129.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310368 (program): Coordination sequence Gal.6.230.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310369 (program): Coordination sequence Gal.5.64.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310370 (program): Coordination sequence Gal.5.109.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310371 (program): Coordination sequence Gal.6.258.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310372 (program): Coordination sequence Gal.4.52.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310373 (program): Coordination sequence Gal.6.150.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310374 (program): Coordination sequence Gal.6.245.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310375 (program): Coordination sequence Gal.5.82.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310378 (program): Coordination sequence Gal.6.320.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310379 (program): Coordination sequence Gal.6.321.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310380 (program): Coordination sequence Gal.6.322.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310393 (program): Coordination sequence Gal.6.193.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310396 (program): Coordination sequence Gal.6.320.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310397 (program): Coordination sequence Gal.4.76.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310398 (program): Coordination sequence Gal.5.136.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310400 (program): Coordination sequence Gal.6.337.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310404 (program): Coordination sequence Gal.6.338.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310405 (program): Coordination sequence Gal.6.339.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310408 (program): Coordination sequence Gal.6.196.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310409 (program): Coordination sequence Gal.3.19.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310410 (program): Coordination sequence Gal.6.344.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310411 (program): Coordination sequence Gal.4.72.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310412 (program): Coordination sequence Gal.5.129.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310413 (program): Coordination sequence Gal.6.323.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310419 (program): Coordination sequence Gal.5.130.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310420 (program): Coordination sequence Gal.6.324.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310421 (program): Coordination sequence Gal.5.131.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310422 (program): Coordination sequence Gal.6.325.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310423 (program): Coordination sequence Gal.6.326.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310438 (program): Coordination sequence Gal.6.194.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310439 (program): Coordination sequence Gal.6.321.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310440 (program): Coordination sequence Gal.6.202.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310441 (program): Coordination sequence Gal.4.77.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310442 (program): Coordination sequence Gal.6.327.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310444 (program): Coordination sequence Gal.6.340.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310446 (program): Coordination sequence Gal.5.137.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310454 (program): Coordination sequence Gal.5.140.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310455 (program): Coordination sequence Gal.6.348.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310456 (program): Coordination sequence Gal.6.322.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310457 (program): Coordination sequence Gal.6.345.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310458 (program): Coordination sequence Gal.4.78.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310461 (program): Coordination sequence Gal.6.350.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310462 (program): Coordination sequence Gal.5.138.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310469 (program): Coordination sequence Gal.5.141.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310471 (program): Coordination sequence Gal.6.346.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310491 (program): Coordination sequence Gal.6.154.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310492 (program): Coordination sequence Gal.6.249.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310493 (program): Coordination sequence Gal.5.86.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310496 (program): Coordination sequence Gal.6.327.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310498 (program): Coordination sequence Gal.3.20.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310499 (program): Coordination sequence Gal.6.351.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310501 (program): Coordination sequence Gal.6.328.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310502 (program): Coordination sequence Gal.5.132.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310503 (program): Coordination sequence Gal.4.73.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310504 (program): Coordination sequence Gal.6.329.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310505 (program): Coordination sequence Gal.6.330.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310509 (program): Coordination sequence Gal.5.142.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310511 (program): Coordination sequence Gal.6.354.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310517 (program): Coordination sequence Gal.6.206.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310518 (program): Coordination sequence Gal.3.21.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310520 (program): Coordination sequence Gal.6.331.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310521 (program): Coordination sequence Gal.5.133.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310523 (program): Coordination sequence Gal.6.355.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310524 (program): Coordination sequence Gal.6.356.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310525 (program): Coordination sequence Gal.4.74.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310526 (program): Coordination sequence Gal.6.332.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310529 (program): Coordination sequence Gal.4.75.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310530 (program): Coordination sequence Gal.5.134.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310531 (program): Coordination sequence Gal.5.135.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310532 (program): Coordination sequence Gal.6.333.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310533 (program): Coordination sequence Gal.6.334.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310564 (program): Coordination sequence Gal.3.23.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310565 (program): Coordination sequence Gal.4.82.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A310704 (program): Coordination sequence Gal.3.2.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311196 (program): Coordination sequence Gal.6.115.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311225 (program): Coordination sequence Gal.6.216.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311257 (program): Coordination sequence Gal.6.115.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311262 (program): Coordination sequence Gal.6.216.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311289 (program): Coordination sequence Gal.5.107.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311290 (program): Coordination sequence Gal.5.62.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311312 (program): Coordination sequence Gal.6.118.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311331 (program): Coordination sequence Gal.6.119.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311332 (program): Coordination sequence Gal.6.120.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311344 (program): Coordination sequence Gal.5.95.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311356 (program): Coordination sequence Gal.6.219.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311384 (program): Coordination sequence Gal.6.220.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311385 (program): Coordination sequence Gal.6.221.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311426 (program): Coordination sequence Gal.6.115.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311434 (program): Coordination sequence Gal.6.216.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311440 (program): Coordination sequence Gal.5.50.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311458 (program): Coordination sequence Gal.5.95.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311475 (program): Coordination sequence Gal.6.118.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311481 (program): Coordination sequence Gal.6.219.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311501 (program): Coordination sequence Gal.4.38.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311512 (program): Coordination sequence Gal.6.130.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311523 (program): Coordination sequence Gal.6.119.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311535 (program): Coordination sequence Gal.5.53.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311536 (program): Coordination sequence Gal.6.120.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311548 (program): Coordination sequence Gal.5.54.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311549 (program): Coordination sequence Gal.6.132.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311552 (program): Coordination sequence Gal.5.55.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311553 (program): Coordination sequence Gal.6.133.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311554 (program): Coordination sequence Gal.6.134.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311586 (program): Coordination sequence Gal.4.58.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311593 (program): Coordination sequence Gal.6.192.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311601 (program): Coordination sequence Gal.6.230.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311612 (program): Coordination sequence Gal.5.98.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311613 (program): Coordination sequence Gal.6.231.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311625 (program): Coordination sequence Gal.5.99.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311626 (program): Coordination sequence Gal.6.232.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311633 (program): Coordination sequence Gal.5.100.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311634 (program): Coordination sequence Gal.6.233.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311635 (program): Coordination sequence Gal.6.234.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311801 (program): Coordination sequence Gal.6.115.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311804 (program): Coordination sequence Gal.6.216.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311807 (program): Coordination sequence Gal.3.12.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311816 (program): Coordination sequence Gal.5.95.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311843 (program): Coordination sequence Gal.4.38.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311861 (program): Coordination sequence Gal.6.130.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311889 (program): Coordination sequence Gal.6.129.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311914 (program): Coordination sequence Gal.4.58.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311924 (program): Coordination sequence Gal.6.118.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311932 (program): Coordination sequence Gal.6.192.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311958 (program): Coordination sequence Gal.5.53.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311964 (program): Coordination sequence Gal.6.131.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A311993 (program): Coordination sequence Gal.5.98.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312065 (program): Coordination sequence Gal.3.10.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312068 (program): Coordination sequence Gal.6.119.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312077 (program): Coordination sequence Gal.5.65.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312100 (program): Coordination sequence Gal.5.54.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312101 (program): Coordination sequence Gal.6.150.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312123 (program): Coordination sequence Gal.6.120.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312125 (program): Coordination sequence Gal.6.221.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312140 (program): Coordination sequence Gal.4.41.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312143 (program): Coordination sequence Gal.5.55.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312144 (program): Coordination sequence Gal.6.151.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312151 (program): Coordination sequence Gal.6.133.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312183 (program): Coordination sequence Gal.4.42.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312184 (program): Coordination sequence Gal.6.155.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312185 (program): Coordination sequence Gal.6.154.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312195 (program): Coordination sequence Gal.5.67.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312205 (program): Coordination sequence Gal.4.43.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312207 (program): Coordination sequence Gal.5.68.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312208 (program): Coordination sequence Gal.5.69.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312209 (program): Coordination sequence Gal.6.158.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312210 (program): Coordination sequence Gal.6.159.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312289 (program): Coordination sequence Gal.6.527.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312472 (program): Coordination sequence Gal.6.149.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312475 (program): Coordination sequence Gal.3.16.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312484 (program): Coordination sequence Gal.5.81.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312506 (program): Coordination sequence Gal.5.109.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312507 (program): Coordination sequence Gal.6.245.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312526 (program): Coordination sequence Gal.6.254.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312549 (program): Coordination sequence Gal.4.61.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312555 (program): Coordination sequence Gal.5.110.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312556 (program): Coordination sequence Gal.6.246.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312561 (program): Coordination sequence Gal.6.247.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312562 (program): Coordination sequence Gal.6.248.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312606 (program): Coordination sequence Gal.6.255.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312620 (program): Coordination sequence Gal.6.256.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312655 (program): Coordination sequence Gal.4.62.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312656 (program): Coordination sequence Gal.6.201.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312658 (program): Coordination sequence Gal.6.249.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312668 (program): Coordination sequence Gal.6.250.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312669 (program): Coordination sequence Gal.5.111.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312680 (program): Coordination sequence Gal.4.63.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312681 (program): Coordination sequence Gal.6.251.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312682 (program): Coordination sequence Gal.5.112.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312683 (program): Coordination sequence Gal.5.113.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312684 (program): Coordination sequence Gal.6.252.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312685 (program): Coordination sequence Gal.6.253.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312890 (program): Coordination sequence Gal.6.115.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312891 (program): Coordination sequence Gal.6.216.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312892 (program): Coordination sequence Gal.5.50.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312893 (program): Coordination sequence Gal.5.95.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312894 (program): Coordination sequence Gal.4.38.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312895 (program): Coordination sequence Gal.4.58.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312896 (program): Coordination sequence Gal.6.130.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312897 (program): Coordination sequence Gal.6.192.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312901 (program): Coordination sequence Gal.3.10.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312902 (program): Coordination sequence Gal.6.129.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312903 (program): Coordination sequence Gal.5.65.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312908 (program): Coordination sequence Gal.5.64.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312909 (program): Coordination sequence Gal.6.150.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312926 (program): Coordination sequence Gal.6.118.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312927 (program): Coordination sequence Gal.6.149.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312928 (program): Coordination sequence Gal.3.16.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312932 (program): Coordination sequence Gal.5.81.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312933 (program): Coordination sequence Gal.6.131.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312935 (program): Coordination sequence Gal.4.105.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312938 (program): Coordination sequence Gal.5.127.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312941 (program): Coordination sequence Gal.5.14.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312943 (program): Coordination sequence Gal.4.41.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312944 (program): Coordination sequence Gal.6.245.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312948 (program): Coordination sequence Gal.5.66.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312950 (program): Coordination sequence Gal.6.151.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312960 (program): Coordination sequence Gal.4.106.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312961 (program): Coordination sequence Gal.6.152.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312963 (program): Coordination sequence Gal.6.153.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312969 (program): Coordination sequence Gal.6.254.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312974 (program): Coordination sequence Gal.4.61.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312975 (program): Coordination sequence Gal.5.110.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A312979 (program): Coordination sequence Gal.6.247.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313023 (program): Coordination sequence Gal.6.130.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313024 (program): Coordination sequence Gal.6.119.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313025 (program): Coordination sequence Gal.5.65.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313026 (program): Coordination sequence Gal.5.54.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313031 (program): Coordination sequence Gal.6.258.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313045 (program): Coordination sequence Gal.6.258.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313046 (program): Coordination sequence Gal.6.454.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313051 (program): Coordination sequence Gal.3.33.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313053 (program): Coordination sequence Gal.5.114.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313054 (program): Coordination sequence Gal.6.318.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313057 (program): Coordination sequence Gal.6.132.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313062 (program): Coordination sequence Gal.6.154.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313076 (program): Coordination sequence Gal.6.156.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313088 (program): Coordination sequence Gal.6.120.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313089 (program): Coordination sequence Gal.6.221.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313090 (program): Coordination sequence Gal.5.114.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313099 (program): Coordination sequence Gal.6.259.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313100 (program): Coordination sequence Gal.5.100.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313110 (program): Coordination sequence Gal.3.13.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313113 (program): Coordination sequence Gal.6.133.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313115 (program): Coordination sequence Gal.4.43.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313116 (program): Coordination sequence Gal.5.116.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313117 (program): Coordination sequence Gal.6.134.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313118 (program): Coordination sequence Gal.6.234.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313124 (program): Coordination sequence Gal.6.250.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313125 (program): Coordination sequence Gal.5.111.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313126 (program): Coordination sequence Gal.6.198.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313127 (program): Coordination sequence Gal.5.69.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313136 (program): Coordination sequence Gal.6.256.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313137 (program): Coordination sequence Gal.6.263.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313145 (program): Coordination sequence Gal.6.264.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313147 (program): Coordination sequence Gal.4.63.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313152 (program): Coordination sequence Gal.5.112.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313201 (program): Coordination sequence Gal.5.115.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313212 (program): Coordination sequence Gal.6.263.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313228 (program): Coordination sequence Gal.6.155.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313229 (program): Coordination sequence Gal.6.201.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313232 (program): Coordination sequence Gal.3.14.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313237 (program): Coordination sequence Gal.6.202.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313241 (program): Coordination sequence Gal.5.86.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313246 (program): Coordination sequence Gal.6.264.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313247 (program): Coordination sequence Gal.6.261.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313251 (program): Coordination sequence Gal.6.203.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313255 (program): Coordination sequence Gal.5.87.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313258 (program): Coordination sequence Gal.4.54.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313259 (program): Coordination sequence Gal.6.204.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313276 (program): Coordination sequence Gal.6.265.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313280 (program): Coordination sequence Gal.3.15.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313289 (program): Coordination sequence Gal.4.55.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313292 (program): Coordination sequence Gal.4.56.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313293 (program): Coordination sequence Gal.5.89.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313295 (program): Coordination sequence Gal.5.90.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313296 (program): Coordination sequence Gal.6.209.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313297 (program): Coordination sequence Gal.6.210.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313416 (program): Coordination sequence Gal.4.106.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313474 (program): Coordination sequence Gal.6.118.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313475 (program): Coordination sequence Gal.6.119.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313476 (program): Coordination sequence Gal.5.53.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313477 (program): Coordination sequence Gal.5.54.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313480 (program): Coordination sequence Gal.4.41.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313485 (program): Coordination sequence Gal.6.254.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313487 (program): Coordination sequence Gal.4.42.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313494 (program): Coordination sequence Gal.6.155.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313498 (program): Coordination sequence Gal.6.255.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313506 (program): Coordination sequence Gal.5.114.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313510 (program): Coordination sequence Gal.3.13.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313514 (program): Coordination sequence Gal.6.154.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313519 (program): Coordination sequence Gal.6.196.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313533 (program): Coordination sequence Gal.6.131.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313534 (program): Coordination sequence Gal.6.231.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313537 (program): Coordination sequence Gal.5.66.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313538 (program): Coordination sequence Gal.5.110.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313540 (program): Coordination sequence Gal.6.151.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313543 (program): Coordination sequence Gal.6.196.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313556 (program): Coordination sequence Gal.6.132.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313560 (program): Coordination sequence Gal.6.201.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313561 (program): Coordination sequence Gal.4.53.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313568 (program): Coordination sequence Gal.3.14.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313569 (program): Coordination sequence Gal.6.197.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313572 (program): Coordination sequence Gal.6.250.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313575 (program): Coordination sequence Gal.6.202.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313580 (program): Coordination sequence Gal.5.111.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313581 (program): Coordination sequence Gal.4.57.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313583 (program): Coordination sequence Gal.6.345.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313610 (program): Coordination sequence Gal.5.136.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313611 (program): Coordination sequence Gal.6.337.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313613 (program): Coordination sequence Gal.4.72.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313614 (program): Coordination sequence Gal.5.129.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313615 (program): Coordination sequence Gal.6.323.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313620 (program): Coordination sequence Gal.6.348.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313622 (program): Coordination sequence Gal.6.203.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313623 (program): Coordination sequence Gal.5.87.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313635 (program): Coordination sequence Gal.4.54.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313680 (program): Coordination sequence Gal.6.120.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313681 (program): Coordination sequence Gal.6.221.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313682 (program): Coordination sequence Gal.5.55.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313683 (program): Coordination sequence Gal.5.100.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313684 (program): Coordination sequence Gal.6.259.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313685 (program): Coordination sequence Gal.4.43.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313687 (program): Coordination sequence Gal.6.202.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313688 (program): Coordination sequence Gal.6.151.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313689 (program): Coordination sequence Gal.6.152.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313692 (program): Coordination sequence Gal.5.136.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313693 (program): Coordination sequence Gal.6.197.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313694 (program): Coordination sequence Gal.4.63.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313696 (program): Coordination sequence Gal.6.327.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313698 (program): Coordination sequence Gal.6.157.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313702 (program): Coordination sequence Gal.6.337.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313703 (program): Coordination sequence Gal.5.129.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313704 (program): Coordination sequence Gal.6.323.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313707 (program): Coordination sequence Gal.6.198.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313717 (program): Coordination sequence Gal.6.151.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313718 (program): Coordination sequence Gal.6.133.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313719 (program): Coordination sequence Gal.5.116.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313720 (program): Coordination sequence Gal.6.153.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313721 (program): Coordination sequence Gal.5.129.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313722 (program): Coordination sequence Gal.6.248.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313726 (program): Coordination sequence Gal.6.340.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313729 (program): Coordination sequence Gal.6.134.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313730 (program): Coordination sequence Gal.6.234.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313735 (program): Coordination sequence Gal.6.646.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313737 (program): Coordination sequence Gal.6.363.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313738 (program): Coordination sequence Gal.6.158.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313739 (program): Coordination sequence Gal.6.159.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313740 (program): Coordination sequence Gal.5.309.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313744 (program): Coordination sequence Gal.6.345.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313745 (program): Coordination sequence Gal.6.199.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313746 (program): Coordination sequence Gal.5.113.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313747 (program): Coordination sequence Gal.6.200.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313752 (program): Coordination sequence Gal.5.300.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313753 (program): Coordination sequence Gal.6.253.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313754 (program): Coordination sequence Gal.4.142.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313769 (program): Coordination sequence Gal.6.339.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313772 (program): Coordination sequence Gal.6.328.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313773 (program): Coordination sequence Gal.5.131.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313774 (program): Coordination sequence Gal.6.622.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313778 (program): Coordination sequence Gal.6.203.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313779 (program): Coordination sequence Gal.6.328.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313780 (program): Coordination sequence Gal.3.23.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313781 (program): Coordination sequence Gal.6.617.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313782 (program): Coordination sequence Gal.5.289.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313788 (program): Coordination sequence Gal.6.326.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313789 (program): Coordination sequence Gal.6.208.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313791 (program): Coordination sequence Gal.6.354.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313793 (program): Coordination sequence Gal.4.134.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313794 (program): Coordination sequence Gal.6.619.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313799 (program): Coordination sequence Gal.3.53.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313801 (program): Coordination sequence Gal.5.291.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313802 (program): Coordination sequence Gal.6.209.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313803 (program): Coordination sequence Gal.6.210.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313826 (program): Coordination sequence Gal.4.78.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313827 (program): Coordination sequence Gal.5.141.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313829 (program): Coordination sequence Gal.6.203.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313831 (program): Coordination sequence Gal.6.328.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313834 (program): Coordination sequence Gal.6.616.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313835 (program): Coordination sequence Gal.5.299.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313836 (program): Coordination sequence Gal.3.23.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313837 (program): Coordination sequence Gal.6.618.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313842 (program): Coordination sequence Gal.5.289.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313846 (program): Coordination sequence Gal.5.308.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313859 (program): Coordination sequence Gal.6.340.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313860 (program): Coordination sequence Gal.5.132.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313862 (program): Coordination sequence Gal.6.354.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313869 (program): Coordination sequence Gal.6.206.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313872 (program): Coordination sequence Gal.6.617.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313873 (program): Coordination sequence Gal.3.21.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313875 (program): Coordination sequence Gal.4.134.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313876 (program): Coordination sequence Gal.6.342.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313879 (program): Coordination sequence Gal.6.343.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313887 (program): Coordination sequence Gal.6.331.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313891 (program): Coordination sequence Gal.4.142.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313894 (program): Coordination sequence Gal.5.133.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313898 (program): Coordination sequence Gal.5.291.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313899 (program): Coordination sequence Gal.6.620.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313900 (program): Coordination sequence Gal.6.621.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313908 (program): Coordination sequence Gal.6.639.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313909 (program): Coordination sequence Gal.6.648.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313913 (program): Coordination sequence Gal.6.331.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313916 (program): Coordination sequence Gal.5.293.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313918 (program): Coordination sequence Gal.6.332.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313922 (program): Coordination sequence Gal.6.356.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313923 (program): Coordination sequence Gal.4.139.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313924 (program): Coordination sequence Gal.6.626.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313926 (program): Coordination sequence Gal.4.140.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313927 (program): Coordination sequence Gal.5.135.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313928 (program): Coordination sequence Gal.5.302.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313929 (program): Coordination sequence Gal.6.334.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313930 (program): Coordination sequence Gal.6.638.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313938 (program): Coordination sequence Gal.6.662.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313962 (program): Coordination sequence Gal.3.53.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313975 (program): Coordination sequence Gal.4.145.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A313982 (program): Coordination sequence Gal.3.57.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314015 (program): Coordination sequence Gal.4.100.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314020 (program): Coordination sequence Gal.6.247.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314021 (program): Coordination sequence Gal.5.84.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314024 (program): Coordination sequence Gal.6.156.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314025 (program): Coordination sequence Gal.6.250.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314026 (program): Coordination sequence Gal.5.130.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314027 (program): Coordination sequence Gal.5.87.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314028 (program): Coordination sequence Gal.6.198.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314029 (program): Coordination sequence Gal.6.328.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314031 (program): Coordination sequence Gal.6.340.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314032 (program): Coordination sequence Gal.6.324.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314034 (program): Coordination sequence Gal.5.132.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314038 (program): Coordination sequence Gal.6.616.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314039 (program): Coordination sequence Gal.5.299.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314040 (program): Coordination sequence Gal.4.133.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314043 (program): Coordination sequence Gal.6.618.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314048 (program): Coordination sequence Gal.6.618.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314049 (program): Coordination sequence Gal.3.51.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314051 (program): Coordination sequence Gal.5.308.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314052 (program): Coordination sequence Gal.6.639.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314056 (program): Coordination sequence Gal.4.135.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314057 (program): Coordination sequence Gal.6.635.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314060 (program): Coordination sequence Gal.6.636.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314067 (program): Coordination sequence Gal.3.53.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314085 (program): Coordination sequence Gal.6.132.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314086 (program): Coordination sequence Gal.6.232.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314087 (program): Coordination sequence Gal.5.67.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314088 (program): Coordination sequence Gal.5.111.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314090 (program): Coordination sequence Gal.4.54.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314091 (program): Coordination sequence Gal.6.153.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314093 (program): Coordination sequence Gal.5.137.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314094 (program): Coordination sequence Gal.6.345.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314095 (program): Coordination sequence Gal.6.204.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314096 (program): Coordination sequence Gal.4.73.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314097 (program): Coordination sequence Gal.6.354.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314098 (program): Coordination sequence Gal.6.339.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314099 (program): Coordination sequence Gal.5.131.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314100 (program): Coordination sequence Gal.6.329.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314106 (program): Coordination sequence Gal.6.199.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314108 (program): Coordination sequence Gal.6.198.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314109 (program): Coordination sequence Gal.6.204.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314110 (program): Coordination sequence Gal.6.200.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314111 (program): Coordination sequence Gal.5.289.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314112 (program): Coordination sequence Gal.4.134.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314117 (program): Coordination sequence Gal.6.330.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314120 (program): Coordination sequence Gal.3.55.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314124 (program): Coordination sequence Gal.6.619.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314127 (program): Coordination sequence Gal.6.326.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314133 (program): Coordination sequence Gal.6.623.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314134 (program): Coordination sequence Gal.6.624.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314135 (program): Coordination sequence Gal.6.489.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314140 (program): Coordination sequence Gal.6.633.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314141 (program): Coordination sequence Gal.5.290.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314142 (program): Coordination sequence Gal.6.636.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314144 (program): Coordination sequence Gal.6.634.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314145 (program): Coordination sequence Gal.4.145.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314148 (program): Coordination sequence Gal.4.139.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314149 (program): Coordination sequence Gal.6.620.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314151 (program): Coordination sequence Gal.6.621.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314156 (program): Coordination sequence Gal.6.651.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314157 (program): Coordination sequence Gal.6.623.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314159 (program): Coordination sequence Gal.6.624.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314161 (program): Coordination sequence Gal.4.140.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314163 (program): Coordination sequence Gal.5.301.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314164 (program): Coordination sequence Gal.5.302.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314165 (program): Coordination sequence Gal.5.307.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314167 (program): Coordination sequence Gal.6.638.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314186 (program): Coordination sequence Gal.6.330.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314189 (program): Coordination sequence Gal.6.636.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314191 (program): Coordination sequence Gal.5.292.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314192 (program): Coordination sequence Gal.6.651.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314193 (program): Coordination sequence Gal.4.141.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314194 (program): Coordination sequence Gal.6.625.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314205 (program): Coordination sequence Gal.5.133.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314208 (program): Coordination sequence Gal.6.619.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314209 (program): Coordination sequence Gal.5.293.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314210 (program): Coordination sequence Gal.6.623.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314211 (program): Coordination sequence Gal.6.650.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314216 (program): Coordination sequence Gal.6.624.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314218 (program): Coordination sequence Gal.5.304.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314220 (program): Coordination sequence Gal.5.306.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314221 (program): Coordination sequence Gal.6.641.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314222 (program): Coordination sequence Gal.6.643.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314225 (program): Coordination sequence Gal.5.316.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314231 (program): Coordination sequence Gal.5.305.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314234 (program): Coordination sequence Gal.6.332.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314236 (program): Coordination sequence Gal.6.626.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314239 (program): Coordination sequence Gal.6.642.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314240 (program): Coordination sequence Gal.6.643.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314244 (program): Coordination sequence Gal.6.644.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314247 (program): Coordination sequence Gal.3.50.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314249 (program): Coordination sequence Gal.4.136.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314250 (program): Coordination sequence Gal.4.137.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314251 (program): Coordination sequence Gal.5.294.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314252 (program): Coordination sequence Gal.5.295.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314253 (program): Coordination sequence Gal.6.627.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314254 (program): Coordination sequence Gal.6.628.1 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314283 (program): Coordination sequence Gal.5.318.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314668 (program): Coordination sequence Gal.6.115.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314669 (program): Coordination sequence Gal.6.216.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314670 (program): Coordination sequence Gal.5.50.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314671 (program): Coordination sequence Gal.5.95.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314672 (program): Coordination sequence Gal.4.38.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314674 (program): Coordination sequence Gal.4.58.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314677 (program): Coordination sequence Gal.3.10.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314680 (program): Coordination sequence Gal.6.149.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314683 (program): Coordination sequence Gal.6.130.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314684 (program): Coordination sequence Gal.6.149.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314685 (program): Coordination sequence Gal.3.16.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314688 (program): Coordination sequence Gal.6.254.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314689 (program): Coordination sequence Gal.6.255.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314692 (program): Coordination sequence Gal.5.81.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314706 (program): Coordination sequence Gal.6.130.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314707 (program): Coordination sequence Gal.6.129.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314708 (program): Coordination sequence Gal.5.65.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314710 (program): Coordination sequence Gal.5.64.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314712 (program): Coordination sequence Gal.6.150.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314720 (program): Coordination sequence Gal.6.245.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314725 (program): Coordination sequence Gal.5.114.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314726 (program): Coordination sequence Gal.6.259.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314736 (program): Coordination sequence Gal.5.115.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314752 (program): Coordination sequence Gal.6.258.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314753 (program): Coordination sequence Gal.4.52.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314754 (program): Coordination sequence Gal.5.82.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314758 (program): Coordination sequence Gal.6.193.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314765 (program): Coordination sequence Gal.6.194.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314776 (program): Coordination sequence Gal.6.478.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314825 (program): Coordination sequence Gal.6.118.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314826 (program): Coordination sequence Gal.6.129.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314827 (program): Coordination sequence Gal.5.53.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314828 (program): Coordination sequence Gal.5.64.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314829 (program): Coordination sequence Gal.4.41.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314830 (program): Coordination sequence Gal.6.150.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314832 (program): Coordination sequence Gal.6.245.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314836 (program): Coordination sequence Gal.6.131.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314837 (program): Coordination sequence Gal.6.231.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314838 (program): Coordination sequence Gal.4.52.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314840 (program): Coordination sequence Gal.5.66.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314841 (program): Coordination sequence Gal.6.151.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314847 (program): Coordination sequence Gal.6.193.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314848 (program): Coordination sequence Gal.5.110.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314849 (program): Coordination sequence Gal.6.246.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314884 (program): Coordination sequence Gal.6.150.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314885 (program): Coordination sequence Gal.6.245.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314886 (program): Coordination sequence Gal.5.114.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314890 (program): Coordination sequence Gal.6.152.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314893 (program): Coordination sequence Gal.6.259.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314894 (program): Coordination sequence Gal.6.194.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314896 (program): Coordination sequence Gal.4.53.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314898 (program): Coordination sequence Gal.5.136.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314899 (program): Coordination sequence Gal.6.153.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314902 (program): Coordination sequence Gal.6.322.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314903 (program): Coordination sequence Gal.6.339.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314915 (program): Coordination sequence Gal.6.248.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314941 (program): Coordination sequence Gal.3.41.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314943 (program): Coordination sequence Gal.6.321.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314945 (program): Coordination sequence Gal.5.84.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314947 (program): Coordination sequence Gal.6.198.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314953 (program): Coordination sequence Gal.6.202.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314954 (program): Coordination sequence Gal.4.77.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314955 (program): Coordination sequence Gal.6.322.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314959 (program): Coordination sequence Gal.6.340.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314961 (program): Coordination sequence Gal.5.137.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314964 (program): Coordination sequence Gal.6.200.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314969 (program): Coordination sequence Gal.4.78.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314971 (program): Coordination sequence Gal.5.138.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314972 (program): Coordination sequence Gal.5.139.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314973 (program): Coordination sequence Gal.6.342.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A314974 (program): Coordination sequence Gal.6.343.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315018 (program): Coordination sequence Gal.6.193.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315019 (program): Coordination sequence Gal.6.320.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315020 (program): Coordination sequence Gal.4.76.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315024 (program): Coordination sequence Gal.6.196.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315026 (program): Coordination sequence Gal.6.337.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315030 (program): Coordination sequence Gal.6.344.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315032 (program): Coordination sequence Gal.4.72.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315033 (program): Coordination sequence Gal.5.129.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315034 (program): Coordination sequence Gal.6.323.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315036 (program): Coordination sequence Gal.4.122.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315050 (program): Coordination sequence Gal.5.140.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315052 (program): Coordination sequence Gal.6.338.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315053 (program): Coordination sequence Gal.6.345.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315056 (program): Coordination sequence Gal.6.348.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315057 (program): Coordination sequence Gal.4.57.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315058 (program): Coordination sequence Gal.6.339.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315060 (program): Coordination sequence Gal.5.141.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315061 (program): Coordination sequence Gal.5.130.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315062 (program): Coordination sequence Gal.6.324.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315064 (program): Coordination sequence Gal.6.347.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315068 (program): Coordination sequence Gal.5.131.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315069 (program): Coordination sequence Gal.6.325.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315075 (program): Coordination sequence Gal.6.350.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315170 (program): Coordination sequence Gal.6.119.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315171 (program): Coordination sequence Gal.6.220.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315172 (program): Coordination sequence Gal.5.54.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315173 (program): Coordination sequence Gal.5.99.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315175 (program): Coordination sequence Gal.4.42.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315177 (program): Coordination sequence Gal.6.255.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315178 (program): Coordination sequence Gal.4.62.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315182 (program): Coordination sequence Gal.6.155.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315183 (program): Coordination sequence Gal.6.201.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315185 (program): Coordination sequence Gal.5.115.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315186 (program): Coordination sequence Gal.6.263.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315187 (program): Coordination sequence Gal.3.14.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315188 (program): Coordination sequence Gal.6.265.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315191 (program): Coordination sequence Gal.5.186.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315196 (program): Coordination sequence Gal.6.202.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315198 (program): Coordination sequence Gal.5.86.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315202 (program): Coordination sequence Gal.6.194.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315203 (program): Coordination sequence Gal.6.321.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315204 (program): Coordination sequence Gal.4.77.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315207 (program): Coordination sequence Gal.5.140.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315208 (program): Coordination sequence Gal.6.348.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315210 (program): Coordination sequence Gal.6.327.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315211 (program): Coordination sequence Gal.3.20.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315212 (program): Coordination sequence Gal.6.351.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315214 (program): Coordination sequence Gal.5.142.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315215 (program): Coordination sequence Gal.6.352.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315216 (program): Coordination sequence Gal.6.353.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315237 (program): Coordination sequence Gal.4.128.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315245 (program): Coordination sequence Gal.6.250.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315247 (program): Coordination sequence Gal.5.87.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315256 (program): Coordination sequence Gal.5.111.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315257 (program): Coordination sequence Gal.4.100.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315259 (program): Coordination sequence Gal.4.54.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315260 (program): Coordination sequence Gal.6.340.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315261 (program): Coordination sequence Gal.6.204.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315264 (program): Coordination sequence Gal.6.328.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315265 (program): Coordination sequence Gal.5.132.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315270 (program): Coordination sequence Gal.5.137.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315271 (program): Coordination sequence Gal.6.345.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315272 (program): Coordination sequence Gal.6.351.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315273 (program): Coordination sequence Gal.4.73.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315274 (program): Coordination sequence Gal.6.354.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315275 (program): Coordination sequence Gal.6.329.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315277 (program): Coordination sequence Gal.6.330.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315302 (program): Coordination sequence Gal.6.152.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315303 (program): Coordination sequence Gal.6.247.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315304 (program): Coordination sequence Gal.5.84.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315305 (program): Coordination sequence Gal.6.338.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315306 (program): Coordination sequence Gal.5.130.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315307 (program): Coordination sequence Gal.6.616.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315308 (program): Coordination sequence Gal.5.299.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315309 (program): Coordination sequence Gal.4.133.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315310 (program): Coordination sequence Gal.6.618.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315311 (program): Coordination sequence Gal.3.51.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315312 (program): Coordination sequence Gal.6.639.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315315 (program): Coordination sequence Gal.6.198.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315316 (program): Coordination sequence Gal.6.324.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315318 (program): Coordination sequence Gal.6.622.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315319 (program): Coordination sequence Gal.5.289.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315320 (program): Coordination sequence Gal.4.135.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315321 (program): Coordination sequence Gal.6.635.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315322 (program): Coordination sequence Gal.6.636.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315326 (program): Coordination sequence Gal.6.204.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315327 (program): Coordination sequence Gal.6.329.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315329 (program): Coordination sequence Gal.6.635.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315333 (program): Coordination sequence Gal.5.292.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315334 (program): Coordination sequence Gal.6.623.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315335 (program): Coordination sequence Gal.6.624.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315339 (program): Coordination sequence Gal.4.141.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315340 (program): Coordination sequence Gal.6.625.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315342 (program): Coordination sequence Gal.5.303.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315343 (program): Coordination sequence Gal.5.304.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315344 (program): Coordination sequence Gal.6.640.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315345 (program): Coordination sequence Gal.6.641.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315361 (program): Coordination sequence Gal.5.328.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315395 (program): Coordination sequence Gal.6.120.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315396 (program): Coordination sequence Gal.6.221.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315397 (program): Coordination sequence Gal.5.55.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315398 (program): Coordination sequence Gal.5.100.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315399 (program): Coordination sequence Gal.4.43.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315401 (program): Coordination sequence Gal.4.63.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315405 (program): Coordination sequence Gal.3.15.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315406 (program): Coordination sequence Gal.6.206.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315410 (program): Coordination sequence Gal.6.322.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315411 (program): Coordination sequence Gal.4.78.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315412 (program): Coordination sequence Gal.5.141.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315413 (program): Coordination sequence Gal.6.157.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315414 (program): Coordination sequence Gal.6.206.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315415 (program): Coordination sequence Gal.6.207.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315416 (program): Coordination sequence Gal.5.142.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315417 (program): Coordination sequence Gal.6.354.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315418 (program): Coordination sequence Gal.3.21.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315420 (program): Coordination sequence Gal.6.355.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315421 (program): Coordination sequence Gal.6.356.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315423 (program): Coordination sequence Gal.5.208.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315426 (program): Coordination sequence Gal.6.331.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315427 (program): Coordination sequence Gal.5.133.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315447 (program): Coordination sequence Gal.5.112.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315452 (program): Coordination sequence Gal.4.55.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315453 (program): Coordination sequence Gal.6.207.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315454 (program): Coordination sequence Gal.6.331.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315455 (program): Coordination sequence Gal.6.208.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315461 (program): Coordination sequence Gal.5.69.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315462 (program): Coordination sequence Gal.6.339.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315463 (program): Coordination sequence Gal.5.113.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315464 (program): Coordination sequence Gal.6.346.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315466 (program): Coordination sequence Gal.6.158.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315467 (program): Coordination sequence Gal.6.159.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315468 (program): Coordination sequence Gal.5.300.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315469 (program): Coordination sequence Gal.4.134.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315470 (program): Coordination sequence Gal.6.253.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315471 (program): Coordination sequence Gal.3.52.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315475 (program): Coordination sequence Gal.5.133.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315476 (program): Coordination sequence Gal.6.619.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315477 (program): Coordination sequence Gal.5.293.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315478 (program): Coordination sequence Gal.6.209.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315479 (program): Coordination sequence Gal.6.210.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315482 (program): Coordination sequence Gal.6.347.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315486 (program): Coordination sequence Gal.6.330.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315488 (program): Coordination sequence Gal.6.343.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315489 (program): Coordination sequence Gal.5.292.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315490 (program): Coordination sequence Gal.4.141.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315491 (program): Coordination sequence Gal.6.625.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315492 (program): Coordination sequence Gal.6.625.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315495 (program): Coordination sequence Gal.5.135.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315496 (program): Coordination sequence Gal.5.306.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315498 (program): Coordination sequence Gal.6.334.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315499 (program): Coordination sequence Gal.6.643.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315505 (program): Coordination sequence Gal.3.59.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315508 (program): Coordination sequence Gal.6.325.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315510 (program): Coordination sequence Gal.5.290.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315511 (program): Coordination sequence Gal.4.139.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315512 (program): Coordination sequence Gal.6.626.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315515 (program): Coordination sequence Gal.6.200.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315516 (program): Coordination sequence Gal.6.326.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315517 (program): Coordination sequence Gal.6.208.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315518 (program): Coordination sequence Gal.5.291.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315519 (program): Coordination sequence Gal.6.332.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315520 (program): Coordination sequence Gal.4.140.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315521 (program): Coordination sequence Gal.6.620.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315522 (program): Coordination sequence Gal.6.621.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315523 (program): Coordination sequence Gal.5.301.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315525 (program): Coordination sequence Gal.3.49.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315526 (program): Coordination sequence Gal.6.637.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315527 (program): Coordination sequence Gal.6.638.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315530 (program): Coordination sequence Gal.4.148.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315534 (program): Coordination sequence Gal.6.624.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315535 (program): Coordination sequence Gal.5.304.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315536 (program): Coordination sequence Gal.5.306.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315537 (program): Coordination sequence Gal.6.641.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315538 (program): Coordination sequence Gal.3.50.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315539 (program): Coordination sequence Gal.6.642.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315540 (program): Coordination sequence Gal.6.643.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315541 (program): Coordination sequence Gal.4.136.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315543 (program): Coordination sequence Gal.4.137.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315546 (program): Coordination sequence Gal.5.294.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315547 (program): Coordination sequence Gal.5.295.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315548 (program): Coordination sequence Gal.6.627.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315549 (program): Coordination sequence Gal.6.628.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315563 (program): Coordination sequence Gal.5.320.2 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315610 (program): Coordination sequence Gal.5.256.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315629 (program): Coordination sequence Gal.6.133.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315630 (program): Coordination sequence Gal.6.233.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315631 (program): Coordination sequence Gal.5.68.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315632 (program): Coordination sequence Gal.5.112.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315633 (program): Coordination sequence Gal.6.261.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315634 (program): Coordination sequence Gal.4.55.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315635 (program): Coordination sequence Gal.5.138.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315636 (program): Coordination sequence Gal.6.346.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315637 (program): Coordination sequence Gal.6.352.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315638 (program): Coordination sequence Gal.6.355.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315639 (program): Coordination sequence Gal.4.74.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315641 (program): Coordination sequence Gal.6.208.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315642 (program): Coordination sequence Gal.6.332.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315643 (program): Coordination sequence Gal.6.199.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315644 (program): Coordination sequence Gal.6.325.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315645 (program): Coordination sequence Gal.6.633.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315646 (program): Coordination sequence Gal.5.290.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315647 (program): Coordination sequence Gal.4.139.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315649 (program): Coordination sequence Gal.6.626.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315650 (program): Coordination sequence Gal.6.623.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315651 (program): Coordination sequence Gal.5.303.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315653 (program): Coordination sequence Gal.5.305.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315654 (program): Coordination sequence Gal.3.49.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315655 (program): Coordination sequence Gal.6.644.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315666 (program): Coordination sequence Gal.6.134.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315667 (program): Coordination sequence Gal.6.234.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315668 (program): Coordination sequence Gal.5.69.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315669 (program): Coordination sequence Gal.5.113.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315671 (program): Coordination sequence Gal.4.56.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315672 (program): Coordination sequence Gal.5.139.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315674 (program): Coordination sequence Gal.6.353.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315675 (program): Coordination sequence Gal.6.356.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315676 (program): Coordination sequence Gal.4.75.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315682 (program): Coordination sequence Gal.6.253.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315683 (program): Coordination sequence Gal.6.634.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315684 (program): Coordination sequence Gal.5.291.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315685 (program): Coordination sequence Gal.4.140.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315686 (program): Coordination sequence Gal.6.209.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315687 (program): Coordination sequence Gal.6.210.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315689 (program): Coordination sequence Gal.6.624.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315690 (program): Coordination sequence Gal.5.135.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315691 (program): Coordination sequence Gal.5.306.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315692 (program): Coordination sequence Gal.6.334.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315693 (program): Coordination sequence Gal.3.50.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315696 (program): Coordination sequence Gal.5.301.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315697 (program): Coordination sequence Gal.6.621.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315698 (program): Coordination sequence Gal.5.302.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315699 (program): Coordination sequence Gal.6.637.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315700 (program): Coordination sequence Gal.6.638.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315701 (program): Coordination sequence Gal.4.136.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315702 (program): Coordination sequence Gal.6.641.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315703 (program): Coordination sequence Gal.6.643.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315704 (program): Coordination sequence Gal.4.137.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315706 (program): Coordination sequence Gal.5.294.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315707 (program): Coordination sequence Gal.5.295.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315709 (program): Coordination sequence Gal.6.627.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315710 (program): Coordination sequence Gal.6.628.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315725 (program): Coordination sequence Gal.6.158.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315726 (program): Coordination sequence Gal.6.252.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315727 (program): Coordination sequence Gal.5.89.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315728 (program): Coordination sequence Gal.6.342.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315729 (program): Coordination sequence Gal.5.134.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315730 (program): Coordination sequence Gal.6.620.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315731 (program): Coordination sequence Gal.5.301.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315732 (program): Coordination sequence Gal.6.640.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315733 (program): Coordination sequence Gal.6.642.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315734 (program): Coordination sequence Gal.4.136.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315735 (program): Coordination sequence Gal.6.159.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315736 (program): Coordination sequence Gal.6.253.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315737 (program): Coordination sequence Gal.5.90.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315738 (program): Coordination sequence Gal.6.343.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315739 (program): Coordination sequence Gal.5.135.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315741 (program): Coordination sequence Gal.6.210.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315742 (program): Coordination sequence Gal.5.302.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315743 (program): Coordination sequence Gal.6.334.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315744 (program): Coordination sequence Gal.6.643.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315745 (program): Coordination sequence Gal.4.137.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315746 (program): Coordination sequence Gal.6.637.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315747 (program): Coordination sequence Gal.6.638.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315748 (program): Coordination sequence Gal.5.294.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315749 (program): Coordination sequence Gal.5.295.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315750 (program): Coordination sequence Gal.6.627.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315751 (program): Coordination sequence Gal.6.628.4 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315754 (program): Coordination sequence Gal.6.209.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315755 (program): Coordination sequence Gal.6.333.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315756 (program): Coordination sequence Gal.6.637.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315757 (program): Coordination sequence Gal.5.294.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315758 (program): Coordination sequence Gal.6.210.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315759 (program): Coordination sequence Gal.6.334.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315760 (program): Coordination sequence Gal.6.638.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315761 (program): Coordination sequence Gal.5.295.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315762 (program): Coordination sequence Gal.6.627.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315763 (program): Coordination sequence Gal.6.628.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315767 (program): Coordination sequence Gal.6.627.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315768 (program): Coordination sequence Gal.6.628.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315847 (program): Coordination sequence Gal.5.232.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315886 (program): Coordination sequence Gal.6.527.6 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315889 (program): Coordination sequence Gal.5.253.5 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315907 (program): Coordination sequence Gal.3.40.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A315943 (program): Coordination sequence Gal.5.229.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A316026 (program): Coordination sequence Gal.3.36.3 where G.u.t.v denotes the coordination sequence for a vertex of type v in tiling number t in the Galebach list of u-uniform tilings.
- A316087 (program): Expansion of 1/(1 + Sum_{k>=1} k^2 * x^k).
- A316131 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 1, negated.
- A316132 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+3) = 1, negated.
- A316133 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+3) = 1.
- A316134 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+3) = 1 (negated).
- A316135 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+3) = 1 (negated).
- A316136 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+3) = 1.
- A316137 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+4) = 1.
- A316138 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 1.
- A316139 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 1.
- A316140 (program): Denominator of the autosequence 2/((n+2)*(n+3)) difference table written by antidiagonals.
- A316161 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 2.
- A316162 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+2) = 2.
- A316163 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 2.
- A316164 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 2.
- A316165 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+3) = 2.
- A316166 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+3) = 2.
- A316167 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 2.
- A316168 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 2, negated.
- A316169 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+2) + 1/(x+4) = 2, negated.
- A316193 (program): Number of symmetric self-avoiding polygons on honeycomb net with perimeter 2*n, not counting rotations and reflections as distinct.
- A316224 (program): a(n) = n*(2*n + 1)*(4*n + 1).
- A316246 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+2) = 3.
- A316248 (program): Decimal expansion of the greatest x such that 1/x + 1/(x+1) + 1/(x+2) = 3.
- A316249 (program): Decimal expansion of the least x such that 1/x + 1/(x+1) + 1/(x+3) = 3.
- A316250 (program): Decimal expansion of the middle x such that 1/x + 1/(x+1) + 1/(x+3) = 3.
- A316252 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+3) = 3.
- A316253 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+3) = 3.
- A316255 (program): Decimal expansion of the least x such that 1/x + 1/(x+2) + 1/(x+4) = 3.
- A316256 (program): Decimal expansion of the middle x such that 1/x + 1/(x+2) + 1/(x+4) = 3.
- A316258 (program): Decimal expansion of the least x such that 1/x + 1/(x+3) + 1/(x+4) = 3 (negated).
- A316261 (program): The number of ways to induce a single pinch on a compact 2-manifold with n handles. (Note: The manifold is embedded in Euclidean 2-space, and each pinch partitions it into at most two submanifolds.)
- A316275 (program): Lucas analog to A101361.
- A316296 (program): a(n) = Sum_{k=1..n} f(k, n), where f(i, j) is the number of multiples of i greater than j and less than 2*j.
- A316297 (program): a(n) = n! times the denominator of the n-th harmonic number H(n).
- A316316 (program): Coordination sequence for tetravalent node in chamfered version of square grid.
- A316317 (program): Coordination sequence for trivalent node in chamfered version of square grid.
- A316319 (program): Coordination sequence for a trivalent node in a chamfered version of the 3^6 triangular tiling of the plane.
- A316320 (program): Coordination sequence for a hexavalent node in a chamfered version of the 3^6 triangular tiling of the plane.
- A316322 (program): Sum of piles of first n primes: a(n) = Sum(prime(i)*(2*i-1): 1<=i<=n).
- A316330 (program): a(n) = A000085(4*n)/2^n.
- A316331 (program): a(n) = A000085(4*n+1)/2^n.
- A316332 (program): a(n) = A000085(4*n+2)/2^(n+1).
- A316333 (program): a(n) = A000085(4*n+3)/2^(n+2).
- A316341 (program): Characteristic function of the factorials 1!, 2!, 3!, …
- A316342 (program): Fibonacci word A003849 with first two terms replaced by 2’s.
- A316344 (program): An example of a word that is uniform morphic, but neither pure morphic, primitive morphic, nor recurrent.
- A316352 (program): Decimal expansion of (BesselI(0,1/2)-BesselI(1,1/2))/(BesselI(0,1/2)-3*BesselI(1,1/2)).
- A316355 (program): 2k-1 appears 2k times after 2k-2 appears once.
- A316357 (program): Partial sums of A316316.
- A316358 (program): Partial sums of A316317.
- A316363 (program): O.g.f. A(x) satisfies: Sum_{n>=1} (x + (-1)^n*A(x))^n / n = 0.
- A316371 (program): G.f.: A(x) = Sum_{n>=0} binomial(3*(n+1), n)/(n+1) * x^n / (1+x)^(2*(n+1)).
- A316386 (program): Binomial transform of [0, 1, 2, -3, -4, 5, 6, -7, -8, …].
- A316457 (program): Expansion of x*(31 + 326*x + 336*x^2 + 26*x^3 + x^4) / (1 - x)^6.
- A316458 (program): Expansion of 60*x*(1 + 4*x + x^2) / (1 - x)^5.
- A316459 (program): Expansion of 30*x*(1 + x) / (1 - x)^4.
- A316466 (program): a(n) = 2*n*(7*n - 3).
- A316505 (program): a(n) is the smallest number k > 1 such that k^n - 1 is divisible by 3^n.
- A316523 (program): Number of odd multiplicities minus number of even multiplicities in the canonical prime factorization of n.
- A316528 (program): a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=1, a(1)=4, a(2)=10.
- A316533 (program): a(n) is the Sprague-Grundy value of the Node-Kayles game played on the generalized Petersen graph P(n,2).
- A316553 (program): Number of elements of order 2 in the group SL(2, Z(n)).
- A316562 (program): Koechel number for the works of W. A. Mozart rounded from age 11.
- A316568 (program): Largest k such that 1^2 + n, 2^2 + n, …, k^2 + n are composite.
- A316571 (program): a(1) = 1; for n > 1: a(n) = smallest number such that (Sum_{k=1..n} a(k)) is divisible by n - 1
- A316592 (program): a(n) equals the coefficient of x^n in Sum_{m>=0} (x^m + 2 + 1/x^m)^m for n >= 1.
- A316626 (program): a(1)=a(2)=a(3)=1; a(n) = a(n-2*a(n-1))+a(n-1-2*a(n-2)) for n > 3.
- A316627 (program): a(1)=2, a(2)=3; a(n) = a(n+1-a(n-1))+a(n-a(n-2)) for n > 2.
- A316631 (program): Expansion of A(x) = x*(1+3*x^2+x^3+3*x^4+x^6)/(1-x^4)^2.
- A316666 (program): Number of simple relaxed compacted binary trees of right height at most one with no sequences on level 1 and no final sequences on level 0.
- A316669 (program): Squares visited by queen moves on a diagonally numbered board and moving to the lowest available unvisited square at each step.
- A316671 (program): Squares visited by moving diagonally one square on a diagonally numbered board and moving to the lowest available unvisited square at each step.
- A316672 (program): Numbers k for which 120*k + 169 is a square.
- A316708 (program): Bisection of the odd-indexed Pell numbers A001653: part 1.
- A316709 (program): Bisection of the odd-indexed Pell numbers A001853: part 2.
- A316711 (program): Decimal expansion of s:= t/(t - 1), with the tribonacci constant t = A058265.
- A316724 (program): Generalized 26-gonal (or icosihexagonal) numbers: m*(12*m - 11) with m = 0, +1, -1, +2, -2, +3, -3, …
- A316725 (program): Generalized 27-gonal (or icosiheptagonal) numbers: m*(25*m - 23)/2 with m = 0, +1, -1, +2, -2, +3, -3, …
- A316726 (program): The number of ways to tile (with squares and rectangles) a 2 X (n+2) strip with the upper left and upper right squares removed.
- A316729 (program): Generalized 30-gonal (or triacontagonal) numbers: m*(14*m - 13) with m = 0, +1, -1, +2, -2, +3, -3, …
- A316742 (program): Stepping through the Mersenne sequence (A000225) one step back, two steps forward.
- A316777 (program): a(n) = Sum_{k=1..n} (k!)^5.
- A316779 (program): Expansion of 1 + (1/(1-x) + 1/(1-3*x))*x/2 + (1/(1-x) - 8/(1-2*x) + 9/(1-3*x))*x^5/2.
- A316824 (program): A second example of a word that is uniform morphic and recurrent, but neither pure morphic nor primitive morphic.
- A316825 (program): Fibonacci word A003849 with its initial term changed to 2.
- A316826 (program): Image of 3 under repeated application of the morphism 3 -> 3,2, 2 -> 1,0,2,0,1,2, 1 -> 1,0,1,2, 0 -> 0,2.
- A316828 (program): Image of the Thue-Morse sequence A010060 under the morphism {1 -> 1,2; 0 -> 0,2}.
- A316829 (program): Image of 0 under repeated application of the morphism 0 -> 0,1,0, 1 -> 1,1,1.
- A316831 (program): Trajectory of 0 under repeated application of the morphism 0 -> 01, 1 -> 21, 2 -> 13, 3 -> 33.
- A316832 (program): In A316831, replace 2’s and 3’s with 0’s.
- A316843 (program): Column 1 of table A316841.
- A316863 (program): Number of times 2 appears in the decimal expansion of n.
- A316864 (program): Number of times 3 appears in decimal expansion of n.
- A316865 (program): Number of times 4 appears in decimal expansion of n.
- A316866 (program): Number of times 5 appears in decimal expansion of n.
- A316867 (program): Number of times 6 appears in decimal expansion of n.
- A316868 (program): Number of times 7 appears in decimal expansion of n.
- A316869 (program): Number of times 8 appears in decimal expansion of n.
- A316936 (program): a(n) is the maximum state complexity of the language C(w) of conjugates of w, over all length-n binary strings w.
- A316937 (program): a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=3, a(1)=10, a(2)=26.
- A316964 (program): Same as A316669, except numbering of the squares starts at 0 rather than 1..
- A316966 (program): Same as A316671, except numbering of the squares starts at 0 rather than 1.
- A316987 (program): G.f.: A(x) = Sum_{n>=0} binomial(2*(n+1), n)/(n+1) * x^n / (1+x)^(3*(n+1)).
- A317016 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 7 * T(n-2,k-1) for k = 0..floor(n/2). T(n,k)=0 for n or k < 0.
- A317026 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 8 * T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
- A317050 (program): a(0) = 0 and for any n >= 0, a(n+1) is obtained by changing the rightmost possible digit in the negabinary representation of a(n) so as to get a value not yet in the sequence.
- A317051 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 9 * T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
- A317054 (program): Triangle read by rows: T(0,0) = 1; T(n,k) = T(n-1,k) + 10 * T(n-2,k-1) for k = 0..floor(n/2); T(n,k)=0 for n or k < 0.
- A317057 (program): a(n) is the number of time-dependent assembly trees satisfying the connected gluing rule for a cycle on n vertices.
- A317094 (program): a(n) = (n + 1)^2 + n!*L_n(-1), where L_n(x) is the Laguerre polynomial.
- A317095 (program): a(n) = 40*n.
- A317096 (program): Expansion of e.g.f. ((1 - x)/(1 - 2*x))*exp(x/(x - 1)).
- A317108 (program): Numbers missing from A317106.
- A317133 (program): G.f.: Sum_{n>=0} binomial(4*(n+1), n)/(n+1) * x^n / (1+x)^(n+1).
- A317134 (program): G.f.: Sum_{n>=0} binomial(4*(n+1), n)/(n+1) * x^n / (1+x)^(2*(n+1)).
- A317137 (program): a(n) is the number of nonzero triangular numbers <= n-th prime.
- A317163 (program): a(n) = 48277590120607451 + (n-1)*8440735245322380.
- A317164 (program): a(n) = 55837783597462913 + (n-1)*13858932213216090.
- A317186 (program): One of many square spiral sequences: a(n) = n^2 + n - floor((n-1)/2).
- A317189 (program): A morphic sequence related to the ternary Thue-Morse sequence.
- A317200 (program): G.f.: -x*(2*x^3+2*x^2+x-2)/(x^4-2*x+1).
- A317202 (program): Decimal expansion of 3 + (t^2+t^4)/2, where t = 0.543689… (A192918) is the real root of x^3+x^2+x=1.
- A317203 (program): Fixed under the morphism 1 -> 132, 2 -> 1, 3 -> 3, starting with 31.
- A317243 (program): a(n) is the number of open intervals (m, m+1) containing at least one fraction n/k, where m and k are integers between 1 and n.
- A317255 (program): a(n) = 149836681069944461 + (n-1)*1723457117682300.
- A317259 (program): a(n) = 136926916457315893 + (n - 1)*9843204333812850.
- A317276 (program): a(n) = Sum_{k=0..n} binomial(n-1,k-1)*binomial(2*k,k)*n!/(k + 1)!.
- A317277 (program): a(n) = Sum_{k=0..n} binomial(n-1,k-1)*k^n*n!/k!.
- A317278 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*k^n*n!/k!.
- A317279 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*n^k*n!/k!.
- A317297 (program): a(n) = (n - 1)*(4*n^2 - 8*n + 5).
- A317298 (program): a(n) = (1/2)*(1 + (-1)^n + 2*n + 4*n^2).
- A317300 (program): Sequence obtained by taking the general formula for generalized k-gonal numbers: m*((k - 2)*m - k + 4)/2, where m = 0, +1, -1, +2, -2, +3, -3, … and k >= 5. Here k = 0.
- A317301 (program): Sequence obtained by taking the general formula for generalized k-gonal numbers: m*((k - 2)*m - k + 4)/2, where m = 0, +1, -1, +2, -2, +3, -3, … and k >= 5. Here k = 1.
- A317302 (program): Square array T(n,k) = (n - 2)*(k - 1)*k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.
- A317303 (program): Numbers k such that both Dyck paths of the symmetric representation of sigma(k) have a central peak.
- A317304 (program): Numbers k with the property that both Dyck paths of the symmetric representation of sigma(k) have a central valley.
- A317311 (program): Multiples of 11 and odd numbers interleaved.
- A317312 (program): Multiples of 12 and odd numbers interleaved.
- A317313 (program): Multiples of 13 and odd numbers interleaved.
- A317314 (program): Multiples of 14 and odd numbers interleaved.
- A317315 (program): Multiples of 15 and odd numbers interleaved.
- A317316 (program): Multiples of 16 and odd numbers interleaved.
- A317317 (program): Multiples of 17 and odd numbers interleaved.
- A317318 (program): Multiples of 18 and odd numbers interleaved.
- A317319 (program): Multiples of 19 and odd numbers interleaved.
- A317320 (program): Multiples of 20 and odd numbers interleaved.
- A317321 (program): Multiples of 21 and odd numbers interleaved.
- A317322 (program): Multiples of 22 and odd numbers interleaved.
- A317323 (program): Multiples of 23 and odd numbers interleaved.
- A317324 (program): Multiples of 24 and odd numbers interleaved.
- A317325 (program): Multiples of 25 and odd numbers interleaved.
- A317326 (program): Multiples of 26 and odd numbers interleaved.
- A317331 (program): Indices m for which A058304(m) = 1.
- A317332 (program): Indices m for which A058304(m) = 8.
- A317333 (program): Indices m for which A058304(m) = 9.
- A317335 (program): a(n) = A317332(n) - 8*n.
- A317336 (program): a(n) = A317333(n) - 8*n.
- A317364 (program): Expansion of e.g.f. exp(2*x/(1 + x)).
- A317365 (program): Expansion of e.g.f. x*exp(x/(1 + x))/(1 + x).
- A317404 (program): a(n) = 3*n*(2^n - 1).
- A317405 (program): a(n) = n * A001353(n).
- A317408 (program): a(n) = n * Fibonacci(2n).
- A317440 (program): Numbers missing from A317438.
- A317451 (program): a(n) = (n*A003500(n) - A231896(n))/2.
- A317483 (program): Circuit rank of the n-Bruhat graph.
- A317487 (program): Number of 4-cycles in the n-Bruhat graph.
- A317498 (program): Triangle read by rows of coefficients in expansions of (-2 + 3x)^n, where n is nonnegative integer.
- A317499 (program): Coefficients in expansion of 1/(1 + 2*x - 3*x^3).
- A317509 (program): Coefficients in Expansion of 1/(1 + x - 2*x^5).
- A317510 (program): Numbers (4p+1)/3 where p is a Sophie Germain prime p > 3.
- A317512 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
- A317527 (program): Number of edges in the n-alternating group graph.
- A317528 (program): Expansion of Sum_{k>=1} mu(k)^2*x^k/(1 + x^k), where mu() is the Moebius function (A008683).
- A317529 (program): Expansion of Sum_{k>=1} x^(k^2)/(1 + x^(k^2)).
- A317538 (program): Indices m for which A317413(m) = 1.
- A317542 (program): Formal inverse of the period-doubling sequence A096268.
- A317543 (program): Positions of 1’s in A317542, the formal inverse of the period-doubling sequence A096268.
- A317551 (program): Fertility numbers.
- A317591 (program): Lexicographically earliest sequence of distinct terms such that erasing the last digit of a(n+1) and adding the resulting integer to a(n) gives back a(n+1).
- A317592 (program): Lexicographically first sequence of different terms such that erasing the last two digits of a(n+1) and adding this new reshaped integer to a(n) gives back a(n+1).
- A317594 (program): Lexicographically first sequence of different terms such that erasing the last three digits of a(n+1) and adding this new reshaped integer to a(n) gives back a(n+1).
- A317613 (program): Permutation of the nonnegative integers: lodumo_4 of A047247.
- A317614 (program): a(n) = (1/2)*(n^3 + n*(n mod 2)).
- A317618 (program): Expansion of e.g.f. sqrt((1 - x)/(1 - 3*x)).
- A317626 (program): Intersections with the x-axis of a bouncing ball on a Sophie Germain billiard table.
- A317633 (program): Numbers congruent to {1, 7, 9} mod 10.
- A317637 (program): a(n) = n*(n+1)*(n+3).
- A317657 (program): Numbers congruent to {15, 75, 95} mod 100.
- A317714 (program): Chessboard rectangles sequence (see Comments), also A037270 interleaved with A163102.
- A317729 (program): Number of nX4 0..1 arrays with every element unequal to 1, 2, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
- A317735 (program): Number of nX2 0..1 arrays with every element unequal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A317759 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A317760 (program): Number of nX4 0..1 arrays with every element unequal to 0, 1 or 2 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A317783 (program): Number of equivalence classes of binary words of length n for the set of subwords {010, 101}.
- A317790 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*(n-5) + a(n-6) for n>5, a(0)=a(1)=1, a(2)=a(3)=7, a(4)=13, a(5)=19.
- A317809 (program): Number of nX2 0..1 arrays with every element unequal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A317849 (program): Number of states of the Finite State Automaton Gn accepting the language of maximal (or minimal) lexicographic representatives of elements in the positive braid monoid An.
- A317914 (program): a(n) = 142099325379199423 + (n-1)*3691994023167450.
- A317945 (program): Filter sequence constructed from the coefficients of the Stern polynomials B(d,t) collected for each divisor d of n. Restricted growth sequence transform of A317944.
- A317951 (program): An S-automatic sequence for the system S = (a*b*, {a,b}, a<b).
- A317952 (program): Trajectory of 1 under repeated application of the morphism 1->121, 2->232, 3->343, 4->414.
- A317960 (program): Trajectory of 12 under the morphism f: X -> XYX, where Y=1 if X contains an odd number of 1’s, otherwise Y = 2.
- A317961 (program): Trajectory of 10 under the morphism f: X -> XYX, where Y=1 if X contains an odd number of 1’s, otherwise Y = 0.
- A317973 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms -1, 2, 3, 6.
- A317974 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,1.
- A317975 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0, 1, 1, 0.
- A317976 (program): a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,0.
- A317980 (program): a(n) = Product_{i=1..n} floor(5*i/2).
- A317982 (program): Expansion of 14*x*(29 + 784*x + 1974*x^2 + 784*x^3 + 29*x^4) / (1 - x)^7.
- A317983 (program): Expansion of 420*x*(1 + x)*(1 + 10*x + x^2) / (1 - x)^6.
- A317984 (program): Expansion of 140*x*(1 + 4*x + x^2) / (1 - x)^5.
- A318010 (program): Number of nX2 0..1 arrays with every element unequal to 0, 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A318047 (program): a(n) = sum of values taken by all parking functions of length n.
- A318054 (program): a(n) = n*(n + 1)*(n^2 + n + 22)/24.
- A318059 (program): a(n) is the numerator of sigma(sigma(n))/n.
- A318060 (program): a(n) is the denominator of sigma(sigma(n))/n.
- A318062 (program): Number of nX2 0..1 arrays with every element unequal to 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A318111 (program): Number of maximal 1-intersecting families of 2-sets of [n] = {1,2,…,n}.
- A318159 (program): Figurate numbers based on the small stellated dodecahedron: a(n) = n*(21*n^2 - 33*n + 14)/2.
- A318162 (program): Number of compositions of 2n-1 into exactly 2n-1 nonnegative parts with largest part n.
- A318192 (program): a(n) = U_{n}(n)/(n+1) where U_{n}(x) is a Chebyshev polynomial of the second kind.
- A318197 (program): a(n) = 2^((n - 1)*(n + 2)/2)*3^(n*(n - 1))*n^n.
- A318215 (program): Expansion of e.g.f. exp(x/(1 + x)^2).
- A318223 (program): Expansion of e.g.f. exp(x/(1 + 2*x)).
- A318224 (program): a(n) = n! * [x^n] exp(x/(1 + n*x)).
- A318236 (program): a(n) = (3*2^(4*n+3) + 1)/5.
- A318249 (program): a(n) = (n - 1)! * d(n), where d(n) = number of divisors of n (A000005).
- A318250 (program): a(n) = (n - 1)! * sigma_2(n), where sigma_2(n) = sum of squares of divisors of n (A001157).
- A318274 (program): Triangle read by rows: T(n,k) = n for 0 < k < n and T(n,0) = T(n,n) = 1.
- A318304 (program): a(n) = A083254(n)/A003557(n) = (2*A173557(n) - A007947(n)).
- A318305 (program): a(n) = product_{p} - product_{p-1}, where p are distinct primes dividing n; a(n) = A007947(n) - A173557(n).
- A318320 (program): a(n) = (psi(n) - phi(n))/2.
- A318338 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A318369 (program): Number of non-isomorphic set multipartitions (multisets of sets) of the multiset of prime indices of n.
- A318376 (program): a(n) = F(n+1)^3 - 3*F(n-1)*F(n)^2, where F(n) = A000045(n), the n-th Fibonacci number.
- A318397 (program): Triangle read by rows: T(n,k) = binomial(n,k)^2 * binomial(2*(n-k), n-k).
- A318417 (program): Scaled g.f. T(u) = Sum_{n>=0} a(n)*(3*u/48)^n satisfies 3*(2*u-1)*T + d/du(4*u*(2*u-1)*(u-1)*T’) = 0, and a(0)=1; sequence gives a(n).
- A318445 (program): a(n) = Sum_{d|n, d<n} A005187(d).
- A318446 (program): Inverse Möbius transform of A005187: a(n) = Sum_{d|n} A005187(d).
- A318454 (program): Denominators of the sequence whose Dirichlet convolution with itself yields A001227, number of odd divisors of n.
- A318455 (program): The 2-adic valuation of A318454(n).
- A318456 (program): a(n) = n OR A001065(n), where OR is bitwise-or (A003986) and A001065 = sum of proper divisors.
- A318457 (program): a(n) = n XOR A001065(n), where XOR is bitwise-xor (A003987) and A001065 = sum of proper divisors.
- A318458 (program): a(n) = n AND A001065(n), where AND is bitwise-and (A004198) & A001065 = sum of proper divisors.
- A318459 (program): a(n) = gcd(n, tau(n), phi(n)), where tau = A000005 and phi = A000010.
- A318467 (program): a(n) = 2*n XOR A000203(n), where XOR is bitwise-xor (A003987) and A000203 = sum of divisors.
- A318491 (program): a(n) is the numerator of Sum_{d|n} Sum_{j|d} 1/j.
- A318505 (program): Sum of divisors of n, up to, but not including the second largest of them A032742(n); a(1) = 0 by convention.
- A318516 (program): a(n) = A032742(n) OR n-A032742(n), where OR is bitwise-or (A003986) and A032742 = the largest proper divisor of n.
- A318517 (program): a(n) = A032742(n) XOR n-A032742(n), where XOR is bitwise-xor (A003987) and A032742 = the largest proper divisor of n.
- A318518 (program): a(n) = A032742(n) AND n-A032742(n), where AND is bitwise-and (A004198) and A032742 = the largest proper divisor of n.
- A318519 (program): a(n) = A000005(n) * A003557(n).
- A318522 (program): Decimal expansion of sqrt(28^(1/3)-27^(1/3)).
- A318591 (program): Number of n-member subsets of [3*n] whose elements sum to a multiple of three.
- A318605 (program): Decimal expansion of geometric progression constant for Coxeter’s Loxodromic Sequence of Tangent Circles.
- A318608 (program): Moebius function mu(n) defined for the Gaussian integers.
- A318609 (program): a(1) = 2, a(2) = 4, a(3) = 6; for n > 3, a(n) = 3*a(n-1) - 3*a(n-2) + 9*a(n-3).
- A318610 (program): a(1) = 0, a(2) = 4, a(3) = 12; for n > 3, a(n) = 3*a(n-1) - 3*a(n-2) + 9*a(n-3).
- A318614 (program): Scaled g.f. S(u) = Sum_{n>0} a(n)*16*(u/16)^n satisfies T(u) = d/du S(u), with T(u) as defined by A318417; sequence gives a(n).
- A318618 (program): a(n) is the number of rooted forests on n nodes that avoid the patterns 321, 2143, and 3142.
- A318623 (program): a(n) = 2^phi(n) mod n.
- A318624 (program): Number of 3-member subsets of [3*n] whose elements sum to a multiple of n.
- A318636 (program): G.f.: Sum_{n>=1} ( (1 + x^n)^n - 1 ).
- A318666 (program): a(n) = 2^{the 3-adic valuation of n}.
- A318702 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the real part of f(n).
- A318703 (program): For any n >= 0 with binary expansion Sum_{k=0..w} b_k * 2^k, let f(n) = Sum_{k=0..w} b_k * i^k * 2^floor(k/2) (where i denotes the imaginary unit); a(n) is the imaginary part of f(n).
- A318742 (program): a(n) = Sum_{k=1..n} floor(n/k)^3.
- A318743 (program): a(n) = Sum_{k=1..n} floor(n/k)^4.
- A318744 (program): a(n) = Sum_{k=1..n} floor(n/k)^5.
- A318750 (program): a(n) = Sum_{k=1..n} k * tau_3(k), where tau_3 is A007425.
- A318755 (program): a(n) = Sum_{k=1..n} tau(k)^3, where tau is A000005.
- A318765 (program): a(n) = (n + 2)*(n^2 + n - 1).
- A318774 (program): Coefficients in expansion of 1/(1 - x - 3*x^4).
- A318778 (program): Number of different positions that a elementary sphinx can occupy in a sphinx of order n.
- A318791 (program): Prime generating polynomial: a(n) = 9*n^2 - 249*n + 1763.
- A318827 (program): a(n) = n - gcd(n - 1, phi(n)).
- A318830 (program): a(n) = phi(n) - gcd(phi(n), n-1).
- A318833 (program): a(n) = n + A023900(n).
- A318841 (program): a(n) = n - A173557(n).
- A318874 (program): Number of divisors d of n for which 2*phi(d) > d.
- A318876 (program): Sum of divisors d of n for which 2*phi(d) > d.
- A318919 (program): Define b(0)=0, b(1)[1]=1, b(1)[2]=1; and for n>=2, b(n)[1] = total number of digits in b(n-1), and b(n)[2] = total number of digits in b(0),…,b(n-1); a(n) = b(n)[2].
- A318930 (program): RUNS transform of A279620.
- A318934 (program): Numbers whose binary expansion begins with exactly two 1’s.
- A318935 (program): a(n) = Sum_{2^m divides n} 2^(3*m).
- A318937 (program): a(n) = 16 times the sum of the cubes of the divisors of 2*n+1.
- A318941 (program): Number of Dyck paths with n nodes and altitude 2.
- A318946 (program): Column 1 of triangle A318945.
- A318960 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(-7). This is the 1 (mod 4) case.
- A318961 (program): One of the two successive approximations up to 2^n for 2-adic integer sqrt(-7). This is the 3 (mod 4) case.
- A318972 (program): The 7x+-1 function (“shortcut” definition): a(n) = (7n+1)/4 if n == +1 (mod 4), a(n) = (7n-1)/4 if n == -1 (mod 4), otherwise a(n) = n/2.
- A319006 (program): Sum of the next n positive integers repeated (A008619).
- A319007 (program): Sum of the next n nonnegative integers repeated (A004526).
- A319013 (program): a(n) is the sum over each permutation of S_n of the least element of the descent set.
- A319014 (program): a(n) = 1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + … + (up to n).
- A319028 (program): Number of permutations pi of [n] such that s(pi) avoids the patterns 132 and 321, where s is West’s stack-sorting map.
- A319034 (program): Decimal expansion of the height that minimizes the total surface area of the four triangular faces of a square pyramid of unit volume.
- A319054 (program): Maximum product of an aperiodic integer partition of n.
- A319074 (program): a(n) is the sum of the first n nonnegative powers of the n-th prime.
- A319085 (program): a(n) = Sum_{k=1..n} k^2*tau(k), where tau is A000005.
- A319086 (program): a(n) = Sum_{k=1..n} k^2*sigma(k), where sigma is A000203.
- A319087 (program): a(n) = Sum_{k=1..n} k^2*phi(k), where phi is the Euler totient function A000010.
- A319089 (program): a(n) = tau(n)^3, where tau is A000005.
- A319100 (program): Number of solutions to x^6 == 1 (mod n).
- A319102 (program): Triangle read by rows: The k-th column has alternating blocks of k 1’s followed by k 0’s (see example).
- A319116 (program): Signs of the Maclaurin coefficients of 1/(exp(x) + Pi/2).
- A319117 (program): Sign of the n-th Maclaurin coefficient of 1/(exp(x) + exp(1)/2).
- A319127 (program): Crossing number of the complete bipartite graph K_{6,n}.
- A319128 (program): Interleave n*(3*n - 2), 3*n^2 + n - 1, n=0,0,1,1, … .
- A319132 (program): a(n) = Sum_{d|n} Sum_{j|d} mu(j)^2*j, where mu = Möbius function (A008683).
- A319158 (program): Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be selected, such that any equilateral triangle of points will include at least one of the selection, if the triangle has the same orientation as the grid.
- A319159 (program): Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be selected, such that any equilateral triangle of points will include at least one of the selection.
- A319170 (program): Triangular numbers of the form 2..21..1; n_times 2 followed with n_times 1; n >= 1.
- A319172 (program): a(n) = 2*(a(n-1) + a(n-3)) - a(n-4), with a(0) = 1, a(1) = 2, a(2) = 5 and a(3) = 12.
- A319187 (program): Number of pairwise coprime subsets of {1,…,n} of maximum cardinality (A036234).
- A319194 (program): a(n) = Sum_{k=1..n} sigma(n,k).
- A319196 (program): a(n) = 2^(n-1)*Fibonacci(n-3), n >= 0.
- A319200 (program): a(n) = -(A(n) - A(n-1)) where A(n) = A057597(n+1), for n >= 0.
- A319201 (program): Expansion of f(t) = F^{[-1]}(t)/t, where F(x) = x/(1 - x^2 - x^3).
- A319204 (program): Sequence used for the Boas-Buck type recurrence for Riordan triangle A319203.
- A319210 (program): a(n) = phi(n^2 - 1)/2 where phi is A000010.
- A319258 (program): a(n) = 1 + 2*3 + 4 + 5*6 + 7 + 8*9 + 10 + 11*12 + … + (up to n).
- A319279 (program): Numbers that are congruent to {0, 3, 7, 10} mod 12.
- A319280 (program): Numbers that are congruent to {0, 4, 7, 11} mod 12.
- A319288 (program): a(n) is the smallest k such that A319284(n, k) >= A319284(n, j) for all 0 <= j <= n.
- A319371 (program): Numbers k such that the characteristic polynomial of a wheel graph of k nodes has exactly one monomial with vanishing coefficient.
- A319384 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), a(0)=1, a(1)=5, a(2)=9, a(3)=21, a(4)=29.
- A319390 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5), a(0)=1, a(1)=2, a(2)=3, a(3)=6, a(4)=8.
- A319392 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*k!*n^k.
- A319410 (program): Twice A032741.
- A319432 (program): The first differences (A129761) of the tribonacci representation numbers (A003714 or A014417) consists of runs of 1’s separated by the terms of the present sequence.
- A319433 (program): Take Zeckendorf representation of n (A014417(n)), drop least significant bit, take inverse Zeckendorf representation.
- A319443 (program): Number of distinct Eisenstein primes in the factorization of n.
- A319445 (program): Number of Eisenstein integers in a reduced system modulo n.
- A319448 (program): Moebius function mu(n) defined for the Eisenstein integers.
- A319451 (program): Numbers that are congruent to {0, 3, 6} mod 12; a(n) = 3*floor(4*n/3).
- A319452 (program): Numbers that are congruent to {0, 3, 6, 10} mod 12.
- A319497 (program): a(0)=0, a(3*n)=9*a(n), a(3*n+1)=9*a(n)+1, a(3*n+2)=9*a(n)+3.
- A319512 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3), a(0) = 1, a(1) = 3, a(2) = 11.
- A319516 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+2,n) = gcd(x+6,n) = gcd(x+8,n) = 1.
- A319526 (program): Square array read by antidiagonals upwards: T(n,k) = sigma(n*k), n >= 1, k >= 1.
- A319527 (program): a(n) = 7 * sigma(n).
- A319528 (program): a(n) = 8 * sigma(n).
- A319534 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+2,n) = gcd(x+6,n) = 1.
- A319536 (program): Number of signed permutations of length n where numbers occur in consecutive order.
- A319556 (program): a(n) gives the alternating sum of length n, starting at n: n - (n+1) + (n+2) - … + (-1)^(n+1) * (2n-1).
- A319572 (program): The x coordinates of the stripe enumeration of N X N where N = {0, 1, 2, …}.
- A319573 (program): The y coordinates of the stripe enumeration of N X N where N = {0, 1, 2, …}.
- A319575 (program): a(n) = (2/3)*n*(n^3 - 6*n^2 + 11*n - 3).
- A319576 (program): a(n) = (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9).
- A319577 (program): a(n) = (4/45)*n*(n - 2)*(n - 1)*(n^3 - 12*n^2 + 47*n - 15).
- A319578 (program): a(n) = (1/3)*(n+2)^2*(3*n+3)!/(n+2)!^3.
- A319588 (program): First of three consecutive triangular numbers that add up to a perfect square.
- A319597 (program): Number of conjugacy classes for a non-abelian group of order p^3, where p is prime: a(n) = p^2 + p - 1 where p = prime(n).
- A319603 (program): a(n) = n^3 + reversal of digits of n^3.
- A319610 (program): a(n) is the minimal number of successive OFF cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell.
- A319611 (program): a(n) is the number of gaps in the n-th generation of the rule-30 1D cellular automaton started from a single ON.
- A319613 (program): a(n) = prime(n) * prime(2n).
- A319622 (program): Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of (not necessarily distinct) sets.
- A319625 (program): Number of non-isomorphic connected weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.
- A319626 (program): Primorial deflation of n (numerator): Let f be the completely multiplicative function over the positive rational numbers defined by f(p) = A034386(p) for any prime number p; f constitutes a permutation of the positive rational numbers; let g be the inverse of f; for any n > 0, a(n) is the numerator of g(n).
- A319627 (program): Let f be the completely multiplicative function over the positive rational numbers defined by f(p) = A034386(p) for any prime number p; f constitutes a permutation of the positive rational numbers; let g be the inverse of f; for any n > 0, a(n) is the denominator of g(n).
- A319635 (program): Number of non-isomorphic weight-n antichains of distinct multisets whose dual is also an antichain of (not necessarily distinct) multisets.
- A319636 (program): a(n) = Sum_{k=1..n} binomial(2*n - 3*k + 1, n - k)*k/(n - k + 1).
- A319638 (program): Number of non-isomorphic weight-n antichains of distinct sets whose dual is also an antichain of distinct sets.
- A319642 (program): Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of (not necessarily distinct) multisets.
- A319645 (program): Number of non-isomorphic weight-n antichains of distinct multisets whose dual is a chain of distinct multisets.
- A319650 (program): a(n) = A073138(n) - n.
- A319654 (program): Write n in 6-ary, sort digits into increasing order.
- A319658 (program): a(n) is the minimal number of successive ON cells that appears in n-th generation of rule-30 1D cellular automaton started from a single ON cell.
- A319667 (program): Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).
- A319674 (program): a(n) = 1 + 2 + 3 - 4 - 5 - 6 + 7 + 8 + 9 - 10 - 11 - 12 + … - (up to n).
- A319676 (program): Numerator of A047994(n)/n where A047994 is the unitary totient function.
- A319677 (program): Denominator of A047994(n)/n where A047994 is the unitary totient function.
- A319690 (program): Fully multiplicative with a(p^e) = (p mod 3)^e.
- A319691 (program): a(n) = 1 if n is either 1 or divisible only by primes congruent to 1 mod 3, 0 otherwise.
- A319697 (program): Sum of even squarefree divisors of n.
- A319701 (program): Filter sequence for sequences that are constant for all odd terms >= 3.
- A319702 (program): Filter sequence for sequences that are constant for all even terms >= 2.
- A319710 (program): a(n) = 1 if n is divisible by the square of its smallest prime factor, 0 otherwise.
- A319723 (program): Write n in 6-ary, sort digits into decreasing order.
- A319743 (program): Row sums of A174158.
- A319762 (program): Number of non-isomorphic intersecting set multipartitions (multisets of sets) of weight n with empty intersection.
- A319764 (program): Number of non-isomorphic intersecting set systems of weight n with empty intersection.
- A319785 (program): a(n) = A073138(n) + A038573(n).
- A319795 (program): a(n) = n^(n+1)/(n-1)^n for n>1, rounded to nearest integer.
- A319806 (program): a(n) = A319723(n) + A319654(n).
- A319840 (program): Table read by antidiagonals: T(n, k) is the number of elements on the perimeter of an n X k matrix.
- A319842 (program): a(n) = 8 * A104720(n) + ceiling(n/2).
- A319852 (program): Difference between 3^n and the product of primes less than or equal to n.
- A319857 (program): Difference between 4^n and the product of primes less than or equal to n.
- A319861 (program): Triangle read by rows, 0 <= k <= n: T(n,k) is the numerator of the k-th Bernstein basis polynomial of degree n evaluated at the interval midpoint t = 1/2; denominator is A319862.
- A319862 (program): Triangle read by rows, 0 <= k <= n: T(n,k) is the denominator of the k-th Bernstein basis polynomial of degree n evaluated at the interval midpoint t = 1/2; numerator is A319861.
- A319866 (program): a(n) = 2*1 + 4*3 + 6*5 + 8*7 + 10*9 + 12*11 + … + (up to the n-th term).
- A319879 (program): a(n) = minimal number m of unit squares needed to make an figure formed from squares (joined edge to edge) which has n holes.
- A319880 (program): Difference between 2^n and the product of primes less than or equal to n.
- A319895 (program): a(n) is the number of partitions of n into consecutive parts, plus the total number of parts in those partitions.
- A319905 (program): Decimal expansion of 4*(sqrt(2) - 1)/3.
- A319924 (program): a(n) = A143565(2n,n) for n > 0, a(0) = 1.
- A319930 (program): a(n) = (1/24)*n*(n - 1)*(n - 3)*(n - 14).
- A319948 (program): a(n) = Product_{i=1..n} floor(3*i/2).
- A319949 (program): a(n) = Product_{i=1..n} floor(4*i/3).
- A319950 (program): a(n) = Product_{i=1..n} floor(5*i/3).
- A319952 (program): Let M = A022342(n) be the n-th number whose Zeckendorf representation is even; then a(n) = A129761(M).
- A319953 (program): List of binary words of lengths 0, 1, 2, etc., including empty word, each prefixed by a 2.
- A319956 (program): Image of 3 under repeated application of the morphism 1 -> 1, 2 -> 22, 3 -> 312.
- A319988 (program): a(n) = 1 if n is divisible by the square of its largest prime factor, 0 otherwise.
- A319993 (program): a(n) = A319997(n) / A173557(n).
- A319995 (program): Number of divisors of n of the form 6*k + 5.
- A319997 (program): a(n) = Sum_{d|n, d is odd} mu(n/d)*d, where mu(n) is Moebius function A008683.
- A319998 (program): a(n) = Sum_{d|n, d is even} mu(n/d)*d, where mu(n) is Moebius function A008683.
- A320006 (program): a(n) = 1 if n encodes a nonnegative combinatorial game (in a style of A106486), otherwise 0; Characteristic function of A126001.
- A320007 (program): If there is k >= 0 such that floor(n/4^k) is odd and A320006(k) is 1, then a(n) = 1, otherwise a(n) = 0.
- A320008 (program): a(0) = 1; for n > 0, a(n) = A000120(n) * a(n-A000120(n)), where A000120(n) is the binary weight of n.
- A320016 (program): a(1) = a(2) = 1; for n > 2, a(n) = A000005(n) * a(A000005(n)), where A000005(n) gives the number of divisors of n.
- A320029 (program): Decimal expansion of sqrt(9 + sqrt(9 + sqrt(9 + sqrt(9 + …)))) = (sqrt(37) + 1)/2.
- A320042 (program): a(n) = a(floor(n/2)) + (-1)^(n*(n+1)/2) with a(1)=0.
- A320047 (program): Consider coefficients U(m,l,k) defined by the identity Sum_{k=1..l} Sum_{j=0..m} A302971(m,j)/A304042(m,j) * k^j * (T-k)^j = Sum_{k=0..m} (-1)^(m-k) * U(m,l,k) * T^k that holds for all positive integers l,m,T. This sequence gives 2-column table read by rows, where n-th row lists coefficients U(1,n,k) for k = 0, 1 and n >= 1.
- A320053 (program): Number of spanning sum-product knapsack partitions of n. Number of integer partitions y of n such that every sum of products of the parts of a multiset partition of y is distinct.
- A320059 (program): Sum of divisors of n^2 that do not divide n.
- A320064 (program): The number of F_2 graphs on { 1, 2, …, n } with a unique cycle of weight 1, which corresponds to the number of reflectable bases of the root system of type D_n.
- A320065 (program): a(n) is the smallest integer i such that binomial(2i,i) > n.
- A320106 (program): Möbius transform of A320107.
- A320111 (program): Number of divisors d of n that are not of the form 4k+2.
- A320156 (program): Decimal expansion of the unique real root of x^3 - 3*x^2 + 8*x - 16 = 0, or equivalently, the unique positive root of x^4*(x + 5) - 4^4 = 0.
- A320158 (program): Decimal expansion of real root of x^3 + 11x^2 + 27x - 27 = 0, x^2*(x + 5)^3 - 2^2*3^3 = 0.
- A320226 (program): Number of integer partitions of n whose non-1 parts are all equal.
- A320258 (program): a(n) = n! * [x^n] exp(x*exp(-n*x)).
- A320259 (program): Terms that are on the y-axis of the square spiral built with 2*k, 2*k+1, 2*k+1 for k >= 0.
- A320281 (program): Terms that are on the positive x-axis of the square spiral built with 2*k, 2*k+1, 2*k+1 for k >= 0.
- A320283 (program): Lexicographical ordering of pure imaginary integers in the base (-1+i) numeral system.
- A320326 (program): a(n) = Sum_{i=0..n} binomial(2*i-1,i)*binomial(2*i,n-i).
- A320327 (program): Triangle T(n,m) = C(2*n,m)*C(2*n-1,n), 0 <= m <= 2*n, n >= 0.
- A320366 (program): Number of nX3 0..1 arrays with every element unequal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
- A320394 (program): Number of ones in binary expansion n^5.
- A320427 (program): a(n) = floor(3*n/2) + ceiling(n/6) + 9.
- A320429 (program): The length of the shortest prefix of the Thue-Morse word decomposable to not less than n palindromes.
- A320431 (program): The number of tiles inside a regular n-gon created by lines that run from each of the vertices of the n edges orthogonal to these edges.
- A320440 (program): Row sums of A225043.
- A320453 (program): a(n) = (n^n + n*(-1)^n)/(n + 1).
- A320465 (program): a(n) = 2^n - (2^(n-1) mod n), where “mod” is the nonnegative remainder operator.
- A320468 (program): a(n) = a(n-1) + 20*a(n-2), n >= 2; a(0)=1, a(1)=41.
- A320469 (program): a(n) = 3*a(n-1) + 10*a(n-2), n >= 2; a(0)=1, a(1)=1.
- A320508 (program): T(n,k) = binomial(n - k - 1, k), 0 <= k < n, and T(n,n) = (-1)^n, triangle read by rows.
- A320519 (program): a(n) = 2*n^n*cos(n*arcsin(sqrt(4*n^2-1)/(2*n))) for n > 0 and a(0) = 2.
- A320522 (program): Numbers k such that k^10 divides 10^k.
- A320524 (program): Number of chiral pairs of a row of n colors using 6 or fewer colors.
- A320531 (program): T(n,k) = n*k^(n - 1), k > 0, with T(n,0) = A063524(n), square array read by antidiagonals upwards.
- A320534 (program): a(n) = ((1 + sqrt(4*n^2 + 1))^n + (1 - sqrt(4*n^2 + 1))^n)/2^n.
- A320565 (program): a(n) = ((1 + sqrt(4*n^2 + 1))^n - (1 - sqrt(4*n^2 + 1))^n)/(2^n * sqrt(4*n^2 + 1)).
- A320570 (program): a(n) = L_n(n), where L_n(x) is the Lucas polynomial.
- A320576 (program): a(n) gives the number of configurations of non-attacking rooks up to symmetry on an n X n chessboard such that the number of distinct distances between the rooks is given by A319476(n).
- A320577 (program): Number of isosceles triangles whose vertices are the vertices of a regular n-gon.
- A320581 (program): a(n) is the number of closed factors of length n in the Fibonacci word.
- A320592 (program): Number of partitions of n with four parts in which no part occurs more than twice.
- A320604 (program): Chromatic number of the n-polygon diagonal intersection graph.
- A320614 (program): Expansion of (1 + x^5) / ((1 - x^2) * (1 - x^3) * (1 - x^7)) in powers of x.
- A320615 (program): Number of ordered set partitions of [n] where k = two is minimal such that for each block b the smallest integer interval containing b has at most k elements.
- A320642 (program): Number of 1’s in the base-(-2) expansion of -n.
- A320661 (program): a(n) = 2^(n+3) - 6*n - 7.
- A320667 (program): First differences of A066194.
- A320674 (program): Positive integers m with binary expansion (b_1, …, b_k) (where k = A070939(m)) such that b_i = [m == 0 (mod prime(i))] for i = 1..k (where prime(i) denotes the i-th prime number and [] is an Iverson bracket).
- A320752 (program): Primes of the form 5*n^2 - 5*n + 13.
- A320770 (program): a(n) = (-1)^floor(n/4) * 2^floor(n/2).
- A320772 (program): Prime generating polynomial: a(n) = (4*n - 29)^2 + 58.
- A320829 (program): Continued fraction of the positive constant t in (1,2) such that the partial denominators form the Beatty sequence {floor((n+1)*t), n >= 0}.
- A320858 (program): a(n) = A320857(prime(n)).
- A320877 (program): a(n) = 1 + Sum_{k=1..n} 2^prime(k).
- A320889 (program): Number of set partitions of strict factorizations of n into factors > 1 such that all the blocks have the same product.
- A320895 (program): a(n) = Sum_{k=1..n} k^3 * tau(k), where tau is A000005.
- A320896 (program): a(n) = Sum_{k=1..n} k * tau(k)^2, where tau is A000005.
- A320897 (program): a(n) = Sum_{k=1..n} k^2 * tau(k)^2, where tau is A000005.
- A320916 (program): Consider A010060 as a 2-adic number …100110010110, then a(n) is its approximation up to 2^n.
- A320926 (program): Concatenation of successive segments generated by the morphism {0 -> {0, 0, 1}, 1 -> {0}}, starting with 0.
- A320927 (program): Concatenation of successive segments generated by the morphism {0 -> {0, 0, 1}, 1 -> {0,1,0}}, starting with 0.
- A320928 (program): Positions of 0 in A320927.
- A320929 (program): Positions of 1 in A320927.
- A320933 (program): a(n) = 2^n - floor((n+3)/2).
- A320934 (program): Number of chiral pairs of color patterns (set partitions) for a row of length n using 4 or fewer colors (subsets).
- A320941 (program): Expansion of Sum_{k>=1} x^k*(1 + x^k)/(1 - x^k)^4.
- A320947 (program): a(n) is the number of dominoes, among all domino tilings of the 2 X n rectangle, sharing a length-2 side with the boundary of the rectangle.
- A320986 (program): Fibonacci rabbit sequence number n coded in base four.
- A320987 (program): Fibonacci rabbit sequence number n coded in base five.
- A320988 (program): Fibonacci rabbit sequence number n coded in base six.
- A320989 (program): Fibonacci rabbit sequence number n coded in base seven.
- A320990 (program): Fibonacci rabbit sequence number n coded in base eight.
- A320991 (program): Fibonacci rabbit sequence number n coded in base nine.
- A320997 (program): An absolute lower bound on the number of components in perfect systems of difference sets (PSDS).
- A321002 (program): a(0)=3; thereafter a(n) = 20*6^(n-1)-2^(n-1).
- A321003 (program): a(n) = 2^n*(4*3^n-1).
- A321014 (program): Number of divisors of n which are greater than 3.
- A321017 (program): a(n) = floor(pi(n)/2).
- A321018 (program): a(n) = round(pi(n)/2).
- A321019 (program): Coordination sequence for 3-D tiling (Cairo tiling) X Z, with respect to a 5-valent point.
- A321025 (program): a(n) = sum of a(n-4) and a(n-5), with the lowest possible initial values that will generate a sequence where a(n) is always > a(n-1): 4, 5, 6, 7 and 8.
- A321029 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+4,n) = gcd(x+6,n) = gcd(x+10,n) = gcd(x+12,n) = 1.
- A321030 (program): Number of integers x such that 1 <= x <= n and gcd(x,n) = gcd(x+4,n) = gcd(x+6,n) = gcd(x+10,n) = gcd(x+12,n) = gcd(x+16,n) = 1.
- A321032 (program): Number of words of length 3n such that all letters of the binary alphabet occur at least once and are introduced in ascending order and which can be built by repeatedly inserting triples into the initially empty word.
- A321069 (program): Greatest prime factor of n^3+2.
- A321090 (program): Sequence {a(n), n>=0} satisfying the continued fraction relation: if z = [a(0) + 1; a(1) + 1, a(2) + 1, a(3) + 1, …, a(n) + 1, …], then 3*z = [a(0) + 9; a(1) + 11, a(2) + 11, a(3) + 11, …, a(n) + 11, …].
- A321091 (program): Continued fraction expansion of the constant z that satisfies: CF(3*z, n) = CF(z, n) + 10, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
- A321093 (program): Continued fraction expansion of the constant z that satisfies: CF(4*z, n) = CF(z, n) + 21, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
- A321095 (program): Continued fraction expansion of the constant z that satisfies: CF(5*z, n) = CF(z, n) + 36, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
- A321097 (program): Continued fraction expansion of the constant z that satisfies: CF(6*z, n) = CF(z, n) + 55, for n >= 0, where CF(z, n) denotes the n-th partial denominator in the continued fraction expansion of z.
- A321100 (program): Sequence {a(n), n>=0} satisfying the continued fraction relation: if z = [a(0) + 1; a(1) + 1, a(2) + 1, a(3) + 1, …, a(n) + 1, …], then 7*z = [a(0) + 9; a(1) + 11, a(2) + 11, a(3) + 11, …, a(n) + 11, …].
- A321101 (program): Sequence generated by: a(3*n) = 0, a(3*n+2) = 3 - a(3*n+1), a(9*n+1) = 1, a(9*n+7) = 2, a(9*n+4) = 3 - a(3*n+1), for n >= 0.
- A321102 (program): Sequence generated by: a(3*n) = 1, a(3*n+2) = 1 - a(3*n+1), a(9*n+1) = 1, a(9*n+7) = 0, a(9*n+4) = 1 - a(3*n+1), for n >= 0.
- A321103 (program): Sequence generated by: a(3*n) = 1, a(3*n+2) = 2 - a(3*n+1), a(9*n+1) = 2, a(9*n+7) = 0, a(9*n+4) = 2 - a(3*n+1), for n >= 0.
- A321104 (program): Sequence generated by: a(3*n) = 1, a(3*n+2) = 2 - a(3*n+1), a(9*n+1) = 0, a(9*n+7) = 2, a(9*n+4) = 2 - a(3*n+1), for n >= 0.
- A321119 (program): a(n) = ((1 - sqrt(3))^n + (1 + sqrt(3))^n)/2^floor((n - 1)/2); n-th row common denominator of A321118.
- A321120 (program): Decimal expansion of (3 + sqrt(3))/12.
- A321123 (program): a(n) = 2^n + 2*n^2 + 2*n + 1.
- A321124 (program): a(n) = (4*n^3 - 6*n^2 + 14*n + 3)/3.
- A321126 (program): T(n,k) = max(n + k - 1, n + 1, k + 1), square array read by antidiagonals (n >= 0, k >= 0).
- A321129 (program): Numerator of Sum_{k=1..n} (k*sin((Pi*k)/3))/sqrt(3).
- A321131 (program): Values of m (mod 25), where A317905(m) = 1.
- A321133 (program): a(n) = 3*a(n-1) + 10*a(n-2), n >= 2; a(0)=-1, a(1)=23.
- A321140 (program): a(n) = Sum_{d|n} sigma_3(d).
- A321171 (program): a(n) is the total number of 1’s in binary that n shares with the positive integers less than n.
- A321173 (program): a(n) = -2*a(n-1) + a(n-2) + a(n-3), a(0) = -1, a(1) = 3, a(2) = -9.
- A321174 (program): a(n) = -2*a(n-1) + a(n-2) + a(n-3), a(0) = -1, a(1) = -4, a(2) = 5.
- A321175 (program): a(n) = -a(n-1) + 2*a(n-2) + a(n-3), a(0) = -1, a(1) = -2, a(2) = 3.
- A321176 (program): Number of integer partitions of n that are the vertex-degrees of some set system with no singletons.
- A321177 (program): Heinz numbers of integer partitions that are the vertex-degrees of some set system with no singletons.
- A321178 (program): One-half the sum of the first 2n + 1 primes.
- A321180 (program): a(n) = 17*n^2 - 1.
- A321195 (program): Minimum number of monochromatic Schur triples over all 2-colorings of [n].
- A321202 (program): Row sums of the irregular triangle A321201.
- A321205 (program): Alternating row sums of Riordan triangle A319203.
- A321207 (program): a(n) = (n*n!)^3.
- A321212 (program): Numbers that are congruent to {2, 3} mod 16.
- A321213 (program): a(n) is the number of divisors of n-th Fermat number (A000215).
- A321220 (program): a(n) = n+2 if n is even, otherwise a(n) = 2*n+1 if n is odd.
- A321232 (program): Length of n-th term of A321225.
- A321233 (program): a(n) is the number of reflectable bases of the root system of type D_n.
- A321234 (program): Denominator of series expansion of the hypergeometric series 3F2([1/2, 1, 1], [3/2, 3/2], x).
- A321237 (program): Start with a square of dimension 1 X 1, and repeatedly append along the squares of the previous step squares with half their side length that do not overlap with any prior square; a(n) gives the number of squares appended at n-th step.
- A321243 (program): a(n) is the product of n and all its decimal digits individually except the leftmost digit.
- A321257 (program): Start with an equilateral triangle, and repeatedly append along the triangles of the previous step equilateral triangles with half their side length that do not overlap with any prior triangle; a(n) gives the number of triangles appended at n-th step.
- A321259 (program): a(n) = sigma_n(n) - n^n.
- A321294 (program): a(n) = Sum_{d|n} mu(n/d)*d*sigma_n(d).
- A321295 (program): a(n) = n * sigma_n(n).
- A321322 (program): a(n) = Sum_{d|n} mu(n/d)*J_2(d), where J_2() is the Jordan function (A007434).
- A321324 (program): a(n) = (n^2 - c(n)) / 7 + 1 where c(n) = c(-n) = c(n+7) for all n in Z and a(n) = 1 if 0 <= n <=3 except a(1) = 0.
- A321341 (program): An unbounded sequence which is 1 infinitely often, with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms.
- A321348 (program): a(n) = Sum_{d|n} tau(d^n), where tau() is the number of divisors (A000005).
- A321349 (program): a(n) = Sum_{d|n} phi(d^n), where phi() is the Euler totient function (A000010).
- A321358 (program): a(n) = (2*4^n + 7)/3.
- A321366 (program): a(n) is the least integer k greater than 1 such that n divides binomial(k, 2) = A000217(k-1).
- A321370 (program): n + [n*s/r] + [n*t/r], where r = 1, s = cos(2*Pi/5), t = sec(2*Pi/5).
- A321371 (program): n + [n*r/s] + [n*t/s], where r = 1, s = cos(2*Pi/5), t = sec(2*Pi/5).
- A321383 (program): Numbers k such that the concatenation k21 is a square.
- A321391 (program): Array read by antidiagonals: T(n,k) is the number of achiral rows of n colors using up to k colors.
- A321398 (program): a(n) = (-1)^(n+1)*n!* x^n.
- A321404 (program): Number of non-isomorphic self-dual set multipartitions (multisets of sets) of weight n with no singletons.
- A321405 (program): Number of non-isomorphic self-dual set systems of weight n.
- A321406 (program): Number of non-isomorphic self-dual set systems of weight n with no singletons.
- A321421 (program): a(n) = 10*(4^n - 1)/3 + 1.
- A321461 (program): a(n) = -a(n-1) + 2*a(n-2) + a(n-3), a(0) = -1, a(1) = -2, a(2) = -4.
- A321463 (program): Decimal expansion of 36*Pi.
- A321483 (program): a(n) = 7*2^n + (-1)^n.
- A321484 (program): Number of non-isomorphic self-dual connected multiset partitions of weight n.
- A321499 (program): Numbers of the form (x - y)(x^2 - y^2) with x > y > 0.
- A321500 (program): Triangular table T(n,k) = (n+k)*(n^2+k^2), n >= k >= 0; read by rows n = 0, 1, 2, …
- A321501 (program): Numbers not of the form (x - y)(x^2 - y^2) with x > y > 0; complement of A321499.
- A321512 (program): Characteristic function of the reverse in the shuffle (perfect faro shuffle with cut): 1 if the sequence of shuffles of n cards contains the reverse of the original order of cards, 0 if not.
- A321531 (program): a(n) is the maximum number of distinct directions between n non-attacking rooks on an n X n chessboard.
- A321539 (program): 3^n with digits rearranged into nonincreasing order.
- A321540 (program): 3^n with digits rearranged into nondecreasing order.
- A321543 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^2.
- A321544 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^5.
- A321545 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^6.
- A321546 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^7.
- A321547 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^8.
- A321548 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^9.
- A321549 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^10.
- A321550 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^11.
- A321551 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^12.
- A321552 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^7.
- A321553 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^8.
- A321554 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^9.
- A321555 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^10.
- A321556 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^11.
- A321557 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^12.
- A321573 (program): Row sums of A321624.
- A321577 (program): a(n) = F_n mod M_n, where F_n = 2^(2^n) + 1 and M_n = 2^n - 1.
- A321579 (program): Number of n-tuples of 4 elements excluding reverse duplicates and those consisting of repetitions of the same element only.
- A321580 (program): Numbers k such that it is possible to reverse a deck of k cards by a sequence of perfect Faro shuffles with cut.
- A321598 (program): a(n) = Sum_{d|n} d*binomial(d+2,3).
- A321601 (program): G.f.: A(x,y) = Sum_{n=-oo…+oo} (x^n + y)^n = Sum_{n>=0} Sum_{k>=0} T(n,k) * x^(n^2 + n*k) * y^k, written here as a rectangle of coefficients T(n,k) read by antidiagonals.
- A321613 (program): Partial products of the unitary totient function (A047994): a(n) = Product_{k=1..n} uphi(k).
- A321632 (program): Expansion of e.g.f. (1 + sin(x))/exp(x).
- A321643 (program): a(n) = 5*2^n - (-1)^n.
- A321663 (program): a(n) = prime(n)^prime(n+2).
- A321672 (program): Number of chiral pairs of rows of length 5 using up to n colors.
- A321703 (program): a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3), a(0) = 1, a(1) = 1, a(2) = 5.
- A321715 (program): a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3), a(0) = 1, a(1) = -1, a(2) = -1 .
- A321741 (program): Product of the first n terms of A007318 (Pascal), read as a sequence.
- A321773 (program): Number of compositions of n into parts with distinct multiplicities and with exactly three parts.
- A321789 (program): Factorials of terms of Pascal’s triangle by row.
- A321798 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^4).
- A321799 (program): G.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^5).
- A321810 (program): Sum of 6th powers of odd divisors of n.
- A321811 (program): Sum of 7th powers of odd divisors of n.
- A321812 (program): Sum of 8th powers of odd divisors of n.
- A321813 (program): Sum of 9th powers of odd divisors of n.
- A321814 (program): Sum of 10th powers of odd divisors of n.
- A321815 (program): Sum of 11th powers of odd divisors of n.
- A321816 (program): Sum of 12th powers of odd divisors of n.
- A321817 (program): a(n) = Sum_{d|n, n/d odd} d^6 for n > 0.
- A321818 (program): a(n) = Sum_{d|n, n/d odd} d^8 for n > 0.
- A321819 (program): a(n) = Sum_{d|n, n/d odd} d^10 for n > 0.
- A321820 (program): a(n) = Sum_{d|n, n/d odd} d^12 for n > 0.
- A321821 (program): a(n) = Sum_{d|n, d==1 mod 4} d^5 - Sum_{d|n, d==3 mod 4} d^5.
- A321822 (program): a(n) = Sum_{d|n, d==1 mod 4} d^6 - Sum_{d|n, d==3 mod 4} d^6.
- A321823 (program): a(n) = Sum_{d|n, d==1 mod 4} d^7 - Sum_{d|n, d==3 mod 4} d^7.
- A321824 (program): a(n) = Sum_{d|n, d==1 mod 4} d^8 - Sum_{d|n, d==3 mod 4} d^8.
- A321825 (program): a(n) = Sum_{d|n, d==1 (mod 4)} d^9 - Sum_{d|n, d==3 (mod 4)} d^9.
- A321826 (program): a(n) = Sum_{d|n, d==1 mod 4} d^10 - Sum_{d|n, d==3 mod 4} d^10.
- A321827 (program): a(n) = Sum_{d|n, d==1 (mod 4)} d^11 - Sum_{d|n, d==3 (mod 4)} d^11.
- A321828 (program): a(n) = Sum_{d|n, d==1 mod 4} d^12 - Sum_{d|n, d==3 mod 4} d^12.
- A321837 (program): Expansion of e.g.f.: exp(x/(1-3*x)).
- A321838 (program): Number of words w of length n such that each letter of the binary alphabet is used at least once and 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.
- A321847 (program): E.g.f.: exp(x/(1 - 4*x)).
- A321848 (program): E.g.f.: exp(x/(1-5*x)).
- A321849 (program): Expansion of e.g.f.: exp(x/(1-6*x)).
- A321850 (program): E.g.f.: exp(x/(1-7*x)).
- A321853 (program): a(n) is the sum of the fill times of all 1-dimensional fountains given by the permutations in S_n.
- A321875 (program): a(n) = Sum_{d|n} d*d!.
- A321879 (program): Partial sums of the Jordan function J_2(k), for 1 <= k <= n.
- A321883 (program): Nonnegative integers n for which n! + 1 is not a square.
- A321885 (program): a(1) = 1, a(n) = n + d(a(n-1)).
- A321907 (program): If n > 1 is the k-th prime number, then a(n) = k!, otherwise a(n) = 0.
- A321942 (program): A sequence related to the Euler-Gompertz constant.
- A321957 (program): a(n) = binomial(3*n, n + 1)*hypergeom([1, 1 - 2*n], [2 + n], -1).
- A321959 (program): a(n) = [x^n] ((1 - x)*x)/((1 - 2*x)^2*(2*x^2 - 2*x + 1)).
- A321965 (program): a(n) = n! [x^n] exp((1/(x - 1)^2 - 1)/2)/(1 - x).
- A321973 (program): Partial sums of the Dedekind psi_2(k) function, for 1 <= k <= n.
- A321986 (program): Number of integer pairs (x,y) with x+y < 3*n/4, x-y < 3*n/4 and -x/2 < y < 2*x.
- A321999 (program): Sum of digits of n minus the number of digits of n.
- A322008 (program): 1/(1 - Integral_{x=0..1} x^(x^n) dx), rounded to the nearest integer.
- A322015 (program): If A003188(n+1) < A003188(n), then a(n) = n+1, otherwise a(n) = 0.
- A322016 (program): a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, otherwise a(n) = 0.
- A322018 (program): a(n) = A006068(A129760(A003188(n))).
- A322029 (program): Denominator of least value of the squared diameters of the enclosing circles of all strictly convex lattice n-gons with minimal area given by A070911. Numerators are A321693.
- A322034 (program): Let p1 <= p2 <= … <= pk be the prime factors of n, with repetition; let s = 1/p1 + 1/(p1*p2) + 1/(p1*p2*p3) + … + 1/(p1*p2*…*pk); a(n) = numerator of s. a(1)=0 by convention.
- A322035 (program): Let p1 <= p2 <= … <= pk be the prime factors of n, with repetition; let s = 1/p1 + 1/(p1*p2) + 1/(p1*p2*p3) + … + 1/(p1*p2*…*pk); a(n) = denominator of s. a(1)=1 by convention.
- A322036 (program): a(n) = A322035(n) - A322034(n).
- A322037 (program): a(n) = 2^b(n), where b(n) = A000031(n).
- A322039 (program): Expansion of (1 + x)^2 / ((1 - x)^2*(1 + 2*x)^2).
- A322042 (program): Maximum edge-distance of a point in the quotient graph E/nE from the origin (see A322041 for further information).
- A322043 (program): Numbers k such that the coefficient of x^k in the expansion of Product_{m >= 1} (1-x^m)^15 is zero.
- A322048 (program): Final elements in rows when A322050 is displayed as a triangle.
- A322051 (program): a(n) is the number of initial terms in the row of length 2^n of A322050 that agree with the limiting sequence A322049.
- A322052 (program): Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits.
- A322054 (program): Number of decimal strings of length n that do not contain a specific string xx (where x is a single digit).
- A322068 (program): a(n) = (1/2)*Sum_{p prime <= n} floor(n/p) * floor(1 + n/p).
- A322071 (program): Triangle read by rows: T(n, k) is the largest integer m such that m*k^k <= 2*n^k.
- A322078 (program): a(n) = n^2 * Sum_{p|n} 1/p^2, where p are primes dividing n.
- A322079 (program): a(n) = n^2 * Sum_{ p^k | n } k / p^2, where p are primes dividing n with multiplicity k.
- A322108 (program): Distance of n-th iteration in an alternating rectangular spiral.
- A322111 (program): Number of non-isomorphic self-dual connected multiset partitions of weight n with multiset density -1.
- A322112 (program): Number of non-isomorphic self-dual connected multiset partitions of weight n with no singletons and multiset density -1.
- A322113 (program): Number of non-isomorphic self-dual connected antichains of multisets of weight n.
- A322116 (program): Main diagonal of triangle A321600; a(n) = A321600(n,n-1) for n >= 1.
- A322129 (program): Digital roots of A057084.
- A322141 (program): a(n) is also the sum of the even-indexed terms of the n-th row of the triangle A237591.
- A322159 (program): Decimal expansion of 1 - 1/sqrt(5).
- A322171 (program): Expansion of x*(3 + 5*x + x^2 + x^3)/((1 - x)^2*(1 + x^2)).
- A322240 (program): a(n) = A084605(n)^2, the square of the central coefficient in (1 + x + 4*x^2)^n.
- A322242 (program): G.f.: 1/sqrt(1 - 6*x - 7*x^2).
- A322243 (program): a(n) = A322242(n)^2, the square of the central coefficient in (1 + 3*x + 4x^2)^n.
- A322244 (program): G.f.: 1/sqrt(1 - 6*x - 55*x^2).
- A322245 (program): a(n) = A322244(n)^2, the square of the central coefficient in (1 + 3*x + 16x^2)^n.
- A322246 (program): Expansion of g.f.: 1/sqrt(1 - 10*x - 11*x^2).
- A322247 (program): a(n) = A322246(n)^2, the square of the central coefficient in (1 + 5*x + 9*x^2)^n.
- A322248 (program): G.f.: 1/sqrt( (1 + 3*x)*(1 - 13*x) ).
- A322249 (program): a(n) = A322248(n)^2, the square of the central coefficient in (1 + 5*x + 16*x^2)^n.
- A322250 (program): Take binary expansion of 2n-1 and delete the trailing block of 1’s, except if the number is 11…1, leave a single 1.
- A322252 (program): a(0) = 1 and a(n) = (5*n)!/(5!*n!^5) for n > 0.
- A322260 (program): Numbers k such that the poset of multiset partitions of a multiset whose multiplicities are the prime indices of k is a lattice.
- A322284 (program): Number of nonequivalent ways to place n nonattacking kings on a 2 X 2n chessboard under all symmetry operations of the rectangle.
- A322303 (program): a(n) = Fibonacci(semiprime(n)).
- A322307 (program): Number of multisets in the swell of the n-th multiset multisystem.
- A322327 (program): a(n) = A005361(n) * A034444(n) for n > 0.
- A322328 (program): a(n) = A005361(n) * 4^A001221(n) for n > 0.
- A322360 (program): Multiplicative with a(p^e) = p^2 - 1.
- A322361 (program): a(n) = gcd(n, A003961(n)), where A003961 is completely multiplicative with a(prime(k)) = prime(k+1).
- A322362 (program): a(n) = gcd(n, A166590(n)), where A166590 is completely multiplicative with a(p) = p+2 for prime p.
- A322382 (program): a(n) = p*a(n/p) + 1, where p is the smallest prime divisor of n; a(1)=0.
- A322406 (program): a(n) = n + n*n^n.
- A322417 (program): a(n) - 2*a(n-1) = period 2: repeat [3, 0] for n > 0, a(0)=5, a(1)=13.
- A322450 (program): Number of permutations of [2n] in which the size of the last cycle is n and the cycles are ordered by increasing smallest elements.
- A322462 (program): Numbers on the 0-1-12 line in a spiral on a grid of equilateral triangles.
- A322465 (program): Numbers on the 0-9-10-line in a spiral on an equilateral triangular lattice.
- A322483 (program): The number of semi-unitary divisors of n.
- A322489 (program): Numbers k such that k^k ends with 4.
- A322490 (program): Numbers k such that k^k ends with 7.
- A322496 (program): Number of tilings of a 3 X n rectangle using V (2m+1)-ominoes (m >= 0) in standard orientation.
- A322533 (program): Position of 1/3^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order.
- A322534 (program): Position of 2/3^n in the sequence of all numbers 1/2^m, 1/3^m, 2/3^m arranged in decreasing order.
- A322544 (program): a(n) is the reciprocal of the coefficient of x^n in the power series of the function defined by ((1+2x)*exp(x) + 3*exp(-x) - 4)/ (4x^2).
- A322546 (program): Numbers k such that every integer partition of k contains a 1 or a prime power.
- A322556 (program): The number of eigenvectors with eigenvalue 1 summed over all linear operators on the vector space GF(2)^n.
- A322573 (program): G.f. = g(f(x)), where f(x) = g.f. of Fibonacci sequence A000045 and g(x) = g.f. of Jacobsthal sequence A001045.
- A322577 (program): a(n) = Sum_{d|n} psi(n/d) * phi(d).
- A322581 (program): Sum of A003958 and its Dirichlet inverse: a(n) = A003958(n) + A097945(n).
- A322582 (program): a(n) = n - A003958(n), where A003958 is fully multiplicative with a(p) = (p-1).
- A322585 (program): a(n) = 1 if n is a product of primorial numbers (A002110), 0 otherwise.
- A322590 (program): Lexicographically earliest such positive sequence a that a(i) = a(j) => A007947(i) = A007947(j) for all i, j.
- A322593 (program): a(n) = 2^n + 2*n^2 + 1.
- A322594 (program): a(n) = (4*n^3 + 12*n^2 - 4*n + 3)/3.
- A322595 (program): a(n) = (n^3 + 9*n + 14*n + 9)/3.
- A322596 (program): Square array read by descending antidiagonals (n >= 0, k >= 0): let b(n,k) = (n+k)!/((n+1)!*k!); then T(n,k) = b(n,k) if b(n,k) is an integer, and T(n,k) = floor(b(n,k)) + 1 otherwise.
- A322597 (program): a(n) = (4*n^3 - 6*n^2 + 20*n + 3)/3.
- A322598 (program): a(n) is the number of unlabeled rank-3 graded lattices with 3 coatoms and n atoms.
- A322628 (program): Number of n-digit decimal numbers containing a fixed 2-digit integer with distinct digits as a substring.
- A322631 (program): a(n) = 2*binomial(7*n-1,2*n)/(7*n-1).
- A322661 (program): Number of graphs with loops spanning n labeled vertices.
- A322665 (program): Partial sums of A089451.
- A322675 (program): a(n) = n * (4*n + 3)^2.
- A322677 (program): a(n) = 16 * n * (n+1) * (2*n+1)^2.
- A322707 (program): a(0)=0, a(1)=5 and a(n) = 22*a(n-1) - a(n-2) + 10 for n > 1.
- A322708 (program): a(0)=0, a(1)=6 and a(n) = 26*a(n-1) - a(n-2) + 12 for n > 1.
- A322709 (program): a(0)=0, a(1)=7 and a(n) = 30*a(n-1) - a(n-2) + 14 for n > 1.
- A322745 (program): a(n) = n * (16*n^2+20*n+5)^2.
- A322746 (program): a(n) = 1/2 * (-1 + Sum_{k=0..n} binomial(2*n,2*k)*(n+1)^(n-k)*n^k).
- A322747 (program): a(n) = sqrt(1 + A322746(2*n)).
- A322755 (program): Numerator of expected payoff in the “Guessing Card Colors” game with a 2n-card deck, using an optimal strategy.
- A322756 (program): Denominator of expected payoff in the “Guessing Card Colors” game with a 2n-card deck, using an optimal strategy.
- A322780 (program): First differences of A237262.
- A322783 (program): a(n) = 1 - n + (2^(n+2) - (-1)^n)/3.
- A322796 (program): a(n) = Kronecker symbol (6/n).
- A322809 (program): Lexicographically earliest such sequence a that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n) = -1 if n is an odd prime, and f(n) = floor(n/2) for all other numbers.
- A322820 (program): a(n) = A052126(n) * A006530(A052126(n)).
- A322829 (program): a(n) = Jacobi (or Kronecker) symbol (n/21).
- A322830 (program): a(n) = 32*n^3 + 48*n^2 + 18*n + 1.
- A322832 (program): Values x + y, where the ordered pairs (x,y) are sorted first by maximal coordinate and then lexicographically.
- A322844 (program): a(n) = (1/12)*n^2*(3*(1 + n^2) - 2*(2 + n^2)*(n mod 2)).
- A322860 (program): If n is practical (in A005153), a(n) = 1, otherwise a(n) = 0.
- A322888 (program): Chebyshev T-polynomials T_n(16).
- A322889 (program): Chebyshev T-polynomials T_n(18).
- A322890 (program): a(n) = value of Chebyshev T-polynomial T_n(20).
- A322899 (program): a(n) = T_{2*n}(n+1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
- A322904 (program): a(n) = Sum_{k=0..n} binomial(2*n+1,2*k+1)*(n^2-1)^(n-k)*n^(2*k).
- A322914 (program): a(0)=0; for n>0, a(n) is the number of rooted 4-regular maps on the torus having n vertices.
- A322925 (program): Expansion of x*(1 + 2*x + 10*x^2)/((1 - x^2)*(1 - 10*x^2)).
- A322927 (program): Expansion of x*(1 + 5*x + 40*x^2)/((1 - x^2)*(1 - 10*x^2)).
- A322938 (program): a(n) = binomial(2*n + 2, n + 2) - 1.
- A322939 (program): a(n) = [x^n] (4*x^2 + x - 1)/(4*x^3 + 3*x^2 + 2*x - 1).
- A322940 (program): a(n) = [x^n] (4*x^2 + x - 1)/(2*x^2 + 3*x - 1).
- A322980 (program): a(n) = 1 if n and d(n) are coprime, 0 otherwise. Here d(n) is the number of divisors of n, A000005.
- A322981 (program): If n is the k-th prime power > 1, a(n) = k, otherwise a(n) = 0.
- A322982 (program): If n is a noncomposite, then a(n) = 2*n - 1, otherwise a(n) = A032742(n), the largest proper divisor of n.
- A322983 (program): Number of iterations of A011371(x) = x - A000120(x) needed to reach an odd number, when starting from x = n.
- A322984 (program): Number of iterations of A011371(x) = x - A000120(x) needed to reach an odd number, when starting from x = 2n.
- A323012 (program): a(n) = (1/sqrt(n^2+1)) * T_{2*n+1}(sqrt(n^2+1)) where T_{n}(x) is a Chebyshev polynomial of the first kind.
- A323048 (program): Sums of no more than two 5-smooth numbers.
- A323071 (program): a(n) = gcd(n, 1+A060681(n)).
- A323072 (program): a(n) = n/A323071(n) = n/gcd(n, 1+A060681(n)).
- A323075 (program): The fixed point reached when map x -> 1+(x-(largest divisor d < x)) is iterated, starting from x = n.
- A323076 (program): Number of iterations of map x -> 1+(x-(largest divisor d < x)), starting from x=n, needed to reach a fixed point, which is always either a prime or 1.
- A323077 (program): Number of iterations of map x -> (x - (largest divisor d < x)) needed to reach 1 or a prime, when starting at x = n.
- A323117 (program): a(n) = T_{n}(n-1) where T_{n}(x) is a Chebyshev polynomial of the first kind.
- A323118 (program): a(n) = U_{n}(n) where U_{n}(x) is a Chebyshev polynomial of the second kind.
- A323129 (program): a(1) = 1, and for any n > 1, let p be the greatest prime factor of n, and e be its exponent, then a(n) = p^a(e).
- A323152 (program): a(n) = 1 if sigma(n) is divisible by all proper divisors of n, 0 otherwise.
- A323153 (program): a(n) = 1 if n is either a prime or a perfect number, 0 otherwise.
- A323158 (program): If n is a square, a(n) = 1-(n mod 2), otherwise a(n) = (n mod 2); a(n) = A049820(n) mod 2, where A049820(n) = n - number of divisors of n.
- A323159 (program): Greatest common divisor of product (1+(p^e)) and product (1+p), where p ranges over prime factors of n, with e corresponding exponent; a(n) = gcd(A034448(n), A048250(n)).
- A323160 (program): a(n) = gcd(n, A323159(n)) = gcd(n, A034448(n), A048250(n)).
- A323161 (program): Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j, where f(n<=3) = -n, f(n) = 0 if n-1 is an odd prime, and f(n) = floor((n-1)/2) for all other numbers.
- A323162 (program): a(n) = 1 if both n and n-1 are composite, 0 otherwise.
- A323166 (program): Greatest common divisor of Product (1+(p_i^e_i)) and n, when n = Product (p_i^e_i); a(n) = gcd(A034448(n), n).
- A323170 (program): a(n) = 1 if (2*phi(n)) < n, 0 otherwise, where phi is Euler totient function (A000010).
- A323178 (program): a(n) = 1 + 100*n^2 for n >= 0.
- A323181 (program): a(n) = U_{2*n-1}(n)/(2*n) where U_{n}(x) is a Chebyshev polynomial of the second kind.
- A323186 (program): a(0) = 0, a’(0) = 0, a’‘(0) = 1, a’‘(1) = -1, a(n) = a(n-1) + a’(n), a’(n) = a’(n-1) + a’‘(n), a’‘(n) = -a’‘(n-1) if a(n-2) = 0, or else a’‘(n-1).
- A323191 (program): Expansion of (1 - x^5) / ((1 + x) * (1 + x^4)) in powers of x.
- A323202 (program): Expansion of (1 - x) * (1 - x^3) / (1 - x^4) in powers of x.
- A323210 (program): a(n) = 9*J(n)^2 where J(n) are the Jacobsthal numbers A001045 with J(0) = 1.
- A323211 (program): Level 1 of Pascal’s pyramid. T(n, k) triangle read by rows for n >= 0 and 0 <= k <= n.
- A323218 (program): a(n) = (4*n^3 + 30*n^2 + 50*n)/3 + 1.
- A323220 (program): a(n) = n*(n + 5)*(n + 7)*(n + 10)/24 + 1.
- A323221 (program): a(n) = n*(n + 5)*(n + 7)/6 + 1.
- A323223 (program): a(n) = [x^n] x/((1 - x)*(1 - 4*x)^(5/2)).
- A323225 (program): a(n) = ((2^n*n + i*(1 - i)^n - i*(1 + i)^n))/4, where i is the imaginary unit.
- A323227 (program): a(n) = [x^n] (-x^4 + 2*x^3 - x^2 + 2*x - 1)/((x - 1)^2*(2*x - 1)).
- A323228 (program): a(n) = binomial(n + 4, n - 1) + 1.
- A323229 (program): a(n) = binomial(2*n, n+1) + 1.
- A323230 (program): a(n) = binomial(2*(n - 1), n - 1) + 1.
- A323231 (program): A(n, k) = [x^k] (1/(1-x) + x/(1-x)^n), square array read by descending antidiagonals for n, k >= 0.
- A323232 (program): a(n) = 2^n*J(n, 1/2) where J(n, x) are the Jacobsthal polynomials as defined in A322942.
- A323239 (program): a(n) = 1 if n is odd and squarefree, otherwise a(n) = 0.
- A323280 (program): a(n) = Sum_{k=0..n} binomial(n,k) * k^(2*k).
- A323294 (program): Number of 3-uniform hypergraphs spanning n labeled vertices where every two edges have two vertices in common.
- A323295 (program): Number of ways to fill a matrix with the first n positive integers.
- A323305 (program): Number of divisors of the number of prime factors of n counted with multiplicity.
- A323308 (program): The number of exponential semiproper divisors of n.
- A323309 (program): The sum of exponential semiproper divisors of n.
- A323325 (program): Coefficients a(n) of x^n*y^n*z^n in function A = A(x,y,z) such that A = 1 + x*B*C, B = 1 + y*C*A, and C = 1 + z*A*B, for n >= 0.
- A323351 (program): Number of ways to fill a (not necessarily square) matrix with n zeros and ones.
- A323363 (program): Dirichlet inverse of Dedekind’s psi, A001615.
- A323397 (program): a(n) = (4^n + 15*n - 1)/9.
- A323403 (program): Sum of sigma and its Dirichlet inverse: a(n) = A000203(n) + A046692(n).
- A323407 (program): Dirichlet inverse of A047994, unitary phi.
- A323409 (program): Greatest common divisor of Product (p_i^e_i)-1 and n, when n = Product (p_i^e_i); a(n) = gcd(n, A047994(n)).
- A323410 (program): Unitary analog of cototient function A051953: a(n) = n - A047994(n).
- A323413 (program): Infinitary analog of cototient function A051953: a(n) = n - A091732(n).
- A323416 (program): a(n) = (n-1)! * (10^n - 1) / 9.
- A323439 (program): Number of ways to fill a Young diagram with the prime indices of n such that all rows and columns are strictly increasing.
- A323466 (program): Number of terms in row n of A323465.
- A323467 (program): Smallest number in row n of A323465.
- A323505 (program): Mirror image of (denominators of) Bernoulli tree, A106831.
- A323540 (program): a(n) = Product_{k=0..n} (k^2 + (n-k)^2).
- A323547 (program): n-th digit in the base-2 expansion of 1/n.
- A323591 (program): n-th digit after the radix point in the base-3 expansion of 1/n.
- A323592 (program): n-th digit in the base-4 expansion of 1/n.
- A323608 (program): The position function the fractalization of which yields A323607.
- A323610 (program): List of 5-powerful numbers (for the definition of k-powerful see A323395).
- A323614 (program): List of 7-powerful numbers (for the definition of k-powerful see A323395).
- A323618 (program): Expansion of e.g.f. (1 + x)*log(1 + x)*(2 + log(1 + x))/2.
- A323620 (program): Expansion of e.g.f. 2*sqrt(1 + x)*sinh(sqrt(5)*log(1 + x)/2)/sqrt(5).
- A323629 (program): List of 6-powerful numbers (for the definition of k-powerful see A323395).
- A323639 (program): a(n) = 3*(10^n - 4)/9.
- A323641 (program): Triangle read by rows in which row n lists the first 2^n terms of A323642, n >= 1.
- A323642 (program): Row n of triangle A323641 when n -> infinity.
- A323648 (program): Numbers k such that the largest Dyck path of the symmetric representation of sigma(k) does not share any line segment with the largest Dyck path of the symmetric representation of sigma(k+1).
- A323649 (program): Corner sequence of the cellular automaton of A323650.
- A323650 (program): Flower garden sequence (see Comments for precise definition).
- A323651 (program): Number of elements added at n-th stage to the toothpick structure of A323650.
- A323669 (program): Decimal expansion of 15/(2*Pi^2) = 1/((4/5)*zeta(2)).
- A323703 (program): Number of values of (X^3 + X) mod prime(n).
- A323704 (program): Number of cubic residues (including 0) modulo the n-th prime.
- A323715 (program): a(n) = Product_{k=0..n} (2^k + 3^k).
- A323716 (program): a(n) = Product_{k=0..n} (3^k + 1).
- A323723 (program): a(n) = (-2 - (-1)^n*(-2 + n) + n + 2*n^3)/4.
- A323724 (program): a(n) = n*(2*(n - 2)*n + (-1)^n + 3)/4.
- A323735 (program): a(n) is the largest minimal distance of a binary LCD [n,2] code.
- A323739 (program): a(n) is the number of residues modulo (4*primorial(n)) of the squares of primes greater than or equal to prime(n+1).
- A323741 (program): a(n) = m-p where m = (2n+1)^2 and p is the largest prime < m.
- A323756 (program): a(1) = 2; for n >= 2, if a(n-1) has not yet been assigned, then a(n-1) = 1 and a(2*n-1) = 2, otherwise a(2*n) = 3.
- A323768 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^k.
- A323769 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^n.
- A323770 (program): Expansion of e.g.f. x*(2 - x)*exp(x/(1 - x))/(2*(1 - x)^2).
- A323775 (program): a(n) = Sum_{k = 1…n} k^(2^(n - k)).
- A323776 (program): a(n) = Sum_{k = 1…n} binomial(k + 2^(n - k) - 1, k - 1).
- A323812 (program): a(n) = n*Fibonacci(n-2) + ((-1)^n + 1)/2.
- A323824 (program): a(0) = 6; thereafter a(n) = 4*a(n-1) + 1.
- A323847 (program): a(n) = (n-1)*(n-2)*(n^2+9*n+12)/24.
- A323868 (program): Number of matrices of size n whose entries cover an initial interval of positive integers.
- A323921 (program): a(n) = (4^(valuation(n, 4) + 1) - 1) / 3.
- A323951 (program): Number of ways to split an n-cycle into connected subgraphs, all having at least three vertices.
- A323952 (program): Regular triangle read by rows where if k > 1 then T(n, k) is the number of connected subgraphs of an n-cycle with any number of vertices other than 2 through k - 1, n >= 1, 1 <= k <= n - 1. Otherwise T(n, 1) = n.
- A323956 (program): Triangle read by rows: T(n, k) = 1 + n * (n - k) for 1 <= k <= n.
- A323976 (program): Records for the number of ‘Reverse and Add’ steps, needed for a Lychrel number to join the trajectory of a smaller Lychrel number (i.e., its seed).
- A323988 (program): a(n) = 2^(n - 1) + binomial(n, floor(n/2))*(n + 1)/2.
- A324015 (program): Number of nonempty subsets of {1, …, n} containing no two cyclically successive elements.
- A324036 (program): Modified reduced Collatz map fs acting on positive odd integers.
- A324048 (program): a(n) = A000203(n) - A083254(n) = n + sigma(n) - 2*phi(n).
- A324050 (program): Numbers satisfying Korselt’s criterion: squarefree numbers n such that for every prime divisor p of n, p-1 divides n-1.
- A324121 (program): a(n) = gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).
- A324122 (program): a(n) = sigma(n) - gcd(n*d(n), sigma(n)), where d(n) = number of divisors of n (A000005) and sigma(n) = sum of divisors of n (A000203).
- A324128 (program): a(n) = 2*n*Fibonacci(n) + (-1)^n + 1.
- A324129 (program): a(n) = n*Fibonacci(n) + ((-1)^n + 1)/2.
- A324151 (program): a(n) = (2/((n+1)*(n+2)))*multinomial(3*n;n,n,n).
- A324152 (program): a(0)=1; for n>0, a(n) = (3/((n+1)*(n+2)*(n+3))) * multinomial(4*n;n,n,n,n).
- A324161 (program): Number of zerofree nonnegative integers <= n.
- A324172 (program): Number of subsets of {1,…,n} that cross their complement.
- A324174 (program): Integers k such that 2*floor(sqrt(k)) divides k.
- A324183 (program): a(n) = d(A163511(n)), where d(n) is A000005, the number of divisors of n.
- A324198 (program): a(n) = gcd(n, A276086(n)).
- A324245 (program): The modified Collatz map considered by Vaillant and Delarue.
- A324265 (program): a(n) = 5*343^n.
- A324266 (program): a(n) = 2*49^n.
- A324267 (program): a(n) = 11*7^(5*n).
- A324268 (program): a(n) = 31*11^(5*n).
- A324269 (program): a(n) = 3*11^(2*n).
- A324270 (program): a(n) = 13*7^(7*n).
- A324272 (program): a(n) = 2*13^(2*n).
- A324275 (program): Numbers k for which A324274(k) is 0, i.e., starting squares in A324274 that yield a path of infinite length.
- A324287 (program): a(n) = A002487(A005187(n)).
- A324288 (program): a(n) = A002487(1+A005187(n)).
- A324293 (program): a(n) = A002487(sigma(n)).
- A324294 (program): a(n) = A002487(1+sigma(n)).
- A324337 (program): a(n) = A002487(A006068(n)).
- A324338 (program): a(n) = A002487(1+A006068(n)).
- A324352 (program): Total number of occurrences of 2 in the (signed) displacement sets of all permutations of [n+2] divided by 2!.
- A324353 (program): Total number of occurrences of 3 in the (signed) displacement sets of all permutations of [n+3] divided by 3!.
- A324354 (program): Total number of occurrences of 4 in the (signed) displacement sets of all permutations of [n+4] divided by 4!.
- A324355 (program): Total number of occurrences of 5 in the (signed) displacement sets of all permutations of [n+5] divided by 5!.
- A324356 (program): Total number of occurrences of 6 in the (signed) displacement sets of all permutations of [n+6] divided by 6!.
- A324357 (program): Total number of occurrences of 7 in the (signed) displacement sets of all permutations of [n+7] divided by 7!.
- A324358 (program): Total number of occurrences of 8 in the (signed) displacement sets of all permutations of [n+8] divided by 8!.
- A324359 (program): Total number of occurrences of 9 in the (signed) displacement sets of all permutations of [n+9] divided by 9!.
- A324360 (program): Total number of occurrences of 10 in the (signed) displacement sets of all permutations of [n+10] divided by 10!.
- A324361 (program): Total number of occurrences of n in the (signed) displacement sets of all permutations of [2n] divided by n!.
- A324377 (program): a(0) = 0; for n > 0, a(n) = A000265(A005187(n)).
- A324378 (program): a(n) = A000265(1+A005187(n)).
- A324379 (program): a(n) = A007814(A005187(n)).
- A324400 (program): Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j) for all i, j >= 1, where f(n) = -1 if n = 2^k and k > 0, and f(n) = n for all other numbers.
- A324465 (program): Exponent of highest power of 2 that divides A324152(n).
- A324466 (program): Exponent of highest power of 2 that divides multinomial(3*n;n,n,n).
- A324467 (program): Three times the binary weight of n: 3*A000120(n).
- A324468 (program): a(n)=r(n)+r(n+1)+r(n+2), where r(n) is the ruler sequence A007814.
- A324469 (program): Exponent of highest power of 3 that divides multinomial(4*n;n,n,n,n).
- A324471 (program): a(n) = 10 mod n.
- A324472 (program): a(n) = 1000 mod n.
- A324476 (program): Packing numbers for n-tripods.
- A324478 (program): a(n) = (6/((n+1)*(n+2)*(n+3))) * multinomial(4*n;n,n,n,n).
- A324487 (program): a(n) = A001350(n)^3.
- A324490 (program): A324487(3*n).
- A324498 (program): Decimal expansion of the real solution to x^2*(x-1)^3 = 1.
- A324502 (program): a(n) = denominator of Sum_{d|n} (1/pod(d)) where pod(k) = the product of the divisors of k (A007955).
- A324529 (program): a(n) = lcm(sigma(n), pod(n)) where sigma(k) = the sum of divisors of k (A000203) and pod(n) = the product of divisors of k (A007955).
- A324560 (program): Numbers > 1 where the minimum prime index is less than or equal to the number of prime factors counted with multiplicity.
- A324580 (program): a(n) = n * A276086(n).
- A324591 (program): E.g.f.: exp(2 * (x + x^2 / 2 + x^3 / 3)).
- A324600 (program): a(n) = (k(n)*(k(n) + 1))/2 with k = A018252 (nonprime numbers), for n >= 1.
- A324646 (program): a(n) = gcd(n, A276086(n-1)).
- A324648 (program): a(n) = n - A318458(n), where A318458(n) is bitwise-AND of n and the sum of proper divisors of n (sigma(n)-n).
- A324650 (program): a(n) = A000010(A276086(n)).
- A324653 (program): a(n) = A000203(A276086(n)).
- A324654 (program): a(n) = A033879(A276086(n)).
- A324655 (program): a(n) = A000005(A276086(n)).
- A324772 (program): The “Octanacci” sequence: Trajectory of 0 under the morphism 0->{0,1,0}, 1->{0}.
- A324893 (program): a(n) = sigma(A097706(n)), where A097706(n) is the part of n composed of prime factors of form 4k+3.
- A324895 (program): Largest proper divisor of A276086(n); a(0) = 1.
- A324902 (program): The 2-adic valuation of A318456(n), where A318456(n) = n OR (sigma(n)-n).
- A324903 (program): a(n) = 1 if A007814(sigma(n)) > A007814(n), 0 otherwise. Here A007814(n) gives the 2-adic valuation of n.
- A324904 (program): The 2-adic valuation of A318466(n), where A318466(n) = 2*n OR sigma(n).
- A324908 (program): a(n) = 1 if n is an odd number which is not a square, 0 otherwise.
- A324910 (program): Multiplicative with a(p^e) = (2^e)-1.
- A324912 (program): Binary weight of A324911(n).
- A324913 (program): a(n) = Sum_{k=1..n} 2^k * phi(k), where phi is the Euler totient function A000010.
- A324914 (program): a(n) = Sum_{k=1..n} 2^k * tau(k), where tau(k) = A000005(k).
- A324915 (program): a(n) = Sum_{k=1..n} 2^k * sigma(k), where sigma(k) = A000203(k).
- A324920 (program): a(n) is the number of iterations of the integer splitting function (A056737) necessary to reach zero.
- A324937 (program): Triangle read by rows: T(n, k) = 2*n*k + n + k - 8.
- A324964 (program): a(n) = A000139(n) mod 2; Characteristic function of odd fibbinary numbers (A022341).
- A324965 (program): Partial sums of A324964.
- A324969 (program): Number of unlabeled rooted identity trees with n vertices whose non-leaf terminal subtrees are all different.
- A324999 (program): Array read by descending antidiagonals: A(n,k) is the number of oriented colorings of the facets (or vertices) of a regular n-dimensional simplex using up to k colors.
- A325000 (program): Array read by descending antidiagonals: T(n,k) is the number of unoriented colorings of the facets (or vertices) of a regular n-dimensional simplex using up to k colors.
- A325001 (program): Array read by descending antidiagonals: A(n,k) is the number of achiral colorings of the facets (or vertices) of a regular n-dimensional simplex using up to k colors.
- A325002 (program): Triangle read by rows: T(n,k) is the number of oriented colorings of the facets (or vertices) of a regular n-dimensional simplex using exactly k colors.
- A325003 (program): Triangle read by rows: T(n,k) is the number of achiral colorings of the facets (or vertices) of a regular n-dimensional simplex using exactly k colors.
- A325006 (program): Array read by descending antidiagonals: A(n,k) is the number of chiral pairs of colorings of the facets of a regular n-dimensional orthotope using up to k colors.
- A325050 (program): a(n) = Product_{k=0..n} (k!^2 + 1).
- A325102 (program): Number of ordered pairs of positive integers up to n with no binary carries.
- A325103 (program): Number of increasing pairs of positive integers up to n with no binary carries.
- A325104 (program): Number of increasing pairs of positive integers up to n with at least one binary carry.
- A325120 (program): Sum of binary lengths of the prime indices of n.
- A325126 (program): a(1) = 1; a(n) = -Sum_{d|n, d<n} rad(n/d) * a(d), where rad = A007947.
- A325153 (program): A column of triangle A322220; a(n) = A322220(n,1) for n >= 1.
- A325168 (program): Number of integer partitions of n with origin-to-boundary graph-distance equal to 2.
- A325169 (program): Origin-to-boundary graph-distance of the Young diagram of the integer partition with Heinz number n.
- A325173 (program): Perfect squares of the form a + b^2 + c^3, where a,b,c are consecutive numbers.
- A325181 (program): Number of integer partitions of n such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1.
- A325191 (program): Number of integer partitions of n such that the difference between the length of the minimal triangular partition containing and the maximal triangular partition contained in the Young diagram is 1.
- A325226 (program): Number of prime factors of n that are less than the largest, counted with multiplicity.
- A325282 (program): Maximum adjusted frequency depth among integer partitions of n.
- A325299 (program): a(n) = 9 * sigma(n).
- A325313 (program): a(n) = A048250(n) - n, where A048250(n) is the sum of squarefree divisors of n.
- A325321 (program): a(n) = 1 if cototient of n is a square, 0 otherwise.
- A325334 (program): Number of integer partitions of n with adjusted frequency depth 3 whose parts cover an initial interval of positive integers.
- A325339 (program): Number of divisors of n^3 that are <= n.
- A325401 (program): minflip(n) = min(n, r(n)) where r(n) is the binary reverse of n.
- A325402 (program): maxflip(n) = max(n, r(n)) where r(n) is the binary reverse of n.
- A325413 (program): Largest sum of the omega-sequence of an integer partition of n.
- A325437 (program): Final digit of primes of the form k^2 + 1.
- A325459 (program): Sum of numbers of nontrivial divisors (greater than 1 and less than k) of k for k = 1..n.
- A325473 (program): Number of compositions of n with no part divisible by 3 and an even number of parts congruent to 4 or 5 modulo 6.
- A325475 (program): a(n) = (24*n)^2.
- A325482 (program): Number of colored set partitions of [n] where colors of the elements of subsets are distinct and in increasing order and exactly two colors are used.
- A325488 (program): Dimensions of space of harmonic polynomials of each degree invariant under the full icosahedral group.
- A325516 (program): Triangle read by rows: T(n, k) = (1/4)*n*(1 - (-1)^(n - k) + 2*(n - k)^2), with 0 <= k < n.
- A325517 (program): a(n) = n*((2*n + 1)*(2*n^2 + 2*n + 3) - 3*(-1)^n)/24.
- A325581 (program): G.f.: Sum_{n>=0} (n+1) * x^n * (1+x)^(n*(n+1)).
- A325586 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * x^n * (1+x)^(n*(n+2)).
- A325587 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)*(n+3)/3! * x^n * (1+x)^(n*(n+3)).
- A325596 (program): a(n) = Sum_{d|n} mu(n/d) * (-1)^(d + 1) * d.
- A325636 (program): a(n) = gcd(2n, sigma(n)).
- A325644 (program): “Sloping quaternary numbers”: write numbers in quaternary under each other (right-justified), read diagonals in upward direction, convert to decimal.
- A325656 (program): a(n) = (1/24)*n*((4*n + 3)*(2*n^2 + 1) - 3*(-1)^n).
- A325657 (program): a(n) = (1/2)*(-1 + (-1)^n)*(n-1) + n^2.
- A325689 (program): Number of length-3 compositions of n such that no part is the sum of the other two.
- A325690 (program): Number of length-3 integer partitions of n whose largest part is not the sum of the other two.
- A325691 (program): Number of length-3 integer partitions of n whose largest part is not greater than the sum of the other two.
- A325692 (program): “Sloping senary numbers”: write numbers in senary (that is, base 6) under each other (right-justified), read diagonals in upward direction, convert to decimal.
- A325693 (program): “Sloping septenary numbers”: write numbers in septenary under each other (right-justified), read diagonals in upward direction, convert to decimal.
- A325695 (program): Number of length-3 strict integer partitions of n such that the largest part is not the sum of the other two.
- A325696 (program): Number of length-3 strict compositions of n such that no part is the sum of the other two.
- A325765 (program): Number of integer partitions of n with a unique consecutive subsequence summing to every positive integer from 1 to n.
- A325770 (program): Number of distinct nonempty contiguous subsequences of the integer partition with Heinz number n.
- A325805 (program): “Sloping octal numbers”: write numbers in octal under each other (right-justified), read diagonals in upward direction, convert to decimal.
- A325814 (program): a(n) = n - A048146(n), where A048146 is the sum of non-unitary divisors of n.
- A325829 (program): “Sloping nonary numbers”: write numbers in nonary under each other (right-justified), read diagonals in upward direction, convert to decimal.
- A325838 (program): Product of divisors of n-th triangular number.
- A325887 (program): Excess of sum of odd integers up to n and coprime to n over sum of even integers up to n and coprime to n.
- A325905 (program): Decimal expansion of 2/e^2.
- A325909 (program): Lexicographically earliest sequence of distinct positive terms such that for any n > 0, n divides Sum_{k = 1..n} (-1)^k * a(k).
- A325911 (program): Screaming numbers in base 16: numbers whose hexadecimal representation is AAAAAAA…
- A325937 (program): Expansion of Sum_{k>=1} (-1)^(k + 1) * x^(2*k) / (1 - x^k).
- A325938 (program): a(n) = omega(n)^tau(n), where omega=A001221 and tau=A000005.
- A325939 (program): Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k).
- A325940 (program): Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k)^2.
- A325941 (program): Expansion of Sum_{k>=1} k * x^(2*k) / (1 + x^k)^2.
- A325943 (program): a(n) = floor(n / omega(n)) where omega = A001221.
- A325958 (program): Sum of the corners of a 2n+1 X 2n+1 square spiral.
- A325964 (program): a(n) = 1 if n and sigma(n) are relatively prime, 0 otherwise, where sigma(n) = sum of divisors of n, A000203; Characteristic function of A014567.
- A325973 (program): Arithmetic mean of {sum of unitary divisors} and {sum of squarefree divisors}: a(n) = (1/2) * (A034448(n) + A048250(n)).
- A325974 (program): Arithmetic mean of {sum of non-unitary divisors} and {sum of nonsquarefree divisors}: a(n) = (1/2)*(A048146(n) + A162296(n)).
- A325977 (program): a(n) = (1/2)*(A034460(n) + A325313(n)).
- A325978 (program): a(n) = (1/2)*(A325314(n) + A325814(n)).
- A326011 (program): a(n) = (n+1) * (2^n + 1)^n.
- A326012 (program): a(n) = (n+1)*(n+2)/2 * (2^n + 1)^n.
- A326013 (program): a(n) = (n+1) * (3^n + 1)^n.
- A326038 (program): Square root of the largest square dividing the sum of divisors of n: a(n) = A000188(sigma(n)).
- A326039 (program): Largest square dividing the sum of divisors of n: a(n) = A008833(sigma(n)).
- A326040 (program): a(n) = sigma(n) - A008833(sigma(n)).
- A326041 (program): a(n) = sigma(A064989(n)).
- A326042 (program): a(n) = A064989(sigma(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes, and A064989 shifts it back towards smaller primes.
- A326044 (program): a(n) = n - {the largest square dividing its sum of divisors}: a(n) = n - A008833(sigma(n)).
- A326045 (program): a(n) is the sum of divisors of n, minus the largest square dividing that sum, minus n: a(n) = sigma(n) - A008833(sigma(n)) - n.
- A326049 (program): a(n) = n - A050449(n), where A050449 is the sum of divisors of the form 4k+1.
- A326050 (program): a(n) = A082052(n) - n, where A082052 is the sum of divisors of n that are not of the form 4k+1.
- A326052 (program): a(n) = n - A050452(n), where A050452 is the sum of divisors of the form 4k+3.
- A326053 (program): Sum of all other divisors of n except the largest square divisor: a(n) = sigma(n) - A008833(n).
- A326054 (program): a(n) = A326053(n) - n, where A326053 gives the sum of all other divisors of n except the largest square divisor.
- A326055 (program): a(n) = n - {the largest square that divides n}.
- A326058 (program): a(n) = n - {the sum of square divisors of n}.
- A326059 (program): a(n) = A285309(n) - n, where A285309 gives the sum of nonsquare divisors of n.
- A326061 (program): Sum of all other divisors of n except the largest proper divisor. a(1) = 0 by convention.
- A326065 (program): Sum of divisors of the largest proper divisor of n: a(n) = sigma(A032742(n)).
- A326066 (program): a(n) = sigma(n) - sigma(A032742(n)), where A032742 gives the largest proper divisor of n.
- A326067 (program): a(n) = sigma(n) - sigma(A032742(n)) - n, where A032742 gives the largest proper divisor of n, and sigma is the sum of divisors of n.
- A326068 (program): a(n) = n - sigma(A032742(n)), where sigma is the sum of divisors of n and A032742 gives the largest proper divisor of n.
- A326118 (program): a(n) is the largest number of squares of unit area connected only at corners and without holes that can be inscribed in an n X n square.
- A326121 (program): Expansion of Sum_{k>=1} k^2 * x^(2*k) / (1 - k * x^k).
- A326122 (program): a(n) = 10 * sigma(n).
- A326123 (program): a(n) is the sum of all divisors of the first n odd numbers.
- A326124 (program): a(n) is the sum of all divisors of the first n positive even numbers.
- A326125 (program): Expansion of Sum_{k>=1} k^2 * x^k / (1 + x^k)^2.
- A326128 (program): a(n) = n - A007913(n), where A007913 gives the squarefree part of n.
- A326135 (program): a(n) = sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.
- A326136 (program): a(n) = sigma(n) - sigma(A028234(n)), where sigma is the sum of divisors of n, and A028234 gives n without any occurrence of its smallest prime factor.
- A326142 (program): Sum of all other divisors of n except its largest squarefree divisor: a(n) = sigma(n) - A007947(n).
- A326143 (program): a(n) = A326142(n) - n, where A326142 gives the sum of all other divisors of n except its largest squarefree divisor.
- A326146 (program): a(n) = sigma(n) - A020639(n) - n, where A020639 gives the smallest prime factor of n, and sigma is the sum of divisors of n.
- A326178 (program): Number of subsets of {1..n} whose product is equal to their sum.
- A326186 (program): a(n) = n - A057521(n), where A057521 gives the powerful part of n.
- A326187 (program): a(n) = sigma(n) - A003557(n).
- A326188 (program): a(n) = A001065(n) - A003557(n), where A001065(n) = the sum of proper divisors of n, and A003557(n) = n divided by its largest squarefree divisor.
- A326194 (program): Number of iterations of x -> A009194(x) needed to reach a fixed point when starting from x = n, where A009194(x) = gcd(x, sigma(x)).
- A326195 (program): Number of iterations of x -> A009195(x) needed to reach 1 when starting from x = n, where A009195(x) = gcd(x, phi(x)).
- A326238 (program): Expansion of Sum_{k>=1} k * x^k * (1 - x^k) / (1 + x^k)^3.
- A326244 (program): Number of labeled n-vertex simple graphs without crossing or nesting edges.
- A326247 (program): Number of labeled n-vertex 2-edge multigraphs that are neither crossing nor nesting.
- A326278 (program): Number of n-vertex, 2-edge multigraphs that are not nesting. Number of n-vertex, 2-edge multigraphs that are not crossing.
- A326289 (program): a(0) = 0, a(n) = 2^binomial(n,2) - 2^(n - 1).
- A326290 (program): Number of non-crossing n-vertex graphs with loops.
- A326299 (program): a(n) = floor(n*log_2(n)).
- A326300 (program): Steinhaus sums.
- A326305 (program): Dirichlet g.f.: zeta(s-1) * (1 - 2^(-s)) / zeta(s).
- A326306 (program): Dirichlet g.f.: zeta(s) * zeta(s-1) * Product_{p prime} (1 - p^(1 - s) + p^(-s)).
- A326329 (program): Number of simple graphs covering {1..n} with no crossing or nesting edges.
- A326345 (program): a(n) is the number of arm movements when expressing n in flag semaphore, counting the movement of each arm separately.
- A326347 (program): Number of unordered pairs of 4-colorings of an n-cycle that differ in the coloring of exactly one vertex.
- A326354 (program): a(n) is the number of fractions reduced to lowest terms with numerator and denominator less than or equal to n in absolute value.
- A326355 (program): Number of permutations of length n with at most two descents.
- A326367 (program): Number of tilings of an equilateral triangle of side length n with unit triangles (of side length 1) and exactly two unit “lozenges” or “diamonds” (also of side length 1).
- A326394 (program): Expansion of Sum_{k>=1} x^k * (1 + x^(2*k)) / (1 - x^(3*k)).
- A326395 (program): Expansion of Sum_{k>=1} x^(2*k) * (1 + x^k) / (1 - x^(3*k)).
- A326398 (program): a(n) is the smallest k > 0 such that the concatenation prime(n)k is composite.
- A326399 (program): Expansion of Sum_{k>=1} k * x^k / (1 - x^(3*k)).
- A326400 (program): Expansion of Sum_{k>=1} k * x^(2*k) / (1 - x^(3*k)).
- A326415 (program): Dirichlet g.f.: zeta(2*s) / zeta(s)^3.
- A326419 (program): a(n) is the number of distinct Horadam sequences of period n.
- A326420 (program): Fixed point of the morphism 1->13, 2->132, 3->1322.
- A326422 (program): Numbers k such that A000045(k) mod 5 is prime.
- A326494 (program): Number of subsets of {1..n} containing all differences and quotients of pairs of distinct elements.
- A326501 (program): a(n) = Sum_{k=0..n} (-k)^k.
- A326503 (program): Expansion of Sum_{k>=1} x^k * (1 - x^(2*k)) / (1 + x^k + x^(2*k))^2.
- A326504 (program): Number of (binary) max-heaps on n elements from the set {0,1} containing exactly three 0’s.
- A326555 (program): a(n) = (2^n + 3^n)^n for n>= 0.
- A326577 (program): a(n) = (2*n - 1) / A326478(2*n - 1).
- A326586 (program): Odd numbers which do not satisfy Korselt’s criterion, complement of A324050.
- A326618 (program): a(n) = n^18 + n^9 + 1.
- A326657 (program): a(n) = 4*floor(n/2) + ceiling((n-1)^2/2).
- A326658 (program): a(n) = 6*floor(n/2) + ceiling((n-1)^2/2).
- A326663 (program): Column 3 of the array at A309157; see Comments.
- A326664 (program): Column 3 of the array at A326661 see Comments.
- A326674 (program): GCD of the set of positions of 1’s in the reversed binary expansion of n.
- A326690 (program): Denominator of the fraction (Sum_{prime p | n} 1/p - 1/n).
- A326691 (program): a(n) = n/denominator(Sum_{prime p | n} 1/p - 1/n).
- A326708 (program): Non-Brazilian squares of primes.
- A326714 (program): a(n) = binomial(n,2) + (2-adic valuation of n).
- A326725 (program): a(n) = (1/2)*n*(5*n - 7); row 5 of A326728.
- A326728 (program): A(n, k) = n*(k - 1)*k/2 - k, square array for n >= 0 and k >= 0 read by ascending antidiagonals.
- A326730 (program): Number of iterations of A326729(x) starting at x = n to reach 0.
- A326732 (program): Number of iterations of A326731(x) starting at x = n to reach 0.
- A326781 (program): No position of a 1 in the reversed binary expansion of n is a power of 2.
- A326790 (program): The rank of the group of functions on the units of Z/nZ generated by the functions f(u) = u*k mod n.
- A326810 (program): The smallest prime that does not divide the prime product form (A276086) of the primorial base expansion of n.
- A326812 (program): Expansion of Sum_{k>=1} (2^k - 1) * x^(2^k - 1) / (1 - x^(2^k - 1)).
- A326813 (program): Dirichlet g.f.: zeta(2*s) / (1 - 2^(-s)).
- A326814 (program): Dirichlet g.f.: (1/zeta(s)) * Product_{p prime} (1 - 2 * p^(-s)).
- A326815 (program): Dirichlet g.f.: zeta(s)^3 * Product_{p prime} (1 - 2 * p^(-s)).
- A326822 (program): T(n, k) = k^0 if k = 1 else 0^n. Triangle read by rows, T(n, k) for 0 <= k <= n.
- A326933 (program): Number of nonconstant irreducible polynomial divisors of the n-th polynomial given in A326926.
- A326934 (program): Table of A(n,k) read by antidiagonals, where A(n,k)=(n*k) mod (n+1).
- A326937 (program): Dirichlet g.f.: (2^s - 1) / (zeta(s-1) * (2^s - 2)).
- A326987 (program): Number of nonpowers of 2 dividing n.
- A326988 (program): Sum of nonpowers of 2 dividing n.
- A326990 (program): Sum of odd divisors of n that are greater than 1.
- A326998 (program): a(n) = 1 + binomial(3*n-1, n) + binomial(3*n-1, n-1)*(binomial(2*n-1, n) + 1).
- A327007 (program): a(n) = number of iterations of f(x)=floor((x^2+n)/(2x)) starting at x=n to reach the value floor(sqrt(n)) (=A000196(n)).
- A327008 (program): a(n) = number of iterations of f(x)=floor((x^2+n^2)/(2x)) starting at x=n^2 to reach the value n.
- A327021 (program): a(n) = (2*n-1)! / 2^(n-1) if n > 0 and a(0) = 1.
- A327032 (program): a(n) = T(n, 4) with T(n, k) = Sum_{d|k} phi(d)*binomial(n - 1 + k/d, k/d).
- A327095 (program): Expansion of Sum_{k>=1} k * x^k * (1 - x^k + x^(2*k)) / (1 - x^(4*k)).
- A327096 (program): Expansion of Sum_{k>=1} sigma(k) * x^k / (1 - x^(2*k)), where sigma = A000203.
- A327122 (program): Expansion of Sum_{k>=1} sigma(k) * x^k / (1 + x^(2*k)), where sigma = A000203.
- A327139 (program): Numbers k such that cos(2k) > cos(2k+2) < cos(2k+4).
- A327142 (program): a(n) is the number of different sizes of integer-sided rectangles which can be placed inside an n X n square and with length greater than n.
- A327152 (program): r values of Triphosian primes.
- A327164 (program): Number of iterations of x -> gcd(usigma(x),x) needed to reach a fixed point, where usigma is the sum of unitary divisors of n (A034448).
- A327171 (program): a(n) = phi(n) * core(n), where phi is Euler totient function, and core gives the squarefree part of n.
- A327180 (program): a(n) = [(2n+1)r] - [(n+1)r] - [nr], where [ ] = floor and r = sqrt(3).
- A327242 (program): Expansion of Sum_{k>=1} tau(k) * x^k / (1 + x^k)^2, where tau = A000005.
- A327247 (program): Number of odd prime powers <= n (with exponents > 0).
- A327251 (program): Expansion of Sum_{k>=1} psi(k) * x^k / (1 - x^k)^2, where psi = A001615.
- A327252 (program): Balanced reversed ternary: Write n as ternary, reverse the order of the digits, then replace all 2’s with (-1)’s.
- A327253 (program): a(n) = floor(2*n*r) - 2*floor(n*r), where r = sqrt(6).
- A327256 (program): a(n) = floor(2*n*r) - 2*floor(n*r), where r = sqrt(8).
- A327276 (program): a(n) = Sum_{d|n, d odd} mu(d) * mu(n/d).
- A327278 (program): a(n) = Sum_{d|n, d odd} d * mu(d) * mu(n/d).
- A327310 (program): a(n) = floor(3*n*r) - 3*floor(n*r), where r = sqrt(8).
- A327319 (program): a(n) = binomial(n, 2) + 6*binomial(n, 4).
- A327326 (program): a(n) = A006218(n) - A005187(n).
- A327327 (program): Partial sums of the sum of nonpowers of 2 dividing n.
- A327329 (program): Twice the sum of all divisors of all positive integers <= n.
- A327367 (program): Number of labeled simple graphs with n vertices, at least one of which is isolated.
- A327374 (program): BII-numbers of set-systems with vertex-connectivity 2.
- A327376 (program): BII-numbers of set-systems with vertex-connectivity 3.
- A327411 (program): a(n) = multinomial(2*n+3; 3, 2, 2, …, 2) (n times ‘2’).
- A327412 (program): a(n) = multinomial(3*n+2; 2, 3, 3, …, 3) (n times ‘3’).
- A327440 (program): a(n) = floor(3*n/10).
- A327470 (program): Maximum valency of the central line in a certain smooth 2D-polarized K3-surface in P^{n+1}.
- A327474 (program): Number of distinct means of subsets of {1..n}, where {} has mean 0.
- A327486 (program): Product of Omegas of positive integers from 2 to n.
- A327491 (program): a(0) = 0. If 4 divides n then a(n) = valuation(n, 2) else a(n) = (n mod 2) + 1.
- A327492 (program): Partial sums of A327491.
- A327493 (program): a(n) = 2^A327492(n).
- A327496 (program): a(n) = a(n - 1) * 4^r where r = valuation(n, 2) if 4 divides n else r = (n mod 2) + 1; a(0) = 1. The denominators of A327495.
- A327497 (program): a(n) = Numerator([x^n] (4*sinh(sqrt(x)/2)^2*cosh(sqrt(x)))/x).
- A327503 (program): Number of steps to reach a fixed point starting with n and repeatedly taking the quotient by the maximum divisor that is 1 or not a perfect power (A327501, A327502).
- A327517 (program): Number of factorizations of n that are empty or have at least two factors, all of which are > 1 and pairwise coprime.
- A327521 (program): Number of factorizations of the n-th squarefree number A005117(n) into squarefree numbers > 1.
- A327555 (program): Decimal expansion of number with continued fraction expansion [1; 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, …].
- A327564 (program): If n = Product (p_j^k_j) then a(n) = Product ((p_j + 1)^(k_j - 1)).
- A327565 (program): Number of transfers of marbles between two sets until the first repetition.
- A327566 (program): Partial sums of the infinitary divisors sum function: a(n) = Sum_{k=1..n} isigma(k), where isigma is A049417.
- A327570 (program): a(n) = n*phi(n)^2, phi = A000010.
- A327572 (program): Partial sums of an infinitary analog of Euler’s phi function: a(n) = Sum_{k=1..n} iphi(k), where iphi is A091732.
- A327573 (program): Partial sums of the number of infinitary divisors function: a(n) = Sum_{k=1..n} id(k), where id is A037445.
- A327582 (program): a(n) = (17 * 7^(2*n+1) + 1)/24. Sequence related to the properties of the partition function A000041 modulo a power of 7.
- A327606 (program): Expansion of e.g.f. exp(x)*(1-x)*x/(1-2*x)^2.
- A327625 (program): Expansion of Sum_{k>=0} x^(3^k) / (1 - x^(3^k))^2.
- A327629 (program): Expansion of Sum_{k>=1} x^(k*(k + 1)/2) / (1 - x^(k*(k + 1)/2))^2.
- A327649 (program): Maximum value of powers of 2 mod n.
- A327650 (program): Maximum value of powers of 3 mod n.
- A327662 (program): Length of shortest word of frequency depth n.
- A327666 (program): a(n) = Sum_{k = 1..n} (-1)^(Omega(k) - omega(k)), where Omega(k) counts prime factors of k with multiplicity and omega(k) counts distinct prime factors.
- A327667 (program): a(n) is the least base >= 2 where n is the least number with its sum of digits.
- A327668 (program): a(n) = n * Sum_{d|n} (-1)^(bigomega(d) - omega(d)) / d.
- A327672 (program): a(n) = Sum_{k=0..n} ceiling(sqrt(k)).
- A327704 (program): The minimal size of a partition lambda of n such that every partition of n with at most 4 parts can be obtained by coalescing the parts of lambda.
- A327705 (program): The minimal size of a partition lambda of n such that every partition of n with at most 5 parts can be obtained by coalescing the parts of lambda.
- A327706 (program): The minimal size of a partition lambda of n such that every partition of n with at most 6 parts can be obtained by coalescing the parts of lambda.
- A327707 (program): The minimal size of a partition lambda of n such that every partition of n with at most 7 parts can be obtained by coalescing the parts of lambda.
- A327708 (program): The minimal size of a partition lambda of n such that every partition of n with at most 8 parts can be obtained by coalescing the parts of lambda.
- A327721 (program): Dimension of quantum lens space needed for non-uniqueness.
- A327724 (program): Product of A003059 and A071797.
- A327730 (program): a(n) = A060594(2n).
- A327737 (program): a(n) is the sum of the lengths of the base-b expansions of n for all b with 1 <= b <= n.
- A327752 (program): Primes powers (A246655) congruent to 1 mod 5.
- A327753 (program): Primes powers (A246655) congruent to 4 mod 5.
- A327760 (program): Primes in Rob Gahan’s arithmetic progression of 27 primes.
- A327765 (program): a(n) is the trace of the n-th power of the 2 X 2 matrix [1 2; 3 4].
- A327767 (program): Period 2: repeat [1, -2].
- A327770 (program): a(n) = (23 * 7^(2*n) + 1)/24. Sequence related to the properties of the partition function A000041 modulo a power of 7.
- A327819 (program): Elements of the unique smallest MSTD set of primes.
- A327821 (program): Number of legal Go positions on a board which is an n-cycle graph.
- A327836 (program): Least k > 0 such that n^k == 1 (mod (n+1)^(n+1)).
- A327853 (program): Triangle read by rows, Sierpinski’s gasket, A047999 * (0,1,2,3,4,…) diagonalized.
- A327858 (program): a(n) = gcd(A003415(n), A276086(n)).
- A327859 (program): a(n) = A276086(A003415(n)), where A003415 is the arithmetic derivative and A276086 converts digits of primorial base representation to exponents in prime factorization.
- A327860 (program): a(n) = A003415(A276086(n)).
- A327866 (program): a(n) = 1 if arithmetic derivative of n is square, 0 otherwise. Cf. A003415.
- A327868 (program): Number of achiral loops (necklaces or bracelets) of length n with integer entries that cover an initial interval of positive integers.
- A327882 (program): a(n) = n*(2*(n-1))! for n > 0, a(0) = 1.
- A327896 (program): a(n) is the minimum number of tiles needed for constructing a polyiamond with n holes.
- A327904 (program): Number of labeled simple graphs with vertices {1..n} such that every edge has a different sum.
- A327916 (program): Triangle T(k, n) read by rows: Array A(k, n) = 2^k*(k + 1+ n), k >= 0, n >= 0, read by antidiagonals upwards.
- A327917 (program): Triangle T read by rows: T(k, n) = A(k-n, k) with the array A(k, n) = F(2*k+n) = A000045(2*k+n), for k >= 0 and n >= 0.
- A327926 (program): a(n) = 99^n.
- A327936 (program): Multiplicative with a(p^e) = p if e >= p, otherwise 1.
- A327938 (program): Multiplicative with a(p^e) = p^(e mod p).
- A327939 (program): Multiplicative with a(p^e) = p^(e-(e mod p)).
- A327961 (program): Sum of products of n-bit numbers with their n-bit reverse.
- A327986 (program): Denominators of the coefficients in the expansion of (4*sinh(sqrt(x)/2)^2*cosh(sqrt(x)))/x.
- A327993 (program): a(n) = [x^n] ((x - 1)*(x + 1)*(2*x^2 - 1))/(2*x^4 + 4*x^3 - x^2 - 3*x + 1).
- A327998 (program): a(n) = (n!/floor(n/2)!^2)^2.
- A327999 (program): a(n) = Sum_{k=0..2n}(k!*(2n - k)!)/(floor(k/2)!*floor((2n - k)/2)!)^2.
- A328002 (program): a(n) = 2^n * Sum_{k=0..n} Product_{j=1..k} (2/j)^((-1)^j).
- A328005 (program): Number of distinct coefficients in functional composition of 1 + x + … + x^(n-1) with itself.
- A328011 (program): The 5x + 1 sequence beginning at 1.
- A328012 (program): Numbers whose binary representations start and end with 1 and contain an even number of zeros between.
- A328034 (program): a(n) = 3n minus the largest power of 2 not exceeding 3n.
- A328055 (program): Expansion of e.g.f. -log(1 - x / (1 - x)^2).
- A328082 (program): Triangle read by rows: columns are Fibonacci numbers F_{2i+1} shifted downwards.
- A328085 (program): Column sums of triangle A328084.
- A328141 (program): a(n) = a(n-1) - (n-2)*a(n-2), with a(0)=1, a(1)=2.
- A328152 (program): a(n) is the number of squares of side length greater than 1 having vertices at the points of an n X n grid of dots.
- A328154 (program): G.f. A(x) satisfies: A(x) = A(x^2) + x / (1 + x)^2.
- A328181 (program): a(n) = (-1)^(bigomega(n) - omega(n)) * Sum_{d|n} (-1)^(bigomega(d) - omega(d)) * d.
- A328182 (program): Expansion of e.g.f. 1 / (2 - exp(3*x)).
- A328183 (program): Expansion of e.g.f. 1 / (2 - exp(4*x)).
- A328184 (program): Denominator of time taken for a vertex of a rolling regular n-sided polygon to reach the ground.
- A328185 (program): Numerators associated with A328184.
- A328203 (program): Expansion of Sum_{k>=1} k * x^k / (1 - x^(2*k))^2.
- A328231 (program): a(n) = gcd(n, A048673(n)).
- A328258 (program): a(n) = Sum_{d|n, gcd(d,n/d) = 1} (-1)^(d + 1) * d.
- A328259 (program): a(n) = n * sigma_2(n).
- A328260 (program): a(n) = n * omega(n).
- A328262 (program): a(n) = a(n-1)*3/2, if noninteger then rounded to the nearest even integer, with a(1) = 1.
- A328263 (program): a(n) = number of letters in a(n-1) (in Polish), with a(1) = 1.
- A328271 (program): Expansion of Sum_{k>=1} x^(k^2) * (1 + x^(k^2)) / (1 - x^(k^2))^3.
- A328283 (program): The maximum number m such that m white, m black and m red queens can coexist on an n X n chessboard without attacking each other.
- A328284 (program): An extension of the Jacobsthal numbers: 0, 0, 1, followed by A001045.
- A328286 (program): Expansion of e.g.f. -log(1 - x - x^2/2).
- A328308 (program): a(n) = 1 if k-th arithmetic derivative of n is zero for some k, otherwise 0.
- A328309 (program): a(n) tells how many numbers there are in range 0..n such that their k-th arithmetic derivative is zero for some k >= 0.
- A328317 (program): Smallest prime not dividing A328316(n), with a(0) = 1 by convention; Equally, for n > 0, smallest prime dividing A328316(1+n).
- A328332 (program): Expansion of (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).
- A328333 (program): Expansion of (1 + 4*x - 6*x^2) / ((1 - x) * (1 - 10*x^2)).
- A328337 (program): The number whose binary indices are the nontrivial divisors of n (greater than 1 and less than n).
- A328348 (program): Let S be any integer in the range 3 <= S <= 17. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and contains at most two distinct nonzero digits p and q such that p+q=S.
- A328350 (program): Let S be any integer in the range 6 <= S <= 24. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and contains at most three distinct nonzero digits d1, d2, d3 such that d1+d2+d3 = S.
- A328351 (program): Let S be any integer in the range 10 <= S <= 30. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and contains at most four distinct nonzero digits d1, d2, d3 and d4 such that d1+d2+d3+d4=S.
- A328352 (program): Similar to A328350, but for 5 digits rather then 3.
- A328353 (program): a(n)*S is the sum of all positive integers whose decimal expansion is up to n digits and uses six distinct nonzero digits d1,d2,d3,d4,d5,d6 such that d1+d2+d3+d4+d5+d6=S.
- A328354 (program): a(n)*S is the sum of all positive integers whose decimal expansion is up to n digits and uses seven distinct nonzero digits d1,d2,d3,d4,d5,d6,d7 such that d1+d2+d3+d4+d5+d6+d7=S.
- A328355 (program): Let S be any integer in the range 36 <= S <= 44. Sequence has the property that a(n)*S is the sum of all positive integers whose decimal expansion has <= n digits and uses eight distinct nonzero digits d1,d2,d3,d4,d5,d6,d7,d8 such that d1+d2+d3+d4+d5+d6+d7+d8=S.
- A328356 (program): a(n) is the sum of all positive integers whose decimal expansion is up to n digits and does not contain the 0 digit.
- A328366 (program): a(n) is the surface area of the stepped pyramid with n levels described in A245092.
- A328372 (program): Expansion of Sum_{k>=1} x^(k^2) / (1 - x^(2*k^2)).
- A328373 (program): Expansion of Sum_{k>=1} x^(k^2) * (1 + x^(2*k^2)) / (1 - x^(2*k^2))^2.
- A328386 (program): a(n) = A276086(n) mod n.
- A328403 (program): a(n) = A276086(A276086(A276086(n))), where A276086(n) converts primorial base expansion of n into its prime product form.
- A328407 (program): G.f. A(x) satisfies: A(x) = A(x^2) + x * (1 + x) / (1 - x)^3.
- A328408 (program): G.f. A(x) satisfies: A(x) = A(x^2) + x * (1 + 4*x + x^2) / (1 - x)^4.
- A328449 (program): Smallest number in whose divisors the longest run is of length n, and 0 if none exists.
- A328484 (program): Dirichlet g.f.: zeta(s)^2 / (1 - 3^(-s)).
- A328485 (program): Dirichlet g.f.: zeta(s)^2 * zeta(s-1) / zeta(2*s-1).
- A328490 (program): Dirichlet g.f.: zeta(s)^2 * zeta(s-2)^2.
- A328502 (program): Dirichlet g.f.: zeta(s-1) / (zeta(s) * zeta(s-2)).
- A328563 (program): Nonsquarefree unitary weird numbers that are also weird numbers.
- A328564 (program): a(n) is the sum of the elements of the set A_n = {(n-k) AND k, k = 0..n} (where AND denotes the bitwise AND operator).
- A328565 (program): a(n) is the sum of the elements of the set X_n = {(n-k) XOR k, k = 0..n} (where XOR denotes the bitwise XOR operator).
- A328566 (program): a(n) is the sum of the elements of the set O_n = {(n-k) OR k, k = 0..n} (where OR denotes the bitwise OR operator).
- A328570 (program): Index of the least significant zero digit in the primorial base expansion of n, when the rightmost digit is in the position 1.
- A328571 (program): Primorial base expansion of n converted into its prime product form, but with all nonzero digits replaced by 1’s: a(n) = A007947(A276086(n)).
- A328572 (program): Primorial base expansion of n converted into its prime product form, but with 1 subtracted from all nonzero digits: a(n) = A003557(A276086(n)).
- A328580 (program): a(n) is the largest primorial dividing A276086(n), where A276086 converts the primorial base expansion of n into its prime product form.
- A328584 (program): Least common multiple of n and A276086(n).
- A328604 (program): G.f.: (1 + 7*x) / (1 - 2*x - 9*x^2).
- A328605 (program): Expansion of (1 + 5*x - 2*x^2 - 15*x^3) / (1 - 12*x^2 + 25*x^4).
- A328606 (program): Expansion of (1 + 9*x) / (1 - 2*x - 11*x^2).
- A328615 (program): Number of digits larger than 1 in primorial base expansion of n.
- A328621 (program): Multiplicative with a(p^e) = p^(2e mod p).
- A328639 (program): Dirichlet g.f.: zeta(2*s) / (zeta(s) * zeta(s-2)).
- A328640 (program): Dirichlet g.f.: zeta(2*s) / (zeta(s) * zeta(s-3)).
- A328641 (program): Dirichlet g.f.: zeta(s)^2 / zeta(s-1)^2.
- A328659 (program): Partial sums of A035100: number of binary digits of the primes.
- A328661 (program): If n is the k-th composite number then a(n) = a(k), otherwise a(n) = n.
- A328683 (program): Positive integers that are equal to 99…99 (repdigit with n digits 9) times the sum of their digits.
- A328694 (program): a(n) = sum of lead terms of all parking functions of length n.
- A328722 (program): Dirichlet g.f.: 1 / zeta(s-1)^2.
- A328729 (program): Dirichlet g.f.: zeta(s) / (zeta(s-1) * zeta(2*s)).
- A328745 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - p^(-s))^p.
- A328749 (program): a(n) = Sum_{k = 0..w and t_k > 0} (-1)^t_k * 2^k, where Sum_{k = 0..w} t_k * 3^k is the ternary representation of n.
- A328778 (program): Number of indecomposable closed walks of length 2n along the edges of a cube based at a vertex.
- A328791 (program): Triangular numbers of the form k^2 + 3.
- A328812 (program): Constant term in the expansion of (Product_{k=1..n} (1 + x_k) + Product_{k=1..n} (1 + 1/x_k))^n.
- A328819 (program): Third digit after decimal point of square root of n.
- A328820 (program): Fourth digit after decimal point of square root of n.
- A328821 (program): Triangular array read by rows. Let P be the poset of all even sized subsets of [2n] ordered by inclusion. T(n,k) is the number of intervals in P with length k, 0<=k<=n, n>=0.
- A328823 (program): a(n) is the least prime factor of A000096(n) = n*(n+3)/2.
- A328824 (program): Numerators of A113405(-n) (see the comment for details).
- A328827 (program): a(n) is the largest prime factor of n + n*(n+1)/2 = n*(n+3)/2.
- A328854 (program): Dirichlet g.f.: Product_{p prime} 1 / (1 - 2 * p^(-s))^2.
- A328865 (program): The first repeating term in the trajectory of n under iterations of A329623, or -1 if no such terms exists.
- A328881 (program): a(n+3) = 2^n - a(n), a(0)=a(2)=1, a(1)=0 for n >= 0.
- A328882 (program): a(n) = n - 2^(sum of digits of n).
- A328886 (program): Squares that end in 444.
- A328890 (program): Number of acyclic edge covers of the complete bipartite graph K_{n,2}.
- A328892 (program): If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)).
- A328898 (program): Sum of p-ary comparisons units required to rank a sequence in parallel when the sequence is partitioned into heaps equal to the prime factors p of the initial sequence length n.
- A328915 (program): If n = Product (p_j^k_j) then a(n) = Product (nextprime(p_j)), where nextprime = A151800.
- A328943 (program): a(n) = 2 + (n mod 4).
- A328946 (program): Product of primorials of consecutive integers (second definition A034386).
- A328950 (program): Numerators for the “Minimum-Redundancy Code” card problem.
- A328979 (program): Trajectory of 0 under repeated application of the morphism 0 -> 0010, 1 -> 1010.
- A328981 (program): Indicator function of numbers whose binary representation ends in an even positive number of 0’s.
- A328982 (program): Sorted list of the numbers of the form 5m+2 (m>=0) together with numbers of the form 5m-2+eps (m>=1), where eps = 1 if the binary expansion of m ends in an odd number of 0’s and is otherwise 0.
- A328984 (program): If n is even, a(n) = floor((5t+1)/2) where t=n/2; if n == 1 (mod 4) then a(n) = 10t+1 where t = (n-1)/4; and if n == 3 (mod 4) then a(n) = 10t+7 where t = (n-3)/4.
- A328985 (program): First differences of A328984.
- A328987 (program): The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 0).
- A328990 (program): a(n) = (3*b(n) + b(n-1) + 1)/2, where b = A005409.
- A328994 (program): a(n) = n^2*(1+n)*(1+n^2)/4.
- A329005 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
- A329007 (program): a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
- A329008 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
- A329009 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
- A329010 (program): a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
- A329014 (program): a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.
- A329015 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.
- A329018 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
- A329019 (program): a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
- A329031 (program): a(n) = A327860(A328841(n)).
- A329114 (program): a(n) = floor(A026532(n)/5).
- A329115 (program): a(n) = floor(A026549(n)/5).
- A329116 (program): Successively count to (-1)^(n+1)*n (n = 0, 1, 2, … ).
- A329119 (program): Orders of the finite groups SL_2(K) when K is a finite field with q = A246655(n) elements.
- A329145 (program): Number of non-necklace compositions of n.
- A329153 (program): Sum of the iterated unitary totient function (A047994).
- A329162 (program): a(n) = Sum_{k<n} ((2^n-1) mod (2^k-1)).
- A329178 (program): Sum of the products of pairs of Padovan numbers which are two apart, starting from A000931(5).
- A329193 (program): a(n) = floor(log_2(n^3)) = floor(3 log_2(n))
- A329194 (program): a(n) = floor(log_3(n^2)) = floor(2 log_3(n))
- A329195 (program): a(n) = floor(log_5(n^2)) = floor(2 log_5(n))
- A329199 (program): a(n) = round(log_3(n)).
- A329202 (program): a(n) = floor(2*log_2(n)) = floor(log_2(n^2)).
- A329208 (program): Decimal expansion of the fundamental frequency of the note C#4/Db4 in hertz.
- A329210 (program): Decimal expansion of the fundamental frequency of the note D#4/Eb4 in hertz.
- A329212 (program): Decimal expansion of the fundamental frequency of the note F4 in hertz.
- A329219 (program): Decimal expansion of 2^(10/12) = 2^(5/6).
- A329221 (program): a(0)=0. If a(n)=k is the first occurrence of k then a(n+1)=a(k), otherwise a(n+1)=n-m where m is the index of the greatest prior term.
- A329227 (program): Products of consecutive terms of the Padovan sequence A000931.
- A329244 (program): Sum of every third term of the Padovan sequence A000931.
- A329249 (program): Starting from n: as long as the decimal representation starts with an odd number, multiply the largest such prefix by 2; a(n) corresponds to the final value.
- A329277 (program): a(n) is the fixed point reached by iterating Euler’s gradus function A275314 starting at n.
- A329278 (program): Irregular table read by rows. The n-th row is the permutation of {0, 1, 2, …, 2^n-1} given by T(n,k) = k(k+1)/2 (mod 2^n).
- A329279 (program): Number of distinct tilings of a 2n X 2n square with 1 x n polyominoes.
- A329301 (program): a(0) = a(1) = a(2) = 1; thereafter a(n) = a(n-1) - (-1)^n*a(n-2) + 2*a(n-3).
- A329304 (program): Numerators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, …].
- A329305 (program): Denominators of convergents to A309930, the constant whose continued fraction representation consists of the cubes, [0; 1, 8, 27, 64, …].
- A329320 (program): a(n) = Sum_{k=0..floor(log_2(n))} 1 - A035263(1 + floor(n/2^k)).
- A329376 (program): Multiplicative with a(p^e) = p when e == 2, otherwise a(p^e) = 1.
- A329379 (program): a(n) = n/A093411(n), where A093411(n) is obtained by repeatedly dividing n by the largest factorial that divides it until an odd number is reached.
- A329393 (program): Number of odd divisors minus number of even divisors of the n-th composite.
- A329402 (program): Number of rectangles (w X h, w <= h) with integer side lengths w and h having area = n * perimeter.
- A329404 (program): Interleave 2*n*(3*n-1), (2*n+1)*(6*n+1) for n >= 0.
- A329422 (program): Maximum length of a binary n-similar word.
- A329444 (program): The sixth moments of the squared binomial coefficients; a(n) = Sum_{m=0..n} m^6*binomial(n, m)^2.
- A329470 (program): a(n) = 2 a(n-1)^2 + 1 for n >=2 , where a(0) = 1, a(1) = 1.
- A329480 (program): a(n) = (1 - A075677(n))/6 if 6|(A075677(n)-1) or a(n) = (A075677(n) + 1)/6 if 6|(A075677(n)+1).
- A329482 (program): Interleave 1 - n + 3*n^2, 1 + 3*n*(1+n) for n >= 0.
- A329484 (program): Dirichlet convolution of the Louiville function with itself.
- A329486 (program): a(n) = 3*A006519(n)/2 + n/2 where A006519(n) is the highest power of 2 dividing n.
- A329488 (program): a(n) = A001350(n)^4.
- A329494 (program): Numerator of 2*(2*n+1)/(n+2).
- A329502 (program): G.f. = (1+x)*(1+2*x)/(1-x).
- A329503 (program): G.f. = (1+x)*(1+2*x+2*x^2)/(1-x).
- A329505 (program): Expansion of (1 + x)*(1 + 2*x - x^2) / (1 - x).
- A329506 (program): Expansion of (1 + x)*(1 + 2*x + 2*x^2 - 2*x^3) / (1 - x).
- A329507 (program): Expansion of (1 + x)*(1 + 2*x + 2*x^2 + 2*x^3 - 3*x^4) / (1 - x).
- A329509 (program): Expansion of (1 + x)*(1 + x + x^2 - x^3) / (1 - x).
- A329510 (program): Expansion of (1 + x)*(1 + x + x^2)*(1 + x^2 - x^3) / (1 - x).
- A329511 (program): Expansion of (1 + x)*(1 + x^2)^2*(1 + x - x^3) / (1 - x).
- A329513 (program): G.f. = (1+x)^2*(1+2*x^2-x^3)/(1-x).
- A329516 (program): G.f. = (x^4 - x^3 - 3*x^2 - 2*x - 1)/(x - 1).
- A329523 (program): a(n) = n * (binomial(n + 1, 3) + 1).
- A329530 (program): a(n) = n * (7*binomial(n, 2) + 1).
- A329533 (program): First differences of A051924, or second differences of Central binomial coefficients A000984.
- A329547 (program): Number of natural numbers k <= n such that k^k is a square.
- A329550 (program): Total number of consecutive triples of the form (odd, even, odd) or (even, odd, even) in all permutations of [n].
- A329562 (program): a(n) = 2^(sum of digits of n).
- A329583 (program): Numerators of 1 + n^2/4 + period 3: repeat [-1, 1, 1].
- A329598 (program): Partial sums of the nontriangular numbers (A014132).
- A329625 (program): Smallest BII-number of a connected set-system with n edges.
- A329664 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.
- A329670 (program): Number of excursions of length n with Motzkin-steps allowing only consecutive steps UH and HD.
- A329673 (program): Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH.
- A329677 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, HD, and DH.
- A329678 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UD and DH.
- A329679 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, UD, HD and DH.
- A329680 (program): Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, HD and DU.
- A329682 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, UD, HU and DD.
- A329683 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, HH and HD.
- A329684 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UD and HH.
- A329686 (program): Number of excursions of length n with Motzkin-steps forbidding all consecutive steps of length 2 except UH, HU, HD and DH.
- A329687 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, UD, HH and DH.
- A329688 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UU, HH, HD and DU.
- A329696 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU, HD and DH.
- A329697 (program): a(n) is the number of iterations needed to reach a power of 2 starting at n and using the map k -> k-(k/p), where p is the largest prime factor of k.
- A329699 (program): Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU and HH.
- A329717 (program): a(n) is n (plus or minus) the number of distinct primes dividing n according to parity (even or odd).
- A329723 (program): Coefficients of expansion of (1-2x^3)/(1-x-x^2) in powers of x.
- A329728 (program): Partial sums of A092261.
- A329753 (program): Doubly square pyramidal numbers.
- A329754 (program): Doubly pentagonal pyramidal numbers.
- A329774 (program): a(n) = n+1 for n <= 2; otherwise a(n) = 3*a(n-3)+1.
- A329791 (program): a(n) = floor(sqrt(2)*n) + floor(sqrt(3)*n).
- A329822 (program): The minimum weight of a Boolean function of algebraic degree at most n-3 whose support contains n linearly independent elements.
- A329825 (program): Beatty sequence for (3+sqrt(17))/4.
- A329826 (program): Beatty sequence for (5+sqrt(17))/4.
- A329827 (program): Beatty sequence for (5+sqrt(37))/6.
- A329828 (program): Beatty sequence for (7+sqrt(37))/6.
- A329829 (program): Beatty sequence for (2+sqrt(10))/3.
- A329830 (program): Beatty sequence for (4+sqrt(10))/3.
- A329831 (program): Beatty sequence for (7+sqrt(65))/8.
- A329832 (program): Beatty sequence for (9+sqrt(65))/8.
- A329833 (program): Beatty sequence for (5+sqrt(73))/8.
- A329834 (program): Beatty sequence for (11+sqrt(73))/8.
- A329835 (program): Beatty sequence for (9+sqrt(101))/10.
- A329836 (program): Beatty sequence for (11+sqrt(101))/10.
- A329837 (program): Beatty sequence for (4+sqrt(26))/5.
- A329838 (program): Beatty sequence for (6+sqrt(26))/5.
- A329839 (program): Beatty sequence for (-1+sqrt(41))/4.
- A329840 (program): Beatty sequence for (9+sqrt(41))/4.
- A329841 (program): Beatty sequence for (7+sqrt(109))/10.
- A329842 (program): Beatty sequence for (13+sqrt(109))/10.
- A329843 (program): Beatty sequence for (1+sqrt(61))/6.
- A329844 (program): Beatty sequence for (11+sqrt(61))/6.
- A329845 (program): Beatty sequence for (3+sqrt(29))/5.
- A329846 (program): Beatty sequence for (7+sqrt(29))/5.
- A329847 (program): Beatty sequence for (3+sqrt(89))/8.
- A329848 (program): Beatty sequence for (13+sqrt(89))/8.
- A329854 (program): Triangle read by rows: T(n,k) = ((n - k)*(n + k - 1) + 2)/2, 0 <= k <= n.
- A329913 (program): The fifth moments of the squared binomial coefficients; a(n) = Sum_{m=0..n} m^5*binomial(n, m)^2.
- A329923 (program): Beatty sequence for (2+sqrt(34))/5.
- A329924 (program): Beatty sequence for (8+sqrt(34))/5.
- A329925 (program): Beatty sequence for (1+sqrt(41))/5.
- A329926 (program): Beatty sequence for (9+sqrt(41))/5.
- A329928 (program): a(n) = (Pi/2)*(2*n+1)!*binomial(2*n+1, (2*n+1)/2).
- A329930 (program): a(n) = n!^2*(Sum_{k=1..n} 1/k).
- A329938 (program): Beatty sequence for sinh x, where csch x + sech x = 1 .
- A329939 (program): Beatty sequence for cosh x, where csch x + sech x = 1 .
- A329940 (program): Square array read by antidiagonals upwards: T(n,k) is the number of right unique relations between set A with n elements and set B with k elements.
- A329943 (program): Square array read by antidiagonals: T(n,k) is the number of right total relations between set A with n elements and set B with k elements.
- A329949 (program): Lexicographically earliest sequence of positive numbers such that following proposition is true: a(n) is the number of occurrences of a(n+1) in the sequence so far, up to and including a(n+1).
- A329952 (program): Numbers k such that binomial(k,3) is divisible by 8.
- A329961 (program): Beatty sequence for 2 + sin x, where x = least positive solution of 1/(2 + sin x) + 1/(2 + cos x) = 1.
- A329962 (program): Beatty sequence for 2 + cos x, where x = least positive solution of 1/(2 + sin x) + 1/(2 + cos x) = 1.
- A329964 (program): a(n) = (n!/floor(1+n/2)!)^2.
- A329965 (program): a(n) = ((1+n)*floor(1+n/2))*(n!/floor(1+n/2)!)^2.
- A329970 (program): a(n) = (-1)^(n + 1) * n * ceiling(n/2) + Sum_{k=1..n} (-1)^k * k^2 * floor(n/k).
- A329974 (program): Beatty sequence for the real solution x of 1/x + 1/(1+x+x^2) = 1.
- A329975 (program): Beatty sequence for 1 + x + x^2, where x is the real solution of 1/x + 1/(1+x+x^2) = 1.
- A329977 (program): Beatty sequence for the number x satisfying 1/x + 1/(log x) = 1.
- A329978 (program): Beatty sequence for log x, where 1/x + 1/(log x) = 1.
- A329987 (program): Beatty sequence for the number x satisfying 1/x + 1/2^x = 1.
- A329988 (program): Beatty sequence for 2^x, where 1/x + 1/2^x = 1.
- A329990 (program): Beatty sequence for the number x satisfying 1/x + 1/3^x = 1.
- A329991 (program): Beatty sequence for 3^x, where 1/x + 1/3^x = 1.
- A329993 (program): Beatty sequence for x^2, where 1/x^2 + 1/2^x = 1.
- A329994 (program): Beatty sequence for 2^x, where 1/x^2 + 1/2^x = 1.
- A329996 (program): Beatty sequence for x^3, where 1/x^3 + 1/3^x = 1.
- A329997 (program): Beatty sequence for 3^x, where 1/x^3 + 1/3^x = 1.
- A329999 (program): Beatty sequence for sqrt(x-1), where 1/sqrt(x-1) + 1/sqrt(x+1) = 1.
- A330000 (program): Beatty sequence for sqrt(x+1), where 1/sqrt(x-1) + 1/sqrt(x+1) = 1.
- A330002 (program): Beatty sequence for x, where 1/x + 1/(x+1)^2 = 1.
- A330003 (program): Beatty sequence for (x+1)^2, where 1/x + 1/(x+1)^2 = 1.
- A330010 (program): Number of length-n ternary strings x with the property that if w is a subword of x and |w| >= 3, then w reversed is not a subword of x.
- A330016 (program): a(n) = Sum_{k=1..n} (-1)^(n - k) * H(k) * k!, where H(k) is the k-th harmonic number.
- A330023 (program): a(n) counts the cube-words immediately before a(n), with a(1) = 0.
- A330025 (program): a(n) = (-1)^floor(n/5) * sign(mod(n, 5)).
- A330033 (program): a(n) = Kronecker(n, 5) * (-1)^floor(n/5).
- A330038 (program): a(1) = 1, a(n) = [n/2] + a([n/2]) + a([(n+1)/2]) for n > 1, where [x] = floor(x).
- A330044 (program): Expansion of e.g.f. exp(x) / (1 - x^3).
- A330045 (program): Expansion of e.g.f. exp(x) / (1 - x^4).
- A330051 (program): a(n) = 1 + F(2*n+1) + (F(n+4) - (-1)^n*F(n-2))/2 where F=A000045.
- A330055 (program): Number of non-isomorphic set-systems of weight n with no singletons or endpoints.
- A330063 (program): Beatty sequence for x, where 1/x + sech(x) = 1.
- A330064 (program): Beatty sequence for cosh(x), where 1/x + sech(x) = 1.
- A330066 (program): Beatty sequence for x, where 1/x + csch(x) = 1.
- A330067 (program): Beatty sequence for sinh(x), where 1/x + 1/sinh(x) = 1.
- A330072 (program): a(n) is the sum of all integers whose binary representation is contained in the binary representation of n (with multiplicity).
- A330082 (program): a(n) = 5*A064038(n).
- A330085 (program): Length of longest binary word with the property that all distinct occurrences of identical-length blocks agree on at most n positions.
- A330094 (program): Beatty sequence for 2^x, where 1/2^x + 1/3^(x-1) = 1.
- A330095 (program): Beatty sequence for 3^(x-1), where 1/2^x + 1/3^(x-1) = 1.
- A330112 (program): Beatty sequence for e^x, where 1/e^x + sech(x) = 1.
- A330113 (program): Beatty sequence for cosh(x), where 1/e^x + sech(x) = 1.
- A330115 (program): Beatty sequence for e^x, where 1/e^x + csch(x) = 1.
- A330116 (program): Beatty sequence for sinh(x), where 1/e^x + csch(x) = 1.
- A330117 (program): Beatty sequence for 1+x, where 1/(1+x) + 1/(1+x+x^2) = 1.
- A330118 (program): Beatty sequence for 1+x+x^2, where 1/(1+x) + 1/(1+x+x^2) = 1.
- A330133 (program): a(n) = (1/16)*(5 + (-1)^(1+n) - 4*cos(n*Pi/2) + 10*n^2).
- A330139 (program): a(1)=1 and a(2)=1; if a(n-1)+a(n-2) == 0 mod n then a(n) = (a(n-1)+a(n-2))/n else a(n) = a(n-1)+a(n-2).
- A330143 (program): Beatty sequence for (3/2)^x, where (3/2)^x + (5/2)^x = 1.
- A330144 (program): Beatty sequence for (5/2)^x, where (3/2)^x + (5/2)^x = 1.
- A330151 (program): Partial sums of 4th powers of the even numbers.
- A330156 (program): Decimal expansion of the continued fraction expansion [1; 1/2, 1/3, 1/4, 1/5, 1/6, …].
- A330168 (program): Length of the longest run of 2’s in the ternary expression of n.
- A330170 (program): a(n) = 2^n + 3^n + 6^n - 1.
- A330171 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(2) - 1, s = sqrt(2), t = sqrt(2) + 1.
- A330172 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = sqrt(2) - 1, s = sqrt(2), t = sqrt(2) + 1.
- A330173 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(2), s = sqrt(2) + 1, t = sqrt(2) + 2.
- A330175 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = sqrt(5) - 2, s = sqrt(5) - 1, t = sqrt(5).
- A330176 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = sqrt(5) - 2, s = sqrt(5) - 1, t = sqrt(5).
- A330179 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = e - 1, s = e, t = e + 1.
- A330180 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = e - 1, s = e, t = e + 1.
- A330181 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = Pi - 1, s = Pi, t = Pi + 1.
- A330185 (program): a(n) = n + floor(ns/r) + floor(nt/r), where r = tau - 1/2, s = tau, t = tau + 1/2, tau = golden ratio = (1+sqrt(5))/2.
- A330186 (program): a(n) = n + floor(nr/t) + floor(ns/t), where r = tau - 1/2, s = tau, t = tau + 1/2, tau = golden ratio = (1+sqrt(5))/2.
- A330197 (program): Number of scalene triangles whose vertices are the vertices of a regular n-gon.
- A330225 (program): Position of first appearance of n in A290103 = LCM of prime indices.
- A330241 (program): a(n) is the greatest k such that there is an increasing sequence of positive integers j(0),j(1),…,j(k) such that n == i (mod j(i)) for each i.
- A330246 (program): a(n) = 4^(n+1) + (4^n-1)/3.
- A330260 (program): a(n) = n! * Sum_{k=0..n} binomial(n,k) * n^(n - k) / k!.
- A330285 (program): The maximum number of arithmetic progressions for a sequence of length n.
- A330298 (program): a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 2 even numbers.
- A330299 (program): a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 3 even numbers.
- A330300 (program): a(n) is the number of subsets of {1..n} that contain exactly 2 odd and 3 even numbers.
- A330302 (program): Number of chains of 2-element subsets of {0,1, 2, …, n} that contain no consecutive integers.
- A330315 (program): a(n) = r(n)*r(n+1), where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
- A330316 (program): a(n) = r(n)*r(n+1)/4, where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
- A330317 (program): a(n) = Sum_{i=0..n} r(i)*r(i+1), where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
- A330318 (program): a(n) = Sum_{i=0..n} r(i)*r(i+1)/4, where r(n) = A004018(n) is the number of ways of writing n as a sum of two squares.
- A330319 (program): a(n) = Sum_{i=1..n} phi(i)*phi(i+1), where phi(n) = A000010(n) is Euler’s totient function.
- A330320 (program): a(n) = Sum_{i=1..n} tau(i)*tau(i+1), where tau(n) = A000005(n) is the number of divisors of n.
- A330321 (program): a(n) = Sum_{i=1..n} tau(i)*tau(i+1)/2, where tau(n) = A000005(n) is the number of divisors of n.
- A330322 (program): a(n) = Sum_{i=1..n} sigma(i)*sigma(i+1), where sigma(n) = A000203(n) is the sum of the divisors of n.
- A330323 (program): a(n) = Moebius(n)*Moebius(n+1).
- A330324 (program): a(n) = Sum_{i=1..n} Moebius(i)*Moebius(i+1), where Moebius(n) = A008683(n).
- A330349 (program): a(n) = A070826(n+1) - 2^(n-1).
- A330357 (program): a(n) = (2*n^2 + 9 - (-1)^n)/4.
- A330390 (program): G.f.: (1 + 15*x) / (1 - 2*x - 17*x^2).
- A330393 (program): A 2-regular sequence whose reciprocal is not 2-regular.
- A330395 (program): Number of nontrivial equivalence classes of S_n under the {1234,3412} pattern-replacement equivalence.
- A330396 (program): Permutation of the nonnegative integers partitioned into triples [3*k+2, 3*k+1, 3*k] for k >= 0.
- A330405 (program): a(1) = 0; thereafter a(n) = (a(n-1)^2+1) mod n.
- A330410 (program): a(n) = 6*prime(n) - 1.
- A330451 (program): a(n) = a(n-3) + 20*n - 30 for n > 2, with a(0)=0, a(1)=3, a(2)=13.
- A330476 (program): a(n) = Sum_{m=2..n} floor(n/m)^2.
- A330479 (program): Decimal expansion of 2*e^2-2 (or 2*(e^2-1)).
- A330492 (program): a(n) = sum of second differences of the sorted divisors of n.
- A330497 (program): a(n) = n! * Sum_{k=0..n} (-1)^k * binomial(n,k) * n^(n - k) / k!.
- A330503 (program): Number of Sós permutations of {0,1,…,n}.
- A330505 (program): Expansion of e.g.f. Sum_{k>=1} arctanh(x^k).
- A330511 (program): Expansion of e.g.f. Sum_{k>=1} arctan(x^k).
- A330520 (program): Sum of even integers <= n times the sum of odd integers <= n.
- A330545 (program): a(1) = 2; thereafter a(n) = a(n-1) + (-1)^(n + 1)*(prime(n) - prime(n - 1) - 1) (where prime(k) denotes the k-th prime).
- A330547 (program): a(1)=2; thereafter a(n) = a(n-1) + (-1)^(n+1)*(prime(n)-prime(n-1)) (where prime(k) denotes the k-th prime).
- A330559 (program): a(n) = (number of primes p <= prime(n) with Delta(p) == 2 mod 4) - (number of primes p <= prime(n) with Delta(p) == 0 mod 4), where Delta(p) = nextprime(p) - p.
- A330560 (program): a(n) = number of primes p <= prime(n) with Delta(p) == 2 mod 4, where Delta(p) = nextprime(p) - p.
- A330561 (program): a(n) = number of primes p <= prime(n) with Delta(p) == 0 mod 4, where Delta(p) = nextprime(p) - p.
- A330565 (program): The thirteen entries from A005848 for which the integers of the cyclotomic field form a Euclidean ring with respect to the norm.
- A330569 (program): a(n) = 1 if n is odd, otherwise a(n) = 2^(v-1)+1 where v is the 2-adic valuation of n (A007814(n)).
- A330570 (program): Partial sums of A097988 (d_3(n)^2).
- A330571 (program): Square of number of unordered factorizations of n as n = i*j.
- A330592 (program): a(n) is the number of subsets of {1,2,…,n} that contain exactly two odd numbers.
- A330602 (program): a(n) = a(n-1) XOR (n+1), with a(0) = 0.
- A330613 (program): Triangle read by rows: T(n, k) = 1 + k - 2*n - 2*k*n + 2*n^2, with 0 <= k < n.
- A330638 (program): a(n) = P(n)*a(n-1) + a(n-2), with a(0) = 0, a(1) = 1 where P(n) is the n-th Pell number.
- A330640 (program): a(n) is the number of partitions of n with Durfee square of size <= 2.
- A330651 (program): a(n) = n^4 + 3*n^3 + 2*n^2 - 2*n.
- A330669 (program): The prime indices of the prime powers (A000961).
- A330700 (program): a(n) = (n - 1)*n*(2*n^2 + 4*n - 1)/6.
- A330707 (program): a(n) = ( 3*n^2 + n - 1 + (-1)^floor(n/2) )/4.
- A330709 (program): Two-column table read by rows: pairs (i,j) in order sorted from the left.
- A330740 (program): a(n) = min(n, A004488(n)), where A004488(n) is base-3 sum n+n without carries.
- A330749 (program): a(n) = gcd(n, A064989(n)), where A064989 is fully multiplicative with a(2) = 1 and a(prime(k)) = prime(k-1) for odd primes.
- A330761 (program): Array read by antidiagonals: T(n,k) is the number of faces on a ring formed by connecting the ends of a prismatic rod whose cross-section is an n-sided regular polygon after applying a twist of k/n turns.
- A330767 (program): a(n) = 25*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 25.
- A330770 (program): a(n) = 19 * 8^n + 17 for n >= 0.
- A330786 (program): Number of steps to reach 1 by iterating the absolute alternating sum-of-divisors function (A206369).
- A330793 (program): a(n) = A193737(2*n, n).
- A330795 (program): Evaluation of the polynomials given by the Riordan square of the Fibonacci sequence with a(0) = 1 (A193737) at 1/2 and normalized with 2^n.
- A330796 (program): a(n) = Sum_{k=0..n} binomial(n, k)*(2^k - binomial(k, floor(k/2)).
- A330797 (program): Evaluation of the Stirling cycle polynomials at -1/2 and normalized with (-2)^n.
- A330800 (program): Evaluation of the Motzkin polynomials at -1/2 and normalized with (-2)^n.
- A330801 (program): a(n) = A080247(2*n, n), the central values of the Big-Schröder triangle.
- A330805 (program): Number of squares and rectangles in the interior of the square with vertices (n,0), (0,n), (-n,0) and (0,-n) in a square (x,y)-grid.
- A330859 (program): The additive version of the ‘Decade transform’ : to obtain a(n) write n as a sum of its power-of-ten parts and then continue to calculate the sum of the adjacent parts until a single number remains.
- A330866 (program): a(n) = Sum_{d|n, d<n} (n/d) * (n-d).
- A330881 (program): Length of longest LB factorization over all binary strings of length n.
- A330892 (program): Square array of polygonal numbers read by descending antidiagonals (the transpose of A317302).
- A330908 (program): a(n+1) = a(n) + (number of divisors of a(n) that are not divisors of other divisors of a(n)) for n>1; a(1)=1.
- A330910 (program): a(n-5) is the number of nonempty subsets of {1,2,…,n} such that the difference of successive elements is at least 5.
- A330926 (program): a(n) = Sum_{k=1..n} (ceiling(n/k) mod 2).
- A330938 (program): Numbers that cannot be written as the sum of four proper powers. A proper power is an integer of the form a^b where a,b are integers greater than or equal to 2.
- A330983 (program): Alternatively add and multiply pairs of the nonnegative integers.
- A330987 (program): Alternatively add and half-multiply pairs of the nonnegative integers.
- A331022 (program): Numbers k such that the number of strict integer partitions of k is a power of 2.
- A331044 (program): a(n) is the greatest prime number of the form floor(n/10^k) for some k >= 0, or 0 if no such prime number exists.
- A331101 (program): Denominators of the best approximations for sqrt(2).
- A331112 (program): Sum of the digits of the n-th prime number in balanced ternary.
- A331115 (program): Numerators of the best approximations for sqrt(2).
- A331134 (program): a(n) = Sum_{primes p <= n} r_2(p)/4, where r_2(n) = A004018(n).
- A331145 (program): Triangle read by rows: T(n,k) (n>=k>=1) = ceiling((n/k)*ceiling(n/k)).
- A331146 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = ceiling((n/k)*ceiling(n/k)).
- A331147 (program): Triangle read by rows: T(n,k) (n>=k>=1) = floor((n/k)*floor(n/k)).
- A331148 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = floor((n/k)*floor(n/k)).
- A331149 (program): Triangle read by rows: T(n,k) (n>=k>=1) = floor((n/k)*ceiling(n/k)).
- A331150 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = floor((n/k)*ceiling(n/k)).
- A331151 (program): Triangle read by rows: T(n,k) (n>=k>=1) = ceiling((n/k)*floor(n/k)).
- A331152 (program): Triangle read by rows: T(n,k) (n>=k>=1) = f(n,n-k+1) where f(n,k) = ceiling((n/k)*floor(n/k)).
- A331162 (program): a(n) is the number of digits in the concatenation of a(0) to a(n-1) that are equal to the corresponding digit in the concatenation of all integers >= 0, with a(0) = 0.
- A331176 (program): a(n) = n - n/gcd(n, phi(n)), where phi is Euler totient function.
- A331190 (program): Expansion of (-5*(9 - 6*x + 2*x^2))/(-1 + x)^3.
- A331211 (program): Number of green nodes in n-th power graph W exponentiation of a cycle graph with 7 blue nodes and one green node.
- A331213 (program): a(n) = 1 + Sum_{i=1..n} (-1)^i * Product_{j=1..i} floor(n/j).
- A331260 (program): Denominator of harmonic mean of 3 consecutive primes. Numerators are A331259.
- A331261 (program): List of pairs of numbers having certain properties (see Comments).
- A331319 (program): a(n) = x^n/(1 - 2*x*(x + 1))^2.
- A331320 (program): a(n) = [x^n] ((x + 1)*(2*x - 1)*(2*x^2 - 1))/(2*x^2 + 2*x - 1)^2.
- A331321 (program): a(n) = [x^n] ((x^2 - 1)*(x^2 + x - 1))/(x^2 + 2*x - 1)^2.
- A331322 (program): a(n) = (3*n + 1)!/(n!)^3.
- A331323 (program): a(n) = [x^n] (1 - 2*x)/(1 - 8*x + 4*x^2)^(3/2).
- A331325 (program): a(n) = n!*[x^n] cosh(x/(1-x))/(1-x).
- A331326 (program): a(n) = n!*[x^n] sinh(x/(1 - x))/(1 - x).
- A331329 (program): a(n) = binomial(5*n, n)*hypergeom([-4*n, -n], [-5*n], -1).
- A331334 (program): a(n) = n! * [x^n] exp(1 - 1/(2*x + 1))/(2*x + 1).
- A331347 (program): Number of permutations w in S_n that form Boolean intervals [s, w] in the Bruhat order for every simple reflection s in the support of w.
- A331353 (program): Number of achiral colorings of the edges (or triangular faces) of a regular 4-dimensional simplex with n available colors.
- A331388 (program): a(n) = Sum_{k=1..n} mu(gcd(n, k)) * k / gcd(n, k).
- A331390 (program): Number of binary matrices with 3 distinct columns and any number of nonzero rows with n ones in every column and rows in nonincreasing lexicographic order.
- A331394 (program): Number of ways of 4-coloring the Fibonacci square spiral tiling of n squares with colors introduced in order.
- A331396 (program): Number of nonnegative integer matrices with 2 distinct columns and any number of nonzero rows with column sums n and columns in decreasing lexicographic order.
- A331397 (program): Number of nonnegative integer matrices with 2 distinct columns and any number of nonzero rows with column sums n and columns in decreasing lexicographic order.
- A331403 (program): E.g.f.: 1 / ((1 + x) * sqrt(1 - 2*x)).
- A331408 (program): Number of subsets of {1..n} that contain three odd numbers.
- A331417 (program): Maximum sum of primes of the parts of an integer partition of n.
- A331418 (program): If A331417(n) is the maximum sum of primes of the parts of an integer partition of n, then a(n) = A331417(n) - n + 1.
- A331419 (program): a(n) is the number of subsets of {1..n} that contain 4 odd numbers.
- A331429 (program): Expansion of x^2*(10-5*x+x^2)/((1-x)^4*(1-x^2)).
- A331433 (program): Column 1 of triangle in A331431.
- A331434 (program): Column 2 of triangle in A331431.
- A331473 (program): Alternating sum of (n+1)*A000108(n+1).
- A331476 (program): The (10^n)-th even-digit number.
- A331477 (program): Number of n element multisets of n element multisets of an n-set.
- A331501 (program): Decimal expansion of exp(3/4).
- A331504 (program): Number of labeled graphs with n nodes and floor(n*(n-1)/4) edges.
- A331505 (program): Number of labeled graphs with n nodes and floor(n/2) edges.
- A331512 (program): a(n) = Sum_{k=0..n} n^(n-k) * (n+k+1) * binomial(n,k) * binomial(n+k,k).
- A331515 (program): Expansion of 1/(1 - 8*x + 4*x^2)^(3/2).
- A331516 (program): Expansion of 1/(1 - 10*x + 9*x^2)^(3/2).
- A331528 (program): a(n) = n^2 * (n+1)^2 * (n^2+n+1) / 12.
- A331551 (program): Expansion of (1 + 3*x)/(1 + 2*x + 9*x^2)^(3/2).
- A331552 (program): Expansion of (1 + 2*x)/(1 + 4*x^2)^(3/2).
- A331574 (program): a(n) is the number of subsets of {1..n} that contain 3 even and 3 odd numbers.
- A331656 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * n^k.
- A331657 (program): a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * binomial(n+k,k) * n^k.
- A331658 (program): E.g.f.: exp(x/(1 - 2*x)) / (1 - x).
- A331677 (program): a(n) is the difference between the number of primes smaller than prime(n) (i.e., n-1) and greater than prime(n) but less than 2*prime(n).
- A331688 (program): E.g.f.: exp(-x/(1 - x)) / (1 - 2*x).
- A331689 (program): E.g.f.: exp(x/(1 - x)) / (1 - 2*x).
- A331714 (program): Number of non-isomorphic set-systems with 3 sets each with n elements.
- A331725 (program): E.g.f.: exp(x/(1 - x)) / (1 + x).
- A331726 (program): E.g.f.: -LambertW(-x/(1 - x)) / (1 - x).
- A331727 (program): E.g.f.: -LambertW(-x/(1 + x)) / (1 + x).
- A331739 (program): a(n) is n minus its largest odd divisor.
- A331743 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A323901(i) = A323901(j) for all i, j.
- A331764 (program): a(n) = ((p-1)^3 - (p-1)^2)/4 where p is the n-th prime.
- A331792 (program): Expansion of ((1 - 4*x)/sqrt(1 - 8*x + 4*x^2) - 1)/(6*x^2).
- A331793 (program): Expansion of ((1 - 5*x)/sqrt(1 - 10*x + 9*x^2) - 1)/(8*x^2).
- A331794 (program): a(n) = Sum_{k=0..n} n^k * binomial(n+1,k) * binomial(n+1,k+1).
- A331795 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n+1,k) * binomial(n+1,k+1).
- A331799 (program): Normalized volume of the Caracol flow polytope. Also equal to the number of “unified diagrams” of the Caracol graph (see Section 4.3 and Section 5 in Benedetti et al. reference).
- A331817 (program): a(n) = (n!)^2 * Sum_{k=0..n} (2*k)! / (2^k * (k!)^3 * (n - k)!).
- A331839 (program): a(n) = (4^(n + 1) - 2)*(2*n)!.
- A331943 (program): a(n) = n^2 + 1 - ceiling((n + 2)/3).
- A331952 (program): a(n) = (-7 + (-1)^(1+n) + 6*n^2) / 8.
- A331954 (program): a(n) is the least positive k such that floor(n/k) is a prime number.
- A331987 (program): a(n) = ((n + 1) - 9*(n + 1)^2 + 8*(n + 1)^3)/6.
- A331999 (program): a(n) is the product of n, the n-th prime and the n-th composite number.
- A332019 (program): The number of cells added in the n-th generation of the following procedure: start by coloring any triangle on the snub square tiling, then repeatedly color every cell that shares a vertex with a colored cell.
- A332023 (program): T(n, k) = binomial(n+2, 3) + binomial(k+1, 2) + binomial(k, 1). Triangle read by rows, T(n, k) for 0 <= k <= n.
- A332026 (program): Savannah problem: number of new possibilities after n weeks.
- A332027 (program): Savannah problem: number of distinct possible populations after n weeks, allowing populations after the empty set.
- A332028 (program): Savannah problem: number of distinct possible populations after n weeks, not allowing new populations after the empty set.
- A332031 (program): G.f.: Sum_{k>=1} k! * x^(k^2) / (1 - x^k).
- A332044 (program): a(n) is the length of the shortest circuit that visits every edge of an undirected n X n grid graph.
- A332048 (program): a(n) = n! * [x^n] 1 / (1 - LambertW(x))^n.
- A332049 (program): a(n) = (1/2) * Sum_{d|n, d > 1} d * phi(d).
- A332051 (program): Number of compositions of 2n where the multiplicity of the first part equals n.
- A332056 (program): a(1) = 1, then a(n+1) = a(n) - (-1)^a(n) Sum_{k=1..n} a(k): if a(n) is odd, add the partial sum, else subtract.
- A332057 (program): Partial sums (and absolute value of first differences) of A332056: if odd (resp. even) add (resp. subtract) the partial sum to get the next term.
- A332063 (program): a(1) = 1, a(n + 1) = a(n) + Sum_{k = 1..n} floor(log_2(a(k)) + 1): add total number of bits of the terms so far.
- A332082 (program): a(n) = Sum_{1 <= m <= n} Sum_{1 <= k <= n+1-m} m*R(k,n+1), where R(k,b) = (b^k - 1)/(b - 1) is the base-b repunit of length k.
- A332097 (program): Maximum of s^n - Sum_{0 < x < s} x^n.
- A332101 (program): Least m such that m^n <= Sum_{k<m} k^n.
- A332102 (program): Least m > 0 such that 2*m^n <= Sum_{k < m} k^n.
- A332104 (program): Triangle read by rows in which row n >= 0 lists numbers from 0 to n starting at floor(n/2) and using alternatively larger respectively smaller numbers than the values used so far.
- A332112 (program): a(n) = (10^(2n+1)-1)/9 + 10^n.
- A332113 (program): a(n) = (10^(2n+1)-1)/9 + 2*10^n.
- A332114 (program): a(n) = (10^(2n+1)-1)/9 + 3*10^n.
- A332115 (program): a(n) = (10^(2n+1)-1)/9 + 4*10^n.
- A332116 (program): a(n) = (10^(2n+1)-1)/9 + 5*10^n.
- A332117 (program): a(n) = (10^(2n+1)-1)/9 + 6*10^n.
- A332118 (program): a(n) = (10^(2n+1)-1)/9 + 7*10^n.
- A332119 (program): a(n) = (10^(2n+1)-1)/9 + 8*10^n.
- A332120 (program): a(n) = 2*(10^(2n+1)-1)/9 - 2*10^n.
- A332121 (program): a(n) = 2*(10^(2n+1)-1)/9 - 10^n.
- A332122 (program): Decimal expansion of unique real root of the polynomial X^3 - X^2 - X/2 - 1/6.
- A332123 (program): a(n) = 2*(10^(2n+1)-1)/9 + 10^n.
- A332124 (program): a(n) = 2*(10^(2n+1)-1)/9 + 2*10^n.
- A332125 (program): a(n) = 2*(10^(2n+1)-1)/9 + 3*10^n.
- A332126 (program): a(n) = 2*(10^(2n+1)-1)/9 + 4*10^n.
- A332127 (program): a(n) = 2*(10^(2n+1)-1)/9 + 5*10^n.
- A332128 (program): a(n) = 2*(10^(2n+1)-1)/9 + 6*10^n.
- A332129 (program): a(n) = 2*(10^(2n+1)-1)/9 + 7*10^n.
- A332130 (program): a(n) = (10^(2n+1)-1)/3 - 3*10^n.
- A332131 (program): a(n) = (10^(2n+1)-1)/3 - 2*10^n.
- A332132 (program): a(n) = (10^(2n+1)-1)/3 - 10^n.
- A332133 (program): Decimal expansion of (1 + sqrt(3))/2, unique positive root of x^2 - x - 1/2.
- A332134 (program): a(n) = (10^(2n+1)-1)/3 + 10^n.
- A332135 (program): a(n) = (10^(2n+1)-1)/3 + 2*10^n.
- A332136 (program): a(n) = 3*(10^(2n+1)-1)/9 + 3*10^n.
- A332137 (program): a(n) = (10^(2n+1)-1)/3 + 4*10^n.
- A332138 (program): a(n) = (10^(2*n+1)-1)/3 + 5*10^n.
- A332139 (program): a(n) = (10^(2*n+1)-1)/3 + 6*10^n.
- A332140 (program): a(n) = 4*(10^(2n+1)-1)/9 - 4*10^n.
- A332141 (program): a(n) = 4*(10^(2*n+1)-1)/9 - 3*10^n.
- A332142 (program): a(n) = 4*(10^(2*n+1)-1)/9 - 2*10^n.
- A332143 (program): a(n) = 4*(10^(2*n+1)-1)/9 - 10^n.
- A332145 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 10^n.
- A332146 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 2*10^n.
- A332147 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 3*10^n.
- A332148 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 4*10^n.
- A332149 (program): a(n) = 4*(10^(2*n+1)-1)/9 + 5*10^n.
- A332150 (program): a(n) = 5*(10^(2n+1)-1)/9 - 5*10^n.
- A332151 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 4*10^n.
- A332152 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 3*10^n.
- A332153 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 2*10^n.
- A332154 (program): a(n) = 5*(10^(2*n+1)-1)/9 - 10^n.
- A332156 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 10^n.
- A332157 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 2*10^n.
- A332158 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 3*10^n.
- A332159 (program): a(n) = 5*(10^(2*n+1)-1)/9 + 4*10^n.
- A332160 (program): a(n) = 6*(10^(2n+1)-1)/9 - 6*10^n.
- A332161 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 5*10^n.
- A332162 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 4*10^n.
- A332163 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 3*10^n.
- A332164 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 2*10^n.
- A332165 (program): a(n) = 6*(10^(2*n+1)-1)/9 - 10^n.
- A332167 (program): a(n) = 6*(10^(2*n+1)-1)/9 + 10^n.
- A332168 (program): a(n) = 6*(10^(2*n+1)-1)/9 + 2*10^n.
- A332169 (program): a(n) = 6*(10^(2*n+1)-1)/9 + 3*10^n.
- A332170 (program): a(n) = 7*(10^(2n+1)-1)/9 - 7*10^n.
- A332171 (program): a(n) = 7*(10^(2n+1)-1)/9 - 6*10^n.
- A332172 (program): a(n) = 7*(10^(2n+1)-1)/9 - 5*10^n.
- A332173 (program): a(n) = 7*(10^(2n+1)-1)/9 - 4*10^n.
- A332174 (program): a(n) = 7*(10^(2n+1)-1)/9 - 3*10^n.
- A332175 (program): a(n) = 7*(10^(2n+1)-1)/9 - 2*10^n.
- A332176 (program): a(n) = 7*(10^(2n+1)-1)/9 - 10^n.
- A332178 (program): a(n) = 7*(10^(2n+1)-1)/9 + 10^n.
- A332179 (program): a(n) = 7*(10^(2n+1)-1)/9 + 2*10^n.
- A332180 (program): a(n) = 8*(10^(2n+1)-1)/9 - 8*10^n.
- A332181 (program): a(n) = 8*(10^(2n+1)-1)/9 - 7*10^n.
- A332182 (program): a(n) = 8*(10^(2n+1)-1)/9 - 6*10^n.
- A332183 (program): a(n) = 8*(10^(2n+1)-1)/9 - 5*10^n.
- A332184 (program): a(n) = 8*(10^(2n+1)-1)/9 - 4*10^n.
- A332185 (program): a(n) = 8*(10^(2n+1)-1)/9 - 3*10^n.
- A332186 (program): a(n) = 8*(10^(2n+1)-1)/9 - 2*10^n.
- A332187 (program): a(n) = 8*(10^(2n+1)-1)/9 - 10^n.
- A332189 (program): a(n) = 8*(10^(2n+1)-1)/9 + 10^n.
- A332190 (program): a(n) = 10^(2n+1) - 1 - 9*10^n.
- A332191 (program): a(n) = 10^(2n+1) - 1 - 8*10^n.
- A332192 (program): a(n) = 10^(2n+1) - 1 - 7*10^n.
- A332193 (program): a(n) = 10^(2n+1) - 1 - 6*10^n.
- A332194 (program): a(n) = 10^(2n+1) - 1 - 5*10^n.
- A332195 (program): a(n) = 10^(2n+1) - 4*10^n - 1.
- A332196 (program): a(n) = 10^(2n+1) - 1 - 3*10^n.
- A332197 (program): a(n) = 10^(2n+1) - 1 - 2*10^n.
- A332202 (program): Largest k >= 0 such that 3^k divides 2^(2^n-1) + 1.
- A332206 (program): Numbers k such that A332205(k) = 0.
- A332209 (program): Starting from sigma(n), number of halving and tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
- A332224 (program): a(n) = A087808(sigma(n)).
- A332231 (program): a(n) = 1/n! * ((n+1)*n)!/Gamma(1 + (n+1)*n/2) * Gamma(1 + (n-1)*n/2)/((n-1)*n)!.
- A332233 (program): Number of integer partitions lambda (of any k) satisfying n = max_{p:lambda} p*m(p,lambda), where m(p,lambda) is the multiplicity of part p in lambda.
- A332243 (program): Starhex honeycomb numbers: a(n) = 13 + 60*n + 60*n^2.
- A332264 (program): Partial sums of A334136.
- A332288 (program): Number of unimodal permutations of the multiset of prime indices of n.
- A332408 (program): a(n) = Sum_{k=0..n} binomial(n,k) * k! * k^n.
- A332409 (program): a(n) = n!! mod Fibonacci(n).
- A332410 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-5) - 2*a(n-6) + a(n-7) with a(0)=0, a(1)=1, a(2)=3, a(3)=6, a(4)=11, a(5)=17, a(6)=24.
- A332420 (program): Number of Maclaurin polynomials of sin x having exactly n positive zeros.
- A332426 (program): Number of unordered pairs of non-selfintersecting paths with nodes that cover all vertices of a convex n-gon.
- A332435 (program): Row sums of the irregular triangle A332434. a(n) equals the number of odd numbers <= n, of the smallest nonnegative reduced residue system modulo (2*n + 1), for n >= 1.
- A332436 (program): The number of even numbers <= n of the smallest nonnegative reduced residue system modulo 2*n + 1, for n >= 0.
- A332437 (program): Decimal expansion of 2*cos(Pi/9).
- A332438 (program): Decimal expansion of (2*cos(Pi/9))^2 = A332437^2.
- A332442 (program): Triangle read by rows, T(n,k) is the number of regular triangles of length k (in some length unit), for k from {1, 2, … , n}, in a matchstick arrangement with enclosing triangle of length n, but only triangles with orientation opposite to the enclosing triangle are counted.
- A332448 (program): a(n) = A007814(A087808(sigma(n))).
- A332452 (program): Starting from sigma(n), number of halving steps to reach 1 in ‘3x+1’ problem, or -1 if this never happens.
- A332453 (program): Starting from sigma(n), number of tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
- A332454 (program): Starting from sigma(n)+1, number of halving steps to reach 1 in ‘3x+1’ problem, or -1 if this never happens.
- A332455 (program): Starting from sigma(n)+1, number of tripling steps to reach 1 in ‘3x+1’ problem, or -1 if 1 is never reached.
- A332459 (program): Odd part of 1+sigma(n).
- A332464 (program): Rule 124 one-dimensional cellular automaton applied for one step to the configuration read from the base-2 expansion of sigma(n), then converted back to decimal.
- A332469 (program): a(n) = Sum_{k=1..n} floor(n/k)^n.
- A332476 (program): The number of unitary divisors of n in Gaussian integers.
- A332490 (program): a(n) = Sum_{k=1..n} k * ceiling(n/k).
- A332491 (program): a(n) = 2*a(n-1) + a(n-3), where a(0) = 3, a(1) = 1, a(2) = 2.
- A332495 (program): a(n-2) = a(n-6) + 5*(1+2*n) with a(0)=0, a(1)=2, a(2)=7, a(3)=15 for n>=4.
- A332497 (program): a(n) = x(w+1) where x(0) = 0 and x(k+1) = 2^(k+1)-1-x(k) (resp. x(k)) when d_k = 1 (resp. d_k <> 1) and Sum_{k=0..w} d_k*3^k is the ternary representation of n. Sequence A332498 gives corresponding y’s.
- A332498 (program): a(n) = y(w+1) where y(0) = 0 and y(k+1) = 2^(k+1)-1-y(k) (resp. y(k)) when d_k = 2 (resp. d_k <> 2) and Sum_{k=0..w} d_k*3^k is the ternary representation of n. Sequence A332497 gives corresponding x’s.
- A332502 (program): Rectangular array read by antidiagonals: T(n,k) = floor(n + k*r), where r = golden ratio = (1+sqrt(5))/2.
- A332517 (program): a(n) = Sum_{k=1..n} gcd(n,k)^n.
- A332519 (program): a(n) = 4*(n^2+n-2).
- A332529 (program): Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = 1+ golden ratio = (1+sqrt(5))/2.
- A332533 (program): a(n) = (1/n) * Sum_{k=1..n} floor(n/k) * n^k.
- A332552 (program): a(n) = A082184(n) - A082183(n).
- A332553 (program): a(n) = n + A082183(n) - A082184(n).
- A332557 (program): Number of inequivalent Z_{2^s}-linear Hadamard codes of length 2^n.
- A332569 (program): a(n) = Sum_{k=1..n} floor(n/k) * ceiling(n/k).
- A332602 (program): Tridiagonal matrix M read by antidiagonals: main diagonal is 1,2,2,2,2,…, two adjacent diagonals are 1,1,1,1,1,…
- A332613 (program): Covering radius of the dihedral group code D_n.
- A332618 (program): a(n) = Sum_{d|n} lcm(d, n/d) / gcd(d, n/d).
- A332619 (program): a(n) = Sum_{d|n} lcm(d, n/d) / d.
- A332620 (program): a(n) = Sum_{k=1..n} n^(n/gcd(n, k)).
- A332621 (program): a(n) = (1/n) * Sum_{k=1..n} n^(n/gcd(n, k)).
- A332623 (program): a(n) = Sum_{k=1..n} ceiling(n/k)^2.
- A332624 (program): a(n) = Sum_{k=1..n} ceiling(n/k)^n.
- A332627 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * k! * k^n.
- A332635 (program): a(n) = n!! mod prime(n).
- A332647 (program): a(n) = 2*a(n-1) + a(n-3) with a(0) = 3, a(1) = 2, a(2) = 4.
- A332652 (program): a(n) = Sum_{k=1..n} n^(k/gcd(n, k)).
- A332653 (program): a(n) = (1/n) * Sum_{k=1..n} n^(k/gcd(n, k)).
- A332654 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^2.
- A332655 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^n.
- A332663 (program): Even bisection of A332662: the x-coordinates of an enumeration of N X N.
- A332679 (program): a(n) = (-1)^n * n! * Laguerre(n, 4*n).
- A332682 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * ceiling(n/k).
- A332683 (program): a(n) = Sum_{k=1..n, gcd(n, k) = 1} ceiling(n/k).
- A332687 (program): a(n) = Sum_{k=1..n} ceiling(n/prime(k)).
- A332692 (program): a(n) = n! * Laguerre(n, 2*n).
- A332693 (program): a(n) = n! * Laguerre(n, 3*n).
- A332694 (program): a(n) = (-1)^n * n! * Laguerre(n, 5*n).
- A332695 (program): a(n) = (-1)^n * n! * Laguerre(n, 6*n).
- A332697 (program): a(n) = (n^4 + 5*n^3 + 11*n^2 + 7*n)/6.
- A332698 (program): a(n) = (8*n^3 + 15*n^2 + 13*n)/6.
- A332699 (program): First row of A332662, also main diagonal of A332667.
- A332705 (program): Number of unit square faces (or surface area) of a stage-n Menger sponge.
- A332711 (program): Sum of all numbers in bijective base-n numeration with digit sum n.
- A332712 (program): a(n) = Sum_{d|n} mu(d/gcd(d, n/d)).
- A332724 (program): Number of length n - 1 ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.
- A332730 (program): a(n) = Sum_{d|n} tau(d/gcd(d, n/d)), where tau = A000005.
- A332732 (program): Dirichlet g.f.: zeta(6*s) / (zeta(s) * zeta(2*s) * zeta(3*s)).
- A332741 (program): Number of unimodal negated permutations of a multiset whose multiplicities are the prime indices of n.
- A332754 (program): a(n) = Sum_{k=1..n-1} ((-1)^(k+n+1)*binomial(k,floor(k/2))).
- A332756 (program): A loop sequence within Pi. Let a(1) = 19. For n > 1, a(n+1) is the position of the first occurrence of a(n) after the decimal point in the decimal expansion of Pi.
- A332757 (program): Number of involutions (plus identity) in the n-fold iterated wreath product of C_2.
- A332758 (program): Number of fixed-point free involutions in the n-fold iterated wreath product of C_2.
- A332774 (program): Given n line segments, the k-th of which is drawn from (k,0) to (x_k,1) where {x_1,x_2,…,x_n} is a permutation of {1,2,…,n}, a(n) is the maximum number of distinct points at which line segments intersect.
- A332775 (program): a(n) = n + sopf(n) - omega(n).
- A332789 (program): First differences of the iterated Beatty sequence A007069.
- A332790 (program): Triangle read by rows: T(n,k) = 1 + 2*n + k + 5*k(n-k) for n >= 0, 0 <= k <= n.
- A332793 (program): a(1) = 1; a(n) = n * Sum_{d|n, d < n} (-1)^(n/d) * a(d) / d.
- A332794 (program): a(n) = Sum_{d|n} (-1)^(d + 1) * d * phi(n/d).
- A332796 (program): Number of compositions of n^2 into parts >= n.
- A332801 (program): a(n) is the number of even results of n mod k, for 1 < k < n.
- A332807 (program): a(n) = A000720(A108546(n)).
- A332844 (program): Dirichlet g.f.: zeta(s) * zeta(s-1) * zeta(2*s).
- A332845 (program): a(n) = (-1)^omega(n) * Sum_{k=1..n} (-1)^omega(n/gcd(n, k)), where omega = A001221.
- A332872 (program): Number of ordered set partitions of {1..n} where no element of any block is greater than any element of a non-adjacent consecutive block.
- A332880 (program): If n = Product (p_j^k_j) then a(n) = numerator of Product (1 + 1/p_j).
- A332881 (program): If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j).
- A332882 (program): If n = Product (p_j^k_j) then a(n) = numerator of Product (1 + 1/p_j^k_j).
- A332883 (program): If n = Product (p_j^k_j) then a(n) = denominator of Product (1 + 1/p_j^k_j).
- A332884 (program): a(n) = -n^2 + 21*n - 1.
- A332917 (program): A332916(n)/2^a(n) is the average number of binary strings of length n with Levenshtein distance <= 3 from a uniform randomly sampled binary string of this length.
- A332919 (program): a(n) is the sum of the sums of squared digits of all n-digit numbers.
- A332921 (program): Number of symmetric non-isomorphic free unrooted snake-shaped polyominoes of maximum length on a quadratic board of n X n squares.
- A332936 (program): Number of blue nodes in n-th power graph W exponentiation of a cycle graph with 7 blue nodes and 1 green node.
- A332937 (program): a(n) is the greatest common divisor of the first two terms of row n of the Wythoff array (A035513).
- A332958 (program): Number of labeled forests with 2n nodes consisting of n-1 isolated nodes and a labeled tree with n+1 nodes.
- A332966 (program): a(n) is the largest value in the sequence s defined by s(1) = 0 and for any k > 0, s(k+1) = (s(k)^2+1) mod n.
- A332993 (program): a(1) = 1, for n > 1, a(n) = n + a(A032742(n)).
- A332994 (program): a(1) = 1, for n > 1, a(n) = n + a(A052126(n)).
- A333046 (program): a(1) = 1; a(n) = n * Sum_{d|n, d < n, gcd(d, n/d) = 1} a(d) / d.
- A333068 (program): a(1) = 1; for n > 1, a(n) = n*(n-1)/2 + ((a(n-1)-1) mod n) + 1, the a(n-1)-th term of the n-th row of the triangle of positive integers, indexed in cyclic manner.
- A333093 (program): a(n) is the n-th order Taylor polynomial (centered at 0) of c(x)^n evaluated at x = 1, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
- A333119 (program): Triangle T read by rows: T(n, k) = (n - k)*(1 - (-1)^k + 2*k)/4, with 0 <= k < n.
- A333125 (program): a(n) = binomial(Fibonacci(n),n).
- A333167 (program): a(n) = r_2(n^2 + 1), where r_2(k) is the number of ways of writing k as a sum of 2 squares (A004018).
- A333168 (program): a(n) = Sum_{k=0..n} r_2(k^2 + 1), where r_2(k) is the number of ways of writing k as a sum of 2 squares (A004018).
- A333169 (program): a(n) = phi(n^2 + 1), where phi is the Euler totient function (A000010).
- A333170 (program): a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010).
- A333171 (program): a(n) = Sum_{k=0..n} d(k^2 + 1), where d(k) is the number of divisors of k (A000005).
- A333172 (program): a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).
- A333173 (program): a(n) = r_4(n^2 + 1), where r_4(k) is the number of ways of writing k as a sum of 4 squares (A000118).
- A333174 (program): a(n) = Sum_{k=0..n} r_4(k^2 + 1), where r_4(k) is the number of ways of writing k as a sum of 4 squares (A000118).
- A333175 (program): If n = Product (p_j^k_j) then a(n) = Sum (a(n/p_j^k_j)), with a(1) = 1.
- A333183 (program): Number of digits in concatenation of first n positive even integers.
- A333194 (program): a(n) = Sum_{k=1..n} (ceiling(n/k) mod 2) * k.
- A333206 (program): a(n) is the least decimal digit of n^3.
- A333236 (program): Largest digit in the decimal expansion of 1/n.
- A333251 (program): Tropical version of Somos-5 sequence A006721.
- A333262 (program): Number of steps to reach 1 by iterating the alternating sum of divisors function A071324 starting from n.
- A333293 (program): a(n) = Sum_{k=1..n-1} k^2*phi(k) + n^2*phi(n)/2, where phi = A000010.
- A333296 (program): Largest number of non-congruent integer-sided bricks that can be assembled into an n X n X n cube.
- A333297 (program): a(n) = Sum_{i=1..n, j=1..n, gcd(i,j)=1} i.
- A333306 (program): a(n) = sqrt(Pi/4)*2^A048881(2*n)*L(2*n) where L(s) = lim_{t->s} (t/2)!/((1-t)/2)!.
- A333315 (program): a(n) = Sum_{k=1..n} phi(prime(k)-1), where phi is the Euler totient function (A000005).
- A333317 (program): Partial sums of A248577.
- A333319 (program): a(n) is the number of subsets of {1..n} that contain exactly 3 odd and 1 even numbers.
- A333320 (program): a(n) is the number of subsets of {1..n} that contain exactly 4 odd and 1 even numbers.
- A333321 (program): a(n) is the number of subsets of {1..n} that contain exactly 1 odd and 4 even numbers.
- A333322 (program): Decimal expansion of (3/8) * sqrt(3).
- A333329 (program): Number of winnable configurations in Lights Out game (played on a digraph) summed over every labeled digraph on n nodes.
- A333344 (program): a(n) = 11*a(n-1) - 9*a(n-2) starting a(0)=1, a(1)=10.
- A333345 (program): Decimal expansion of (11 + sqrt(85))/2.
- A333355 (program): Number of bits in binary expansion of n minus the number of digits of n when written in base 3.
- A333363 (program): Horizontal visibility sequence at the onset of chaos in the 3-period cascade.
- A333378 (program): a(n) = F(n) * (-1)^(n*(n-1)/2) where F(n) = A000045(n) Fibonacci numbers.
- A333385 (program): a(n) = 3^n + 2 * 17^n for n >= 0.
- A333392 (program): a(0) = 1; thereafter a(n) = 2^(prime(n)-1) + Sum_{k=1..n} 2^(prime(n)-prime(k)).
- A333415 (program): Odd positive integers in base 2 read backwards.
- A333451 (program): Expansion of golden ratio (1 + sqrt(5))/2 in base 3.
- A333461 (program): a(n) = gcd(2*n, binomial(2*n,n))/2.
- A333462 (program): a(n) is the number of Gaussian integers z such that (n-1)/2 < |z| <= n/2, divided by 4.
- A333463 (program): a(n) = Sum_{k=1..n} floor(n/k) * gcd(n,k).
- A333465 (program): a(n) = Sum_{k=1..n} ceiling(n/k) * gcd(n,k).
- A333470 (program): Lexicographically earliest sequence of distinct positive terms such that a(n) is the number of commas that a(n) has to step over (to the right) to be met by an odd term. This odd term might not be the closest odd term to a(n).
- A333472 (program): a(n) = [x^n] ( c (x/(1 + x)) )^n, where c(x) = (1 - sqrt(1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
- A333473 (program): a(n) = [x^n] ( S(x/(1 + x) )^n, where S(x) = (1 - x - sqrt(1 - 6*x + x^2))/(2*x) is the o.g.f. of the large Schröder numbers A006318.
- A333510 (program): Number of self-avoiding walks in the n X 2 grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side.
- A333516 (program): Irregular triangle read by rows in which row n lists the first A000217(n) terms of A002260, n >= 1.
- A333525 (program): Degree of polytope representing the number n.
- A333535 (program): Card{ k<=n, k such that all prime divisors of k are < sqrt(k) }.
- A333557 (program): a(n) = Sum_{d|n, gcd(d, n/d) = 1} uphi(d) * uphi(n/d), where uphi = unitary totient function (A047994).
- A333561 (program): a(n) = Sum_{j = 0..2*n} binomial(n+j-1,j)*2^j.
- A333562 (program): a(n) = Sum_{j = 0..3*n} binomial(n+j-1,j)*2^j.
- A333564 (program): a(n) = [x^n] ( c(x)/c(-x) )^n, where c(x) = (1 - sqrt( 1 - 4*x))/(2*x) is the o.g.f. of the Catalan numbers A000108.
- A333565 (program): O.g.f.: (1 + 4*x)/((1 + x)*sqrt(1 - 8*x)).
- A333569 (program): a(n) = Sum_{d|n} (-1)^(bigomega(d) - omega(d)) * phi(n/d).
- A333572 (program): a(n) is the number of Gaussian integers z with 0 < |z| <= n/2.
- A333573 (program): a(n) = A333572(n)/4.
- A333574 (program): Number of Hamiltonian paths in the n X 2 grid graph which start at any of the n vertices on left side of the graph and terminate at any of the n vertices on the right side.
- A333576 (program): a(1) = 1; thereafter a(n) = n * uphi(n) / 2.
- A333588 (program): a(n) = floor(-(3/2)*a(n-1)), a(1)=-2.
- A333592 (program): a(n) = Sum_{k = 0..n} binomial(n + k - 1, k)^2.
- A333593 (program): a(n) = Sum_{k = 0..n} (-1)^(n + k)*binomial(n + k - 1, k)^2.
- A333596 (program): a(0) = 0; for n > 0, a(n) = a(n-1) + (number of 1’s and 3’s in base-4 representation of n) - (number of 0’s and 2’s in base-4 representation of n).
- A333599 (program): a(n) = Fibonacci(n) * Fibonacci(n+1) mod Fibonacci(n+2).
- A333609 (program): The number of iterations of the infinitary totient function iphi (A091732) required to reach from n to 1.
- A333611 (program): Sum of the iterated infinitary totient function iphi (A091732).
- A333616 (program): Expansion of x*(1 + 2*x + x^2 - 4*x^3 - x^4 + 2*x^5)/((1 - x)^3*(1 + x)^2).
- A333637 (program): The number of cells which contain multiple squares of a Genealodron formed from 2^n - 1 equal-sized squares (when viewed from above).
- A333645 (program): a(n) = Sum_{d|n} uphi(d).
- A333675 (program): Partial sums of non-Lucas numbers A057854.
- A333694 (program): G.f.: Sum_{k>=1} k * x^k / (1 - x^(k^2)).
- A333695 (program): Numerators of coefficients in expansion of Sum_{k>=1} phi(k) * log(1/(1 - x^k)).
- A333696 (program): Denominators of coefficients in expansion of Sum_{k>=1} phi(k) * log(1/(1 - x^k)).
- A333714 (program): Squares visited by a chess king moving on a square-spiral numbered board where the king moves to the adjacent unvisited square containing the spiral number with the most divisors. In case of a tie it chooses the square with the highest spiral number.
- A333718 (program): a(n) = L(8*n+4)/7, where L=A000032 (the Lucas sequence).
- A333747 (program): Numbers that are either the product of two consecutive primes or two primes with a prime in between.
- A333760 (program): Number of self-avoiding closed paths in the 4 X n grid graph which pass through all vertices on four (left, right, upper, lower) sides of the graph.
- A333766 (program): Maximum part of the n-th composition in standard order. a(0) = 0.
- A333767 (program): Length of shortest run of zeros after a one in the binary expansion of n. a(0) = 0.
- A333768 (program): Minimum part of the n-th composition in standard order. a(0) = 0.
- A333772 (program): a(n) = n * 2^n * (n!)^2.
- A333780 (program): a(n) = g(-n) - g(n), where g corresponds to the inverse of A333773.
- A333781 (program): G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k^2) / (1 - x^k).
- A333782 (program): G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^(k^2) / (1 - x^k).
- A333783 (program): a(n) = sigma(n) - A332993(n).
- A333784 (program): a(n) = sigma(n) - A332994(n).
- A333787 (program): Fully multiplicative with a(2) = 2 and a(p) = p-1 for odd primes p.
- A333791 (program): Difference of sums of two subsets of divisors of n, those obtained by repeatedly dividing with the smallest remaining prime factor (A332993) and those obtained by repeatedly dividing with the largest remaining prime factor (A332994).
- A333794 (program): a(1) = 1, for n > 1, a(n) = n + a(n-A052126(n)).
- A333813 (program): a(n) = 2^(1 + floor(n*log_2(3))) - (3^n + 1).
- A333841 (program): Integers n such that n! = x^2 + y^3 + z^4 where x, y and z are nonnegative integers, is soluble.
- A333848 (program): a(n) gives the sum of the odd numbers of the smallest nonnegative reduced residue system modulo 2*n + 1, for n >= 0.
- A333870 (program): The number of iterations of the absolute Möbius divisor function (A173557) required to reach from n to 1.
- A333871 (program): Sum of the iterated absolute Möbius divisor function (A173557).
- A333884 (program): Difference between smallest cube > n and n.
- A333906 (program): For n >= 2, a(n) = Sum_{k=2..n} prevpower2(k) + nextpower2(k) - 2*k, where prevpower2(k) is the largest power of 2 < k, nextpower2(k) is the smallest power of 2 > k.
- A333937 (program): Triangle read by rows: T(n, k) = (k-1)*n - binomial(n, 2) + floor((n-k)/2) + 1, transposed.
- A333990 (program): a(n) = Sum_{k=0..n} n^k * binomial(2*n,2*k).
- A333991 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(2*n,2*k).
- A333996 (program): Number of composite numbers in the triangular n X n multiplication table.
- A334000 (program): a(n) = (2*n+1)!! * Sum_{k=0..n} k/(2*k+1).
- A334032 (program): The a(n)-th composition in standard order (graded reverse-lexicographic) is the unsorted prime signature of n.
- A334033 (program): The a(n)-th composition in standard order (graded reverse-lexicographic) is the reversed unsorted prime signature of n.
- A334039 (program): For any n > 0: start with x = n; for k = 1..n, if k divides x then divide x by k; a(n) corresponds to the final value of x.
- A334041 (program): (a(n-2) XOR a(n-1)) OR (highest bit of a(n-2))*2 OR 1; a(0)=2, a(1)=3.
- A334042 (program): Write n^2 in binary, interchange 0’s and 1’s, convert back to decimal.
- A334045 (program): Bitwise NOR of binary representation of n and n-1.
- A334051 (program): The difference between the number of prime numbers in the ranges (1, p_n] and (p_n, 2*p_n], where p_n is the n-th prime.
- A334066 (program): a(n) = (2n-1)!!*(Sum_{k=1..n}k/(2*k-1)).
- A334070 (program): Number of even-order elements in the multiplicative group of integers modulo n.
- A334076 (program): a(n) = bitwise NOR of n and 2n.
- A334084 (program): Integers m such that only 2 binomial coefficients C(m,k), with 0<=k<=m, are practical numbers.
- A334085 (program): GCD of n and the product of all primes < n.
- A334090 (program): a(1) = 0, and then after the first differences of A064097.
- A334091 (program): a(1) = 0, then after the first differences of A329697.
- A334122 (program): a(n) is the sum of all primes <= n, mod n.
- A334136 (program): a(n) = (n-1)*sigma(n) where sigma is the sum of divisors A000203.
- A334155 (program): a(n) is the number of length n decorated permutations avoiding the pattern 001.
- A334169 (program): a(n) is the number of ON-cells in the n-th full level of ON-cells of a triangular wedge in the hexagonal grid of A151723 (after 2^k >= n generations have been computed).
- A334172 (program): Bitwise XNOR of prime(n) and prime(n + 1).
- A334195 (program): a(1) = 0, then after the first differences of A064415.
- A334196 (program): a(1) = 0, then after the first differences of A003434.
- A334202 (program): a(n) = A064097(n) - A323077(n).
- A334210 (program): a(n) = sigma(prime(n) + 1) - sigma(prime(n)).
- A334224 (program): Consider a graph as defined in A306302 formed from a row of n adjacent congruent squares with the diagonals of all possible rectangles; a(n) is the minimum edge length of the squares such that the vertices formed by all intersections have integer x and y coordinates.
- A334227 (program): Length of the shortest prefix of the Thue-Morse sequence (A010060) containing, as subwords, all length-n blocks appearing in A010060.
- A334237 (program): a(n) = 2*Sum_{k=0..n-1} binomial(n,k)^2*binomial(n,k+1)^2.
- A334277 (program): Perimeters of almost-equilateral Heronian triangles.
- A334293 (program): First quadrisection of Padovan sequence.
- A334316 (program): E.g.f. A(x) satisfies: A(x) = x * exp(A(x)) * (1 - A(x)).
- A334320 (program): Number of even integers in base n with exactly two distinct digits.
- A334341 (program): a(n) = Sum_{p|n, p prime} (n - p).
- A334363 (program): Decimal expansion of Sum_{k>=0} 1/(4*k+1)!.
- A334364 (program): Decimal expansion of Sum_{k>=0} 1/(4*k+2)!.
- A334366 (program): Decimal expansion of Sum_{k>=0} 1/(4*k)!!.
- A334367 (program): Decimal expansion of Sum_{k>=0} 1/(4*k+2)!!.
- A334378 (program): Decimal expansion of Sum_{k>=0} 1/((2*k+1)!)^2.
- A334379 (program): Decimal expansion of Sum_{k>=0} 1/((2*k)!)^2.
- A334380 (program): Decimal expansion of Sum_{k>=0} (-1)^k/((2*k)!!)^2.
- A334381 (program): Decimal expansion of Sum_{k>=0} 1/(2^k*(k!)^2).
- A334383 (program): Decimal expansion of Sum_{k>=0} (-1)^k/(2^k*(k!)^2).
- A334387 (program): The difference version of the ‘Decade transform’ : to obtain a(n) write n as a sum of its power-of-ten parts and then continue to calculate the absolute value of the difference between the adjacent parts until a single number remains.
- A334396 (program): Number of fault-free tilings of a 3 X n rectangle with squares and dominos.
- A334397 (program): Decimal expansion of (e - 2)/e.
- A334413 (program): First differences of A101803.
- A334414 (program): First differences of A334415.
- A334415 (program): Nearest integer to n*(2-phi), where phi is the golden ratio (A001622).
- A334422 (program): Decimal expansion of Pi/128.
- A334463 (program): a(n) is the sum of all parts of all partitions of n into consecutive parts that differ by 3.
- A334501 (program): Eventual period of a single cell in rule 190 cellular automaton in a cyclic universe of width n.
- A334520 (program): Primes that are the sum of two cubes.
- A334562 (program): E.g.f.: exp(-(x + x^2 + x^3)).
- A334563 (program): a(n) is the maximum number of 4-cycles possible in an n-vertex planar graph.
- A334569 (program): E.g.f.: exp(-(x + x^2/2 + x^3/3)).
- A334572 (program): Let x(n, k) be the exponent of prime(k) in the factorization of n, then a(n) = Max_{k} abs(x(n,k)- x(n-1,k)).
- A334573 (program): Partial sums of A334572.
- A334576 (program): a(n) is the X-coordinate of the n-th point of the space filling curve P defined in Comments section; sequence A334577 gives Y-coordinates.
- A334578 (program): Double subfactorials: a(n) = (-1)^floor(n/2) * n!! * Sum_{i=0..floor(n/2)} (-1)^i/(n-2*i)!!.
- A334580 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.
- A334582 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^3.
- A334585 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^4.
- A334603 (program): Period length of the fraction 1/11^n for n >= 1.
- A334604 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^5.
- A334605 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^6.
- A334614 (program): a(n) = pi(prime(n) - n) + n, where pi is the prime counting function.
- A334625 (program): Maximal size of a subset T of S = {1,2,…,n} with a cyclic arrangement of T such that any three neighbors can be reordered in an arithmetic progression.
- A334628 (program): Total area of all distinct rectangles whose length and width are relatively prime and L + W = n.
- A334632 (program): Decimal expansion of Sum_{k>=0} (-1)^k / ((2*k)!)^2.
- A334656 (program): a(n) is the number of words of length n on the alphabet {0,1,2} with the number of 0’s plus the number of 1’s congruent to the number of 2’s modulo 3.
- A334657 (program): Dirichlet g.f.: 1 / zeta(s-2).
- A334659 (program): Dirichlet g.f.: 1 / zeta(s-3).
- A334660 (program): Dirichlet g.f.: 1 / zeta(s-4).
- A334668 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^7.
- A334669 (program): Denominator of Sum_{k=1..n} (-1)^(k+1)/k^7.
- A334670 (program): a(n) = (2*n+1)!! * (Sum_{k=1..n} 1/(2*k+1)).
- A334673 (program): a(n) = 23*a(n-1) - a(n-2) + 1 for n > 1, a(0)=0, a(1)=1.
- A334680 (program): a(n) is the total number of down-steps after the final up-step in all 2-Dyck paths of length 3*n (n up-steps and 2*n down-steps).
- A334682 (program): a(n) is the total number of down-steps after the final up-step in all 3-Dyck paths of length 4*n (n up-steps and 3*n down-steps).
- A334694 (program): a(n) = (n/4)*(n^3+2*n^2+5*n+8).
- A334702 (program): Array read by antidiagonals: T(n,k) = binomial(n*k,3), n>=0, k>=0.
- A334703 (program): Triangle read by rows: T(n,k) = binomial(n*k,3) (0 <= k <= n).
- A334706 (program): Number of collinear triples in a 4 X n rectangular grid.
- A334716 (program): a(n) = !n + n * n!, where !n = A000166(n) is subfactorial of n.
- A334719 (program): a(n) is the total number of down-steps after the final up-step in all 4-Dyck paths of length 5*n (n up-steps and 4*n down-steps).
- A334721 (program): Denominator of the product of n and the n-th harmonic alternating number, Sum_{k=1..n} (-1)^(k+1)/k.
- A334724 (program): Denominator of the sum of all elements of the n X n matrix M with M[i,j] = (-1)^(i+j)*i/j for i,j = 1..n.
- A334734 (program): Denominator of Sum_{k=1..n} k^4 / Product_{k=1..n} k^4.
- A334735 (program): Denominator of Sum_{k=1..n} k^2 / Product_{k=1..n} k^2.
- A334762 (program): a(n) = ceiling (n / A000005(n)).
- A334764 (program): a(n) = Product_{k=1..n} d(2*k - 1), where d() is the number of divisors function A000005.
- A334767 (program): a(n) = Product_{k=1..n} d(2*k), where d() is the number of divisors function A000005.
- A334789 (program): a(n) = 2^log_2*(n) where log_2*(n) = A001069(n) is the number of log_2(log_2(…log_2(n))) iterations needed to reach < 2.
- A334841 (program): a(0) = 0; for n > 0, a(n) = (number of 1’s and 3’s in base 4 representation of n) - (number of 0’s and 2’s in base 4 representation of n).
- A334843 (program): Decimal expansion of arclength between (0,0) and (Pi/6,1/2) on y = sin x.
- A334852 (program): a(1) = 1, a(n) = a(n-1) / gcd(a(n-1),n) if this gcd is > 1, else a(n) = a(n-1) + 2.
- A334854 (program): E.g.f. A(x) satisfies: A(x) = arctan(x * exp(A(x))).
- A334891 (program): Number of ways to choose 4 points that form an square from the A000292(n) points in a regular tetrahedral grid where each side has n vertices.
- A334907 (program): Comtet’s expansion of the e.g.f. (sqrt(1 + sqrt(8*s)) - sqrt(1 - sqrt(8*s)))/ sqrt(8*s * (1 - 8*s)).
- A334908 (program): Area/6 of primitive Pythagorean triangles generated by {{2, 0}, {1, -1}}^n*{{2}, {1}}, for n >= 0.
- A334909 (program): Area/6 of primitive Pythagorean triangles given in A334638 as triples.
- A334913 (program): a(n) is the sum of digits of n in signed binary nonadjacent form.
- A334930 (program): Numbers that generate rotationally symmetrical XOR-triangles featuring singleton zero bits in a hexagonal arrangement.
- A334940 (program): Partial sums of A230595.
- A334954 (program): a(n) is 1 plus the number of divisors of n.
- A334957 (program): Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k self loops, n>=0, 0<=k<=n.
- A334958 (program): GCD of consecutive terms of the factorial times the alternating harmonic series.
- A334987 (program): Sum of centered triangular numbers dividing n.
- A334988 (program): Sum of tetrahedral numbers dividing n.
- A334991 (program): a(n) = 4^n + 3 * 18^n.
- A334995 (program): Twice the area of triangle with coordinates (Fn, Fn+k), (Fn+2k, Fn+3k) and (Fn+4k, Fn+5k), where Fn is the n-th Fibonacci number A000045.
- A335021 (program): a(n) = Sum_{d|n, 1 < d < n} (-1)^(d + 1).
- A335022 (program): a(n) = Sum_{d|n, 1 < d < n} (-1)^(d + 1) * d.
- A335025 (program): Largest side lengths of almost-equilateral Heronian triangles.
- A335026 (program): a(n) = (n + 1)^2*a(n - 2) + a(n - 1), starting 0, 9, ….
- A335032 (program): Dirichlet g.f.: zeta(s) * zeta(s-1) * Product_{p prime} (1 + p^(1 - s) - p^(-s)).
- A335048 (program): Minimum sum of primes (see Comments).
- A335063 (program): a(n) = Sum_{k=0..n} (binomial(n,k) mod 2) * k.
- A335073 (program): a(n) = Sum_{k=1..n} 2^(bigomega(k) - omega(k)).
- A335087 (program): Row sums of A335436.
- A335090 (program): a(n) = ((2*n+1)!!)^2 * (Sum_{k=1..n} 1/(2*k+1)^2).
- A335091 (program): a(n) = ((2*n+1)!!)^3 * (Sum_{k=1..n} 1/(2*k+1)^3).
- A335092 (program): a(n) = ((2*n+1)!!)^4 * (Sum_{k=1..n} 1/(2*k+1)^4).
- A335110 (program): a(n) = Sum_{k=0..n} (Stirling1(n,k) mod 2) * k.
- A335111 (program): a(n) = n! * Sum_{k=0..n-1} (-2)^k / k!.
- A335115 (program): a(2*n) = 2*n - a(n), a(2*n+1) = 2*n + 1.
- A335129 (program): a(n) is the number of distinct lines created inside an n-gon when connecting vertex k to vertex 2k mod n.
- A335139 (program): a(n) = (prime(n + 1) +- k) / 2 where k is the smallest possible odd number such that a(n) is prime and a(n + 1) >= a(n).
- A335184 (program): a(n) is the number of subsets of {1,2,…,n} with at least two elements and the difference between successive elements at least 6.
- A335242 (program): a(n) = 2*a(n-1) + a(n-3) for n >= 4, with initial values a(0) = 1, a(1) = 0, a(2) = 2, and a(3) = 3.
- A335259 (program): Triangle read by rows: T(n,k) = k^ceiling(n/k) for 1 <= k <= n.
- A335262 (program): Triangle of triangular numbers, read by rows, constructed like this: Given a sequence t, start row 0 with t(0). Compute row n for n > 0 by reversing row n-1 and prepending t(n). The sequence t is here chosen as the triangular numbers.
- A335274 (program): a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4.
- A335285 (program): a(n) is the greatest possible greatest part of any partition of n into prime parts.
- A335298 (program): a(n) is the squared distance between the points P(n) and P(0) on a plane, n>=0, such that the distance between P(n) and P(n+1) is n+1 and, going from P(n) to P(n+2), a 90-degree-left-turn is taken in P(n+1).
- A335309 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * n^(n-k).
- A335310 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n+k,k) * (-n)^(n-k).
- A335322 (program): Triangle read by rows: T(n, k) = binomial(n, floor((n+k+1)/2) with k <= n.
- A335324 (program): Square part of 4th-power-free part of n.
- A335334 (program): Sum of the integers in the reduced residue system of A002110(n).
- A335340 (program): North-East paths from (0,0) to (n,n) with k cyclic descents.
- A335341 (program): Sum of divisors of A003557(n).
- A335344 (program): E.g.f.: exp(x^2/(2*(1 - x)^2)).
- A335386 (program): Tri-unitary highly composite numbers: where the number of tri-unitary divisors (A335385) increases to a record.
- A335402 (program): Numbers m such that the only normal integer partition of m whose run-lengths are a palindrome is (1)^m.
- A335408 (program): Diameter of nearest neighbor interchange distance for free 3-trees.
- A335429 (program): Partial sums of A329697.
- A335439 (program): a(n) = n*(n-1)/2 + 2^(n-1) - 1.
- A335489 (program): Number of strict permutations of the prime indices of n.
- A335519 (program): Number of contiguous divisors of n.
- A335551 (program): Number of words of length n over the alphabet {0,1,2} that contain the substring 12 but not the substring 01.
- A335559 (program): a(n) = 3*a(n-1) + 4*a(n-2) - 2*a(n-3) with a(0)=0, a(1)=1, a(2)=2.
- A335567 (program): Number of distinct positive integer pairs (s,t) such that s <= t < n where neither s nor t divides n.
- A335587 (program): a(n) is the sum of the numbers k such that 0 <= k <= n and n AND k = 0 (where AND denotes the bitwise AND operator).
- A335595 (program): E.g.f.: exp(-x * (2 + x)) / (1 - x)^2.
- A335607 (program): Rectangular array by antidiagonals: T(n,k) = floor(n + k*r), where r = sqrt(2).
- A335608 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 2) missing one edge.
- A335612 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are incident to the same vertex in the three point part.
- A335616 (program): a(n) is twice the number of partitions of n into consecutive parts, minus the number of partitions of n into consecutive parts that contain 1 as a part.
- A335647 (program): a(n) = binomial(4*n+1,n+1).
- A335648 (program): Partial sums of A006010.
- A335649 (program): a(n) is the frequency of multi-pairs in a sequence of multi-set designs with 2 blocks.
- A335690 (program): a(1) = 1, a(2) = a(3) = 2; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3).
- A335691 (program): A000166(n)^2.
- A335699 (program): Irregular tree read by rows: take the Stern-Brocot tree A007305(n)/A007306(n) and set a(n) = A007306(n) - A007305(n) mod 3.
- A335700 (program): A variant of A000179 and A102761.
- A335718 (program): a(n) = 2*a(n-1) + 3*a(n-2) + 5*a(n-3), a(0) = 0, a(1) = 1, a(2) = 2.
- A335720 (program): a(n) = 2*a(n-1) + 3*a(n-2) + 5*a(n-3), a(0) = 0, a(1) = 1, a(2) = 1.
- A335741 (program): Number of Pell numbers (A000129) <= n.
- A335749 (program): a(n) = n!*[x^n] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(6).
- A335756 (program): A cup filling problem starting with 2 empty cups of sizes 3 and n, where a(n) is the number of unreachable states (see details in comments).
- A335789 (program): a(n) = time to the nearest second at the n-th instant (n>=0) when the hour and minute hands on a clock face coincide, starting at time 0:00.
- A335807 (program): Number of vertices in the n-th simplex graph of the complete graph on three vertices (K_3).
- A335819 (program): E.g.f.: exp((3/2) * x * (2 + x)).
- A335821 (program): Triangular array T(n, k) = n^2 - k^2, read by rows.
- A335840 (program): Expansion of x*(1+2*x)/((1-2*x)*(1-x+4*x^2)).
- A335841 (program): Number of distinct rectangles that can be made with one even and one odd side length that are divisors of 2n.
- A335843 (program): a(n) is the number of n-digit positive integers with exactly two distinct base 10 digits.
- A335857 (program): a(n) is the determinant of the n X n Hankel matrix A with A(i,j) = A000108(i+j+6) for 0<=i,j<=n-1.
- A335858 (program): Nonnegative integers ordered by binary length and then lexicographically by run lengths (considering least significant runs first).
- A335860 (program): Partial sums of A064097.
- A335862 (program): Decimal expansion of the zero x1 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
- A335863 (program): Decimal expansion of the negative of the zero x2 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
- A335864 (program): Decimal expansion of the negative of the zero x3 of the cubic polynomial x^3 - 2*x^2 - 10*x - 6.
- A335865 (program): Moduli a(n) = v(n) for the simple difference sets of Singer type of order m(n) (v(n), m(n)+1, 1) in the additive group modulo v(n) = m(n)^2 + m(n) + 1, with m(n) = A000961(n).
- A335873 (program): Total number of points in all permutations of [n] that are fixed or reflected.
- A335876 (program): a(1) = 2, and for n > 1, a(n) = n + (n/p), where p is largest prime dividing n, A006530(n).
- A335903 (program): Column 1 in the matrix of A279212 (whose indexing starts at 0).
- A335927 (program): a(n+1) = Sum_{k=1..n} (a(k) + k*(n-k)), with a(1)=1.
- A335950 (program): Sparse rulers with length a(n) cannot be perfect rulers.
- A335956 (program): a(n) = (2^n - 1)*2^valuation(n, 2) for n > 0 and a(0) = 0.
- A335965 (program): a(n) = number of odd numbers in the n-th row of the Narayana triangle A001263.
- A335979 (program): Number of partitions of n into exactly two parts with no decimal carries.
- A336017 (program): a(n) = floor(frac(Pi*n)*n), where frac denotes the fractional part.
- A336018 (program): a(n) = floor(frac(log_2(n))*n), where frac denotes the fractional part.
- A336040 (program): Characteristic function of refactorable numbers (A033950).
- A336102 (program): Number of inseparable multisets of size n covering an initial interval of positive integers.
- A336109 (program): First column of dispersion array A120861.
- A336113 (program): a(n) is the numerator of Sum_{odd d|n} 1/d.
- A336114 (program): The hafnian of a symmetric Toeplitz matrix of order 2*n, n>=2 with the first row (0,1,2,…,2,1); a(0)=a(1)=1.
- A336122 (program): Numbers k for which A335884(k) = 2.
- A336126 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A007814(1+A000265(i)) = A007814(1+A000265(j)), for all i, j >= 1.
- A336146 (program): Lexicographically earliest infinite sequence such that a(i) = a(j) => A000035(i) = A000035(j) and A000265(i) = A000265(j), for all i, j >= 1.
- A336165 (program): G.f. A(x) satisfies: A(x) = 1 + x * ((1 - x) * A(x))^2.
- A336174 (program): Number of non-symmetric binary n X n matrices M over the reals such that M^2 is the transpose of M.
- A336180 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k)^3.
- A336181 (program): a(n) = Sum_{k=0..n} (-2)^k * binomial(n,k)^3.
- A336182 (program): a(n) = Sum_{k=0..n} (-3)^k * binomial(n,k)^3.
- A336186 (program): Side length of a square block of integers, with 1 at the top-left corner, on a diagonally numbered 2D board such that the sum of the integers in the square is a perfect square.
- A336188 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k)^n.
- A336194 (program): Table read by antidiagonals upwards: T(n,k) = (n - 1)*k^3 - 1, with n > 1 and k > 0.
- A336202 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k)^n.
- A336204 (program): a(n) = Sum_{k=0..n} 2^k * binomial(n,k)^n.
- A336212 (program): a(n) = Sum_{k=0..n} 3^k * binomial(n,k)^n.
- A336213 (program): a(n) = Sum_{k=0..n} k^k * binomial(n,k)^n, with a(0)=1.
- A336214 (program): a(n) = Sum_{k=0..n} k^n * binomial(n,k)^n, with a(0)=1.
- A336231 (program): Integers whose binary digit expansion has an even number of 0’s between any two consecutive 1’s.
- A336234 (program): Edge length of ‘Prime squares’: sum the four numbers at the corners of a square drawn on a diagonally numbered 2D board, with 1 at the corner of the square. The sequence gives the size of the square such that the sum is a prime number.
- A336236 (program): a(n) = prime(n-2) - a(n-2) for n > 2, starting with a(1)=1, a(2)=1.
- A336241 (program): a(n) = (n!)^2 * Sum_{d|n} 1 / (d!)^2.
- A336247 (program): a(n) = (n!)^n * Sum_{k=0..n} 1 / (k!)^n.
- A336257 (program): a(n) = Catalan(n) mod (2*n+1).
- A336266 (program): Decimal expansion of (3/16)*Pi.
- A336276 (program): a(n) = Sum_{k=1..n} mu(k)*k^2.
- A336277 (program): a(n) = Sum_{k=1..n} mu(k)*k^3.
- A336278 (program): a(n) = Sum_{k=1..n} mu(k)*k^4.
- A336283 (program): Row sums of A192933.
- A336286 (program): The hafnian of a symmetric Toeplitz matrix of order 2n, n>=2 with the first row (0,1,2,…,2,0); a(0)=a(1)=1.
- A336288 (program): Numbers of squares formed by this procedure on n-th step: Step 1, draw a unit square. Step n, draw a unit square with center in every intersection of lines of the figure in step n-1.
- A336291 (program): a(n) = (n!)^2 * Sum_{k=1..n} 1 / (k * ((n-k)!)^2).
- A336292 (program): a(n) = (n!)^2 * Sum_{k=1..n} (-1)^(n-k) / (k * ((n-k)!)^2).
- A336293 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * binomial(2*k,k) * (n-k)!.
- A336298 (program): Greatest prime < prime(n)/2.
- A336302 (program): a(n) = n^2 mod ceiling(sqrt(n)).
- A336305 (program): Alternating row sums of triangle A211343.
- A336308 (program): Decimal expansion of (5/32)*Pi.
- A336337 (program): Total number of records over all length n ternary words (words on alphabet {0,1,2}).
- A336339 (program): Numbers composite(n) such that gcd(n,composite(n)) is even.
- A336341 (program): a(n) = (1/2)A336339(n).
- A336388 (program): Number of prime divisors of sigma(n) that divide n; a(1) = 0.
- A336398 (program): Number of rational knots (or two-bridge knots) with n crossings (chiral pairs counted as distinct).
- A336407 (program): a(n) is the number of composites < n-th odd composite.
- A336409 (program): Distance from prime(n) to the nearest odd composite that is < prime(n).
- A336410 (program): Numbers k such that prime(k) - oc(k) = 2, where oc(k) is the greatest odd composite < prime(k).
- A336457 (program): a(n) = A065330(sigma(n)), where A065330 is fully multiplicative with a(2) = a(3) = 1, and a(p) = p for primes p > 3.
- A336466 (program): Fully multiplicative with a(p) = A000265(p-1) for any prime p, where A000265(k) gives the odd part of k.
- A336475 (program): Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = (e+1)*p^e.
- A336476 (program): a(n) = gcd(A000593(n), A336475(n)).
- A336477 (program): a(n) = 1 if a regular n-gon is constructible with ruler (or, more precisely, an unmarked straightedge) and compass, 0 otherwise.
- A336483 (program): Floor(n/10) + (5 times last digit of n).
- A336495 (program): a(n) = (-1)^n * Sum_{k=0..n} (-2)^k * binomial(n,k) * binomial(n^2+k+1,n)/(n^2+k+1).
- A336502 (program): Partial sums of A057003.
- A336513 (program): a(n) = Sum_{i=1..n} Product_{j=(i-1)*n+1..i*n} j.
- A336524 (program): Triangular array read by rows. T(n,k) is the number of unlabeled binary trees with n internal nodes and exactly k distinguished external nodes (leaves) for 0 <= k <= n+1 and n >= 0.
- A336529 (program): a(n) = (n^3+5*n+3)/3 + 2*floor(n/2) + a(n-2), with a(0)=1 and a(1)=3.
- A336535 (program): a(n) = (m(n)^2 + 3)*(m(n)^2 + 7)/32, where m(n) = 2*n - 1.
- A336537 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n^2+k+1,n)/(n^2+k+1).
- A336538 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^3 * (2 + A(x)).
- A336540 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x)^4 * (2 + A(x)).
- A336551 (program): a(n) = A003557(n) - 1.
- A336563 (program): Sum of proper divisors of n that are divisible by every prime that divides n.
- A336564 (program): a(n) = n - A308135(n), where A308135(n) is the sum of non-coreful divisors of n.
- A336567 (program): Sum of proper divisors of {n divided by its largest squarefree divisor}.
- A336602 (program): a(n) = 8*a(n-1) - 21*a(n-2) + 20*a(n-3) - 5*a(n-4), with initial terms a(0)=1, a(1)=7, a(2)=35, a(3)=154.
- A336614 (program): Number of n X n (0,1)-matrices A over the reals such that A^2 is the transpose of A.
- A336623 (program): First member of the Diophantine pair (m, k) that satisfies 8*(m^2 + m) = k^2 + k; a(n) = m
- A336624 (program): Triangular numbers that are one-eighth of other triangular numbers; T(t) such that 8*T(t)=T(u) for some u where T(k) is the k-th triangular number.
- A336625 (program): Indices of triangular numbers that are eight times other triangular numbers.
- A336626 (program): Triangular numbers that are eight times another triangular number.
- A336627 (program): Coordination sequence for the Manhattan lattice.
- A336630 (program): a(n) = 2*F(2*n+1) + 4*F(n+1)*F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).
- A336634 (program): Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(-x) * BesselI(0,2*sqrt(x))^2.
- A336642 (program): One less than the largest square dividing n: a(n) = A008833(n)-1.
- A336643 (program): Squarefree kernel of n divided by the squarefree part of n: a(n) = rad(n) / core(n).
- A336649 (program): Sum of divisors of A336651(n) (odd part of n divided by its largest squarefree divisor).
- A336650 (program): a(n) = p^e, where p is the smallest odd prime factor of n, and e is its exponent, with a(n) = 1 when n is a power of two.
- A336651 (program): Odd part of n divided by its largest squarefree divisor.
- A336652 (program): Sum of positive divisors of odd part of n that are divisible by every (odd) prime dividing it: a(n) = A057723(A000265(n)).
- A336691 (program): Number of distinct prime factors of 1+sigma(n).
- A336692 (program): Binary weight of 1+sigma(n).
- A336694 (program): a(n) = A329697(1+sigma(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.
- A336696 (program): Sum of odd divisors of 1+sigma(n).
- A336698 (program): a(n) = A000265(1+A000265(sigma(n))), where A000265(k) gives the odd part of k.
- A336699 (program): a(n) = A000265(1+A000265(sigma(A000265(n)))), where A000265(k) gives the odd part of k.
- A336705 (program): Coordination sequence for the half-Manhattan lattice.
- A336728 (program): a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-n)^(n-k) * binomial(n,k) * binomial(n,k-1) for n > 0.
- A336729 (program): G.f. A(x) satisfies: A(x) = 1 + x * A(x) / (1 + 3 * x * A(x)).
- A336743 (program): a(n) is the product of the first n positive evil numbers.
- A336751 (program): Smallest side of integer-sided triangles whose sides a < b < c are in arithmetic progression.
- A336753 (program): Largest side of integer-sided triangles whose sides a < b < c are in arithmetic progression.
- A336754 (program): Perimeters in increasing order of integer-sided triangles whose sides a < b < c are in arithmetic progression.
- A336756 (program): Perimeters in increasing order of primitive integer-sided triangles whose sides a < b < c are in arithmetic progression.
- A336804 (program): a(n) = (n!)^2 * Sum_{k=0..n} 2^(n-k) / (k!)^2.
- A336805 (program): a(n) = (n!)^2 * Sum_{k=0..n} 3^(n-k) / (k!)^2.
- A336807 (program): a(n) = (n!)^2 * Sum_{k=0..n} 4^(n-k) / (k!)^2.
- A336808 (program): a(n) = (n!)^2 * Sum_{k=0..n} 5^(n-k) / (k!)^2.
- A336809 (program): a(n) = (n!)^2 * Sum_{k=0..n} (k+1) / ((n-k)!)^2.
- A336819 (program): Odd values of D > 0 for which the generalized Ramanujan-Nagell equation x^2 + D = 2^m has two or more solutions in the positive integers.
- A336828 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2 * k^n.
- A336829 (program): a(n) = Sum_{k=0..n} binomial(n+k,k)^n.
- A336840 (program): Inverse Möbius transform of A048673.
- A336842 (program): Number of trailing 1-bits in the binary representation of A003961(n): a(n) = A007814(1+A003961(n)).
- A336843 (program): Period of binary representation of 1/A003961(n): a(n) = A007733(A003961(n)).
- A336845 (program): a(n) = A000005(n) * A003961(n), where A003961 is the prime shift towards larger primes, and A000005 gives the number of divisors of n, and also of A003961(n).
- A336846 (program): a(n) = gcd(sigma(A003961(n)), A000005(n)*A003961(n)).
- A336847 (program): a(n) = A003973(n) - A336846(n).
- A336849 (program): a(n) = A003961(n) / gcd(A003961(n), sigma(A003961(n))), where A003961 is the prime shift towards larger primes.
- A336850 (program): a(n) = gcd(A003961(n), sigma(A003961(n))), where A003961 is the prime shift towards larger primes.
- A336851 (program): a(n) = sigma(A003961(n)) - A003961(n), where A003961 is a prime shift towards larger primes, sigma is the sum of divisors.
- A336852 (program): a(n) = sigma(A003961(n)) - sigma(n).
- A336853 (program): a(n) = A003961(n) - n, where A003961 is the prime shift towards larger primes.
- A336856 (program): Prime-shifted analog of gcd(d(n), sigma(n)): a(n) = gcd(A000005(n), A003973(n)).
- A336861 (program): a(n) = ceiling((n-1-sqrt(n+1))/2).
- A336867 (program): Numbers k such that k! does not have distinct prime multiplicities.
- A336868 (program): Indicator function for numbers k such that k! has distinct prime multiplicities.
- A336882 (program): a(0) = 1; for k >= 0, 0 <= i < 2^k, a(2^k + i) = m_k * a(i), where m_k is the least odd number not in terms 0..2^k - 1.
- A336898 (program): a(n) = numerator(n / (4^n - 2^n)) for n > 0 and a(0) = 1.
- A336899 (program): a(n) = denominator(n / (4^n - 2^n)) for n > 0 and a(0) = 1.
- A336923 (program): a(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0.
- A336924 (program): a(n) = spf(1+sigma(n)), where spf is the smallest prime factor and sigma is the sum of divisors function.
- A336928 (program): a(n) = A329697(sigma(n)), where A329697 is totally additive with a(2) = 0 and a(p) = 1 + a(p-1) for odd primes.
- A336932 (program): The 2-adic valuation of A003973(n), the sum of divisors of prime shifted n.
- A336937 (program): The 2-adic valuation of sigma(n), the sum of divisors of n.
- A336945 (program): a(n) = binomial(3*n,n)/(2*n + 1) - 2*binomial(3*(n - 1),n - 1)/(2*n - 1) for n > 0 with a(0) = 1.
- A336947 (program): E.g.f.: 1 / (exp(-2*x) - x).
- A336948 (program): E.g.f.: 1 / (exp(-3*x) - x).
- A336949 (program): a(n) = n! * [x^n] 1 / (exp(-n*x) - x).
- A336950 (program): E.g.f.: 1 / (1 - x * exp(2*x)).
- A336951 (program): E.g.f.: 1 / (1 - x * exp(3*x)).
- A336952 (program): E.g.f.: 1 / (1 - x * exp(4*x)).
- A336955 (program): a(n) = Sum_{k=0..n} k^k * binomial(n, k)^2.
- A336958 (program): E.g.f.: 1 / (exp(2*x) - x).
- A336959 (program): E.g.f.: 1 / (1 - x * exp(-2*x)).
- A336969 (program): a(n) = n! * [x^n] 1 / (exp(n*x) - x).
- A337000 (program): E.g.f.: 1 / ((1 - x)*(2 - exp(x))).
- A337001 (program): a(n) = n! * Sum_{k=0..n} k^3 / k!.
- A337002 (program): a(n) = n! * Sum_{k=0..n} k^4 / k!.
- A337003 (program): a(n) = Sum_{k=1..n, gcd(n,k) = 1} binomial(n,k)^2.
- A337004 (program): Turn sequence of the R5 dragon curve.
- A337024 (program): Number of ways to tile a 2n X 2n square with 1 X 1 white and n X n black squares.
- A337025 (program): Number of n-state 2-symbol halt-free Turing machines.
- A337030 (program): a(n) is the number of squarefree composite numbers < prime(n).
- A337046 (program): Integers n such that n! = x^2 + y^3 + z^6 where x, y and z are nonnegative integers, is soluble.
- A337099 (program): Largest positive number using exactly n segments on a calculator display (when ‘6’ and ‘7’ are represented using 6 resp. 3 segments).
- A337101 (program): Number of partitions of n into two positive parts (s,t), s <= t, such that the harmonic mean of s and t is an integer.
- A337106 (program): Number of nontrivial divisors of n!.
- A337110 (program): Number of length three 1..n vectors that contain their geometric mean.
- A337130 (program): a(n) is the sum of all products of pairs of numbers joined by the diagonals of an n-gon when its vertices are numbered from 1 to n in order.
- A337132 (program): a(n) is the number of squares at distance n from the central square of a Vicsek fractal.
- A337134 (program): a(n) = Sum_{k=1..n} floor(sqrt(2k-1)).
- A337140 (program): Numbers n = a + b with a and b positive integers such that their product a*b = k^2 is a square.
- A337142 (program): a(n) is the number of words of length n over the alphabet {0,1,2} with at least two 1’s and exactly one occurrence of the subword 22.
- A337151 (program): a(n) = (n!)^2 * Sum_{k=0..n} (-1)^(n-k) * (k+1) / ((n-k)!)^2.
- A337152 (program): a(n) = 2^n * (n!)^2 * Sum_{k=0..n} 1 / ((-2)^k * (k!)^2).
- A337153 (program): a(n) = 3^n * (n!)^2 * Sum_{k=0..n} 1 / ((-3)^k * (k!)^2).
- A337154 (program): a(n) = 4^n * (n!)^2 * Sum_{k=0..n} 1 / ((-4)^k * (k!)^2).
- A337155 (program): a(n) = 5^n * (n!)^2 * Sum_{k=0..n} 1 / ((-5)^k * (k!)^2).
- A337167 (program): a(n) = 1 + 3 * Sum_{k=0..n-1} a(k) * a(n-k-1).
- A337168 (program): a(n) = (-1)^n + 2 * Sum_{k=0..n-1} a(k) * a(n-k-1).
- A337169 (program): a(n) = (-1)^n + 3 * Sum_{k=0..n-1} a(k) * a(n-k-1).
- A337171 (program): a(n) = A004186(n) mod n.
- A337173 (program): a(n) = Sum_{k=1..floor(n/2)} k^2 * (n-k)^2.
- A337174 (program): Number of pairs of divisors of n (d1,d2) such that d1 <= d2 and d1*d2 >= n.
- A337175 (program): Number of pairs of divisors of n, (d1,d2), such that d1 <= d2 and d1*d2 < n.
- A337177 (program): Sum of the divisors d of n such that d is not equal to n/d.
- A337178 (program): Number of biconnected geodetic graphs with n unlabeled vertices.
- A337180 (program): a(n) = Sum_{d|n} d * gcd(d,n/d).
- A337191 (program): If cards numbered 1 through n are “Down Two Table” shuffled (top two put on bottom one at a time, third from top card dealt to table) until all of the cards are placed on the table, a(n) is the number of the last card dealt.
- A337194 (program): a(n) = 1 + A000265(sigma(n)), where A000265 gives the odd part.
- A337195 (program): The 2-adic valuation of 1+A000265(sigma(n)), where A000265 gives the odd part.
- A337246 (program): Sum of the first coordinates of all pairs of prime divisors of n, (p,q), such that p <= q.
- A337252 (program): Digits of 2^n can be rearranged with no leading zeros to form t^2, for t not a power of 2.
- A337273 (program): Number of distinct positive integer pairs, (s,t), such that s < t < n where neither s nor t divides n.
- A337281 (program): a(n) = n*T(n), where T(n) = A000073(n) = n-th tribonacci number.
- A337282 (program): Partial sums of A337281.
- A337283 (program): a(n) = Sum_{i=0..n} i*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
- A337284 (program): a(n) = Sum_{i=1..n} (i-1)*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
- A337286 (program): a(n) = Sum_{i=0..n} i^2*T(i)^2, where T(i) = A000073(i) is the i-th tribonacci number.
- A337291 (program): a(n) = 3*binomial(4*n,n)/(4*n-1).
- A337292 (program): a(n) = 4*binomial(5*n,n)/(5*n-1).
- A337297 (program): Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 < d2.
- A337298 (program): Sum of the coordinates of all relatively prime pairs of divisors of n, (d1,d2), such that d1 <= d2.
- A337300 (program): Partial sums of the geometric Connell sequence A049039.
- A337302 (program): Number of X-based filling of diagonals in a diagonal Latin square of order n with fixed main diagonal.
- A337313 (program): a(n) is the number of n-digit positive integers with exactly three distinct base 10 digits.
- A337314 (program): a(n) is the number of n-digit positive integers with exactly four distinct base 10 digits.
- A337319 (program): a(n) = Sum_{i = 1..floor(log_2(n))+1} g(frac(n/2^i)), where g(t) = [0 if t = 0, -1 if 0 < t < 1/2, 1 if t >= 1/2], and where frac(x) denotes the fractional part.
- A337328 (program): Number of pairs of squarefree divisors of n, (d1,d2), such that d1 <= d2.
- A337333 (program): Number of pairs of odd divisors of n, (d1,d2), such that d1 <= d2.
- A337336 (program): a(n) = A048673(n^2).
- A337348 (program): Numbers formed as the product of two numbers without consecutive equal binary digits and sharing no common bits between them.
- A337349 (program): To get a(n), take 3*n+1 and divide out any power of 2; then multiply by 3, subtract 1 and divide out any power of 2.
- A337350 (program): a(n) is the number of lattice paths from (0,0) to (2n,2n) using only the steps (1,0) and (0,1) and which do not touch any other points of the form (2k,2k).
- A337360 (program): Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 <= d2.
- A337370 (program): Expansion of sqrt(2 / ( (1-12*x+4*x^2) * (1-2*x+sqrt(1-12*x+4*x^2)) )).
- A337387 (program): a(n) = Sum_{k=0..n} n^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
- A337388 (program): a(n) = Sum_{k=0..n} n^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
- A337390 (program): Expansion of sqrt((1-2*x+sqrt(1-12*x+4*x^2)) / (2 * (1-12*x+4*x^2))).
- A337391 (program): a(n) is the smallest n-digit number divisible by n^3.
- A337392 (program): Minimum m such that the convergence speed of m^^m is equal to n >= 2, where A317905(n) represents the convergence speed of m^^m (and m = A067251(n), the n-th non-multiple of 10).
- A337393 (program): Expansion of sqrt((1-5*x+sqrt(1-6*x+25*x^2)) / (2 * (1-6*x+25*x^2))).
- A337394 (program): Expansion of sqrt(2 / ( (1-6*x+25*x^2) * (1-5*x+sqrt(1-6*x+25*x^2)) )).
- A337396 (program): Expansion of sqrt((1-8*x+sqrt(1+64*x^2)) / (2 * (1+64*x^2))).
- A337397 (program): Expansion of sqrt(2 / ( (1+64*x^2) * (1-8*x+sqrt(1+64*x^2)) )).
- A337418 (program): Number of sets (in the Hausdorff metric geometry) at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the removed edges are not incident to the same vertex in the 3 point part but are incident to the same vertex in the other part.
- A337420 (program): a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n,2*k).
- A337421 (program): Expansion of sqrt((1-6*x+sqrt(1-4*x+36*x^2)) / (2 * (1-4*x+36*x^2))).
- A337422 (program): Expansion of sqrt((1-7*x+sqrt(1-2*x+49*x^2)) / (2 * (1-2*x+49*x^2))).
- A337465 (program): a(n) = Sum_{k=0..n} (-n)^(n-k) * binomial(2*k,k) * binomial(2*n+1,2*k).
- A337466 (program): Expansion of sqrt(2 / ( (1-4*x+36*x^2) * (1-6*x+sqrt(1-4*x+36*x^2)) )).
- A337467 (program): Expansion of sqrt(2 / ( (1-2*x+49*x^2) * (1-7*x+sqrt(1-2*x+49*x^2)) )).
- A337483 (program): Number of ordered triples of positive integers summing to n that are either weakly increasing or weakly decreasing.
- A337484 (program): Number of ordered triples of positive integers summing to n that are neither strictly increasing nor strictly decreasing.
- A337493 (program): Decimal expansion of 10800/Pi, number of minutes of arc in a radian.
- A337495 (program): Maximum number of preimages that a permutation of length n can have under the consecutive-123-avoiding stack-sorting map.
- A337499 (program): a(n) is the number of ballot sequences of length n tied or won by at most 2 votes.
- A337500 (program): a(n) is the number of ballot sequences of length n tied or won by at most 3 votes.
- A337501 (program): Minimum number of painted cells in an n X n grid to avoid unpainted trominoes.
- A337502 (program): Minimum number of painted cells in an n X n grid to avoid unpainted tetrominoes.
- A337503 (program): Minimum number of painted cells in an n X n grid to avoid unpainted pentominoes.
- A337509 (program): Number of partitions of n into two distinct parts (s,t), such that (t-s) | n, and where n/(t-s) <= s < t.
- A337519 (program): Length of the shortest walk in an n X n grid graph that starts in one corner and visits every edge.
- A337521 (program): a(n) = L(n)*a(n-1) + a(n-2) with a(0) = a(1) = 1 and L(n) the Lucas numbers A000032.
- A337524 (program): a(n) = d(n) * (d(n) - 1), where d is the number of divisors of n (A000005).
- A337527 (program): G.f.: Sum_{n>=0} (2^n + 1)^n * x^n / (1 + (2^n + 1)*x)^(n+1).
- A337535 (program): For n>1, a(n) is the least base b>2 such that the digits of n in base b contain the digit b-1; a(1)=1.
- A337549 (program): a(n) = A003972(n) - n.
- A337566 (program): a(n) is the number of possible decompositions of the polynomial n * (x + x^2 + … + x^q), where q > 1, into a sum of k polynomials, not necessarily all different; each of these polynomials is to be of the form b_1 * x + b_2 * x^2 + … + b_q * x^q where each b_i is one of the numbers 1, 2, 3, …, q and no two b_i are equal.
- A337569 (program): Decimal expansion of the real solution to x^3 = 3 - x.
- A337570 (program): Decimal expansion of the real positive solution to x^4 = 4-x.
- A337571 (program): Decimal expansion of the real positive solution to x^4 = x+4.
- A337623 (program): a(n) is the least positive multiple of 2*n-1 containing only the digits 0 and 1 in base n.
- A337624 (program): a(n) is the least positive integer in base n that when multiplied by 2n-1 will contain only the digits 0 and 1.
- A337631 (program): a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,…,n}.
- A337640 (program): a(n) = one-half of the number of cells in the central rectangle of the graph described in row 2n+1 of A333288.
- A337723 (program): a(n) = prime(n-2) - ceiling(a(n-2)/2); a(1)=0, a(2)=1.
- A337724 (program): a(n) = prime(n-2) - floor(a(n-2)/2); a(1)=0, a(2)=1.
- A337725 (program): a(n) = (3*n+1)! * Sum_{k=0..n} 1 / (3*k+1)!.
- A337726 (program): a(n) = (3*n+2)! * Sum_{k=0..n} 1 / (3*k+2)!.
- A337727 (program): a(n) = (4*n)! * Sum_{k=0..n} 1 / (4*k)!.
- A337728 (program): a(n) = (4*n+1)! * Sum_{k=0..n} 1 / (4*k+1)!.
- A337729 (program): a(n) = (4*n+2)! * Sum_{k=0..n} 1 / (4*k+2)!.
- A337730 (program): a(n) = (4*n+3)! * Sum_{k=0..n} 1 / (4*k+3)!.
- A337747 (program): Maximal number of 4-point circles passing through n points on a plane.
- A337749 (program): a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k / (n-2*k)!.
- A337750 (program): a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k / (n-3*k)!.
- A337751 (program): a(n) = n! * Sum_{k=0..floor(n/4)} (-1)^k / (n-4*k)!.
- A337753 (program): The number of n-digit numbers which are divisible by 3 and where all decimal digits are odd.
- A337771 (program): Number of positive integer pairs, (s,t), with s,t composite, such that s < t < n, and neither s nor t divides n.
- A337821 (program): For n >= 0, a(4n+1) = 0, a(4n+3) = a(2n+1) + 1, a(2n+2) = a(n+1).
- A337823 (program): a(n) = prime(n-1) - floor(a(n-1)/2); a(1)=1.
- A337843 (program): a(n) is n + the number of digits in the decimal expansion of n.
- A337851 (program): a(n) = (2^n + 2)^n.
- A337852 (program): a(n) = (2^(n+1) + 1)^n.
- A337855 (program): Number of n-digit positive integers that are the product of two integers ending with 5.
- A337864 (program): Numbers formed by removing from n each digit if it is a duplicate of the previous digit, from left to right.
- A337879 (program): a(n) is the length of the n-th line segment to draw the squares of the Fibonacci spiral without lifting the pencil, including superpositions.
- A337895 (program): Number of oriented colorings of the tetrahedral facets (or vertices) of a regular 4-dimensional simplex using n or fewer colors.
- A337896 (program): Number of chiral pairs of colorings of the 8 triangular faces of a regular octahedron or the 8 vertices of a cube using n or fewer colors.
- A337897 (program): Number of achiral colorings of the 8 triangular faces of a regular octahedron or the 8 vertices of a cube using n or fewer colors.
- A337898 (program): Number of achiral colorings of the 6 square faces of a cube or the 6 vertices of a regular octahedron using n or fewer colors.
- A337899 (program): Number of chiral pairs of colorings of the edges of a regular tetrahedron using n or fewer colors.
- A337900 (program): The number of walks of length 2n on the square lattice that start from the origin (0,0) and end at the vertex (2,0).
- A337901 (program): The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (3,0).
- A337902 (program): The number of walks of length 2n+1 on the square lattice that start from the origin (0,0) and end at the vertex (2,1).
- A337909 (program): Distinct terms of A080079 in the order in which they appear.
- A337923 (program): a(n) is the exponent of the highest power of 2 dividing the n-th Fibonacci number.
- A337928 (program): Numbers w such that (F(2n+1)^2, -F(2n)^2, -w) are primitive solutions of the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 1, where F(n) is the n-th Fibonacci number (A000045).
- A337929 (program): Numbers w such that (F(2*n-1)^2, -F(2*n)^2, w) are primitive solutions of the Diophantine equation 2*x^3 + 2*y^3 + z^3 = 1, where F(n) is the n-th Fibonacci number (A000045).
- A337934 (program): Sums of two distinct abundant numbers.
- A337937 (program): a(n) = Euler totient function phi = A000010 evaluated at N(n) = floor((3*n-1)/2) = A001651(n), for n >= 1.
- A337940 (program): Triangle read by rows: T(n, k) = T(n+2) - T(n-k), with the triangular numbers T = A000217, for n >= 1, k = 1, 2, …, n.
- A337945 (program): Numbers m with a solution (s,t,k) such that s^2 + t^2 = k*m, s + t = m, 1 <= s <= t and 1 <= k <= m - 1.
- A337949 (program): a(n) = 2^(n*(n-1)/2) + 2^(n*(n+1)/2) for n > 0, with a(0) = 1.
- A337951 (program): a(n) = 4^(n*(n-1)/2) + 4^(n*(n+1)/2) for n > 0, with a(0) = 1.
- A337957 (program): Number of unoriented colorings of the 8 cubic facets of a tesseract or of the 8 vertices of a hyperoctahedron.
- A337958 (program): Number of achiral colorings of the 8 cubic facets of a tesseract or of the 8 vertices of a hyperoctahedron.
- A337969 (program): a(n) = 3^(n*(n-1)/2) + 3^(n*(n+1)/2) for n > 0, with a(0) = 1.
- A337971 (program): a(n) = 5^(n*(n-1)/2) + 5^(n*(n+1)/2) for n > 0, with a(0) = 1.
- A337976 (program): Number of partitions of n into two distinct parts (s,t), such that s | t, (t-s) | n, and where n/(t-s) <= s < t.
- A337985 (program): a(n) is the exponent of the highest power of 2 dividing the n-th Bell number.
- A337997 (program): Triangle read by rows, generalized Eulerian polynomials evaluated at x = 1.
- A338020 (program): a(n) is the number of circles of positive integer area with radii less than n and greater than n - 1.
- A338041 (program): Draw n rays from each of two distinct points in the plane; a(n) is the number of regions thus created. See Comments for details.
- A338042 (program): Draw n rays from each of two distinct points in the plane; a(n) is the number of vertices thus created. See Comments for details.
- A338043 (program): Draw n rays from each of two distinct points in the plane; a(n) is the number of edges thus created. See Comments for details.
- A338045 (program): G.f.: Sum_{k>=0} x^(2^k) / (1 - x^(2^k))^3.
- A338046 (program): G.f.: Sum_{k>=0} x^(2^k) / (1 - x^(2^k))^4.
- A338062 (program): Numbers k such that the Enots Wolley sequence A336957(k) is odd.
- A338064 (program): Numbers k such that the Enots Wolley sequence A336957(k) is even.
- A338075 (program): Diagonal terms in the expansion of (1+x*y*z)/(1-x-y-z).
- A338076 (program): Diagonal terms in the expansion of 1/(1-x-2*y-3*z).
- A338086 (program): Duplicate the ternary digits of n, so each 0, 1 or 2 becomes 00, 11 or 22 respectively.
- A338100 (program): Number of spanning trees in the n X 2 king graph.
- A338101 (program): Smallest odd prime dividing n is a(n)-th prime, or 0 if no such prime exists.
- A338109 (program): a(n)/A002939(n+1) is the Kirchhoff index of the join of the disjoint union of two complete graphs on n vertices with the empty graph on n+1 vertices.
- A338110 (program): Number of spanning trees in the join of the disjoint union of two complete graphs each on n vertices with the empty graph on n vertices.
- A338112 (program): Least number that is both the sum and product of n distinct positive integers.
- A338117 (program): Number of partitions of n into two parts (s,t) such that (t-s) | n, where s < t.
- A338130 (program): Positive numbers k such that the ternary representation of k^k ends with that of k.
- A338157 (program): Numbers that follow from the alternating series a(n) = d(1) - d(2) + d(3) -d(4) + … + (-1)^(n+1) d(n), where d(k) denotes the k-th term of the digit sequence of the Golden Ratio.
- A338164 (program): Dirichlet g.f.: (zeta(s-2) / zeta(s))^2.
- A338186 (program): Expansion of (2-6*x-12*x^2)/((1-x)^2*(1-9*x)).
- A338199 (program): a(n) = v(1 + F(4*n - 3)), where F(x) = (3*x + 1)/2^v(3*x + 1), x is any odd natural number, and v(y) is the 2-adic valuation of y.
- A338200 (program): The number of similarity classes of pointed reflection spaces of residue two in an n-dimensional vector space over GF(2).
- A338204 (program): a(n) is the sum of odd-indexed terms (of every row) of the first n rows of the triangle A237591.
- A338206 (program): Inverse of A160016.
- A338215 (program): a(n) = A095117(A062298(n)).
- A338225 (program): a(n) = F(n+3) * F(n+1) + (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
- A338226 (program): a(n) = Sum_{i=0..n-1} i*10^i - Sum_{i=0..n-1} (n-1-i)*10^i.
- A338227 (program): a(n) = x(n) mod floor(sqrt(x(n))), where x(n) = floor((n^2)/2).
- A338228 (program): Number of numbers less than or equal to n whose square does not divide n.
- A338229 (program): Number of ternary strings of length n that contain at least one 0 and at most two 1’s.
- A338230 (program): Number of ternary strings of length n that contain at least two 0’s and at most one 1.
- A338231 (program): Sum of the numbers less than or equal to n whose square does not divide n.
- A338233 (program): Number of numbers less than n whose square does not divide n.
- A338234 (program): Sum of the numbers less than n whose square does not divide n.
- A338236 (program): Number of numbers less than or equal to sqrt(n) whose square does not divide n.
- A338242 (program): a(n) = -A338241(2*n) for any n >= 0.
- A338243 (program): a(0) = 0, a(n) = A338241(2*n-1) for any n > 0.
- A338245 (program): Nonnegative values in A117966, in order of appearance.
- A338246 (program): Nonpositive values in A117966, in order of appearance and negated.
- A338247 (program): Inverse permutation to A338245.
- A338248 (program): Nonnegative values in A053985, in order of appearance.
- A338249 (program): Nonpositive values in A053985, in order of appearance and negated.
- A338280 (program): Triangle T read by rows: T(n, k) = k*n^(n-k-1) with 0 < k < n.
- A338281 (program): a(n) is the sum of n and the largest proper divisor of n.
- A338321 (program): Trace of complement matrix for polynomial triangle centers of degree n (on the Nagel line).
- A338329 (program): First differences of A326118.
- A338337 (program): Coefficient of x^(6*n)*y^(6*n)*z^(6*n) in the expansion of 1/(1-x-y^2-z^3).
- A338353 (program): A (0,1)-matrix in the first quadrant read by downward antidiagonals: an example of a non-uniformly recurrent 2-D word having uniformly recurrent rows and columns.
- A338354 (program): A (0,1)-matrix in the first quadrant read by downward antidiagonals: an example of a uniformly recurrent 2-D word in which row 0 is non-recurrent.
- A338361 (program): Indices of primes in A283312.
- A338363 (program): a(n) = n + pi(n) - pi(floor(n/2)), where pi = A000720.
- A338369 (program): Triangle read by rows: T(n,k) = (Sum_{i=0..n-k}(1+k*i)^3)/(Sum_{i=0..n-k} (1+k*i)) for 0 <= k <= n.
- A338429 (program): Maximum number of copies of a 1234 permutation pattern in an alternating (or zig-zag) permutation of length n + 5.
- A338432 (program): Triangle read by rows: T(n, k) = (n - k + 1)^2 + 2*k^2, for n >= 1, and k = 1, 2, …, n.
- A338467 (program): a(n+1) = prime(n) + 2*n - a(n). a(1) = 1.
- A338506 (program): a(n) is the number of subsets of divisors of n.
- A338522 (program): Number of cyclic Latin squares of order n.
- A338524 (program): prime(n) Gray code decoding.
- A338529 (program): a(n) = prime(n+2)*prime(n+3)-prime(n)*prime(n+1).
- A338530 (program): a(n) = (prime(n) + a(n-1)) mod prime(n-1), a(1) = 1.
- A338544 (program): a(n) = (5*floor((n-1)/2)^2 + (4+(-1)^n)*floor((n-1)/2)) / 2.
- A338546 (program): For n > 0, a(n) is the number of 1’s among the first T(n) terms of the sequence 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, …, k 1’s, k 0’s, where T(n) is the n-th triangular number.
- A338550 (program): Number of binary trees of height n such that the number of nodes at depth d equals d+1 for every d = 0..n.
- A338576 (program): a(n) = n * pod(n) where pod(n) = the product of divisors of n (A007955).
- A338588 (program): a(n)/A002939(n+1) is the Kirchhoff index of the disjoint union of two complete graphs each on n and n+1 vertices with the empty graph on n+1 vertices.
- A338589 (program): Sum of the remainders (s*t mod n), where s + t = n and 1 <= s <= t.
- A338595 (program): Denominators of resistance values < 1 ohm that can be obtained from a network of exactly 5 one-ohm resistors, but not from any network with fewer than 5 one-ohm resistors. Numerators are in A338580.
- A338610 (program): Integers m such that there exist one prime p and one positive integer k, for which the expression k^3 + k^2*p is a perfect cube m^3.
- A338616 (program): a(n) is twice the number of parts in all partitions of n into consecutive parts.
- A338623 (program): a(n) is the length of the longest block of consecutive terms appearing twice (possibly with overlap) among the first n terms of the Thue-Morse sequence (A010060).
- A338630 (program): Least number of odd primes that add up to n, or 0 if no such representation is possible.
- A338647 (program): a(n) = Sum_{k=1..n} 2^(k/gcd(n,k) - 1).
- A338648 (program): Number of divisors of n which are greater than 4.
- A338649 (program): Number of divisors of n which are greater than 5.
- A338650 (program): Number of divisors of n which are greater than 6.
- A338651 (program): Number of divisors of n which are greater than 7.
- A338652 (program): Number of divisors of n which are greater than 8.
- A338653 (program): Number of divisors of n which are greater than 9.
- A338666 (program): a(1)=1 and a(2)=2. For all n > 2, a(n) is the smallest number > a(n-1) by a number > the difference between a(n-1) and a(n-2) so that consecutive terms of sequence are always relatively prime.
- A338695 (program): a(n) = Sum_{d|n} 2^(d-1) * binomial(d, n/d).
- A338717 (program): a(n) = sum of 4th powers of entries in row n of Stern’s triangle A337277.
- A338718 (program): Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = floor(b(n)).
- A338719 (program): Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = ceiling(b(n)).
- A338720 (program): Define b(1)=1 and for n>1, b(n)=n/b(n-1); then a(n) = nearest integer to b(n).
- A338722 (program): Row sums in triangle A338721.
- A338726 (program): a(n) = Catalan(n) + 2^n - n - 1.
- A338727 (program): a(n) = C(n+1)^2 - 2*C(n+1)*C(n) + C(n)^2, where C() is a Catalan number.
- A338731 (program): Generating function Sum_{n >= 0} a(n)*x^n = Sum_{k>=1} x^(k*(3*k+1)/2)/(1-x^k).
- A338733 (program): Partial sums of A054843.
- A338758 (program): a(n) is the sum of even-indexed terms (of every row) of first n rows of the triangle A237591.
- A338760 (program): Subword complexity of a certain infinite word.
- A338795 (program): Each term of A003215 (centered hexagonal numbers) is multiplied by the corresponding term of A003154 (centered dodecagonal numbers).
- A338796 (program): Triangle T read by rows: T(n, k) is the k-th row sum of the symmetric Toeplitz matrix M(n) whose first row consists of a single zero followed by successive positive integers repeated (A004526).
- A338803 (program): Product of the nonzero digits of (n written in base 5).
- A338814 (program): Expansion of e.g.f. log(Product_{k>0} (1 + x^k)^(1/k)).
- A338824 (program): Lexicographically earliest sequence of nonnegative integers such that for any distinct m and n, a(m) OR a(m+1) <> a(n) OR a(n+1) (where OR denotes the bitwise OR operator).
- A338852 (program): a(n) = (7*floor(a(n-1)/3)) + (a(n-1) mod 3) with a(1) = 3.
- A338854 (program): Product of the nonzero digits of (n written in base 4).
- A338857 (program): With S(n,k) = Sum_{n<=j<=k} 1/(2*j+1), a(n)=k+1 such that S(n,k-1) < 1 <= S(n,k) for n>=0 and a(0)=1.
- A338863 (program): Product of the nonzero digits of (n written in base 6).
- A338878 (program): Numerators in a set of expansions of the single-term Machin-like formula for Pi.
- A338880 (program): Product of the nonzero digits of (n written in base 7).
- A338882 (program): Product of the nonzero digits of (n written in base 9).
- A338888 (program): a(n) = (a(n-2) bitwise-OR a(n-1)) + 1; a(1)=0, a(2)=0.
- A338896 (program): Inradii of Pythagorean triples of A338895.
- A338901 (program): Position of the first appearance of prime(n) as a factor in the list of squarefree semiprimes.
- A338913 (program): Greater prime index of the n-th semiprime.
- A338920 (program): a(n) is the number of times it takes to iteratively subtract m from n where m is the largest nonzero proper suffix of n less than or equal to the remainder until no further subtraction is possible.
- A338929 (program): a(n) is the smallest prime number p larger than A072668(n) such that p is equal to 1 (mod A072668(n)).
- A338935 (program): a(n) = Sum_{d|n} (d^2 mod n).
- A338939 (program): a(n) is the number of partitions n = a + b such that a*b is a perfect square.
- A338979 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k) * Catalan(k).
- A338991 (program): a(n) = Sum_{k=1..floor(n/2)} (n-2*k) * floor((n-k)/k).
- A338995 (program): Triangle T(n,m):=binomial(n+3*m+2,n-m).
- A338996 (program): Numbers of squares and rectangles of all sizes in 3*n*(n+1)/2-ominoes in form of three-quarters of Aztec diamonds.
- A339012 (program): Written in factorial base, n ends in a(n) consecutive non-0 digits.
- A339013 (program): Class number m containing n in a partitioning of the natural numbers into classes B_m by William J. Keith.
- A339032 (program): Expansion of (4*x^5 - 9*x^4 + 17*x^3 - 15*x^2 + 6*x - 1)/((2*x - 1)^2*(x - 1)^3).
- A339034 (program): Row sums of A339033.
- A339048 (program): a(n) = 2*n^2 + 9.
- A339051 (program): Even bisection of the infinite Fibonacci word A096270.
- A339052 (program): Odd bisection of the infinite Fibonacci word A096270.
- A339053 (program): a(n) = least k such that the first n-block in A339051 occurs in A339052 beginning at the k-th term.
- A339114 (program): Least semiprime whose prime indices sum to n.
- A339124 (program): a(n) is the number of squares at distance n from the central square of a golden square fractal.
- A339136 (program): Number of (undirected) cycles in the graph C_3 X P_n.
- A339146 (program): a(n) = a(floor(n / 5)) * (n mod 5 + 1); initial terms are 1.
- A339183 (program): Number of partitions of n into two parts such that the smaller part is a nonzero square.
- A339194 (program): Sum of all squarefree semiprimes with greater prime factor prime(n).
- A339196 (program): Number of (undirected) cycles on the n X 2 king graph.
- A339217 (program): a(n) = Sum_{k=1..n} floor((2*n-k)/k).
- A339240 (program): a(n) = n*2^(2*n-2) + n*binomial(2*n,n)/2.
- A339252 (program): a(0) = 1, a(1) = 4, a(2) = 11, and a(n) = 4*a(n-1) - 4*a(n-2) for n >= 3.
- A339255 (program): Leading digit of n in base 5.
- A339256 (program): Leading digit of n in base 6.
- A339265 (program): Expansion of Product_{n >= 1} (1 - x^(2*n))*(1 - x^(2*n-1))*(1 - x^(2*n+1)).
- A339267 (program): Level of the Calkin-Wilf tree in which the n-th convergent of the continued fraction for e appears.
- A339308 (program): Partial sums of products of proper divisors of n (A007956).
- A339311 (program): a(n) = Sum_{k=1..n} (k!)^n.
- A339332 (program): Sums of antidiagonals in A283683.
- A339353 (program): G.f.: Sum_{k>=1} k^2 * x^(k*(k + 1)) / (1 - x^k).
- A339354 (program): G.f.: Sum_{k>=1} k^3 * x^(k*(k + 1)) / (1 - x^k).
- A339355 (program): Maximum number of copies of a 12345 permutation pattern in an alternating (or zig-zag) permutation of length n + 7.
- A339356 (program): Maximum number of copies of a 123456 permutation pattern in an alternating (or zig-zag) permutation of length n + 9.
- A339358 (program): Maximum number of copies of a 1234567 permutation pattern in an alternating (or zig-zag) permutation of length n + 11.
- A339360 (program): Sum of all squarefree numbers with greatest prime factor prime(n).
- A339370 (program): a(n) = Sum_{k=1..floor(n/2)} (n-k) * floor((n-k)/k).
- A339391 (program): Maximum, over all binary strings w of length n, of the size of the smallest string attractor for w.
- A339411 (program): Product of partial sums of odd squares.
- A339423 (program): If n = p_1 * … * p_m with primes p_i <= p_{i+1}, a(n) = Sum_{k<m} Product_{j <= k} p_j.
- A339448 (program): a(n) = (prime(n) - a(n-1)) mod 3; a(0)=0.
- A339451 (program): Gray-code-like sequence in which, at each step, the least significant bit that has never been toggled from the previous value, is toggled.
- A339464 (program): a(n) = (prime(n)-1) / gpf(prime(n)-1) where gpf(m) is the greatest prime factor of m, A006530.
- A339470 (program): Decimal expansion of log(phi)^2, where phi is the golden ratio (A002390^2).
- A339480 (program): Numbers of the form (k^2 - 2) / 2 where k - 1 and k + 1 are both odd composite numbers.
- A339483 (program): Number of regular polygons that can be drawn with vertices on a centered hexagonal grid with side length n.
- A339487 (program): a(n) is the area of the n-gon with vertices (3^i, 5^i) for 0 <= i <= n-1.
- A339488 (program): a(n) = H(n-1, n, n+1) where H(a, b, c) = (a + b + c)*(a + b - c)*(b + c - a)*(c + a - b) is Heron’s polynomial.
- A339516 (program): a(n+1) = (a(n) - 2*(n-1)) * (2*n-1), where a(1)=1.
- A339531 (program): Numbers b > 1 such that the smallest two primes, i.e., 2 and 3 are base-b Wieferich primes.
- A339570 (program): Denote the van der Corput sequence of fractions 1/2, 1/4, 3/4, 1/8, 5/8, 3/8, 7/8, 1/16, … (A030101/A062383) by v(n), n >= 1. Then a(n) = denominator of v(A014486(n)).
- A339572 (program): If n even, a(n) = A000071(n/2+1); if n odd, a(n) = A001610((n-1)/2).
- A339573 (program): a(n) = floor(n*(n+1)/6) - 1.
- A339576 (program): Row sums of triangle A236104.
- A339577 (program): a(n) = product of nonzero entries in row n of A235791.
- A339597 (program): When 2*n+1 first appears in A086799.
- A339601 (program): Starting from x_0 = n, iterate by dividing with 3 (discarding any remainder), until zero is reached: x_1 = floor(x_0/3), x_2 = floor(x_1/3), etc. Then a(n) = Sum_{i=0..} (x_i AND 2^i), where AND is bitwise-and.
- A339609 (program): Consider a triangle drawn on the perimeter of a triangular lattice with side length n. a(n) is the number of regions inside the triangle after drawing unit circles centered at each lattice point inside the triangle.
- A339610 (program): Expansion of x*(2 - x - x^2 - 2*x^3)/(1 - x - x^2)^2.
- A339623 (program): Consider a square drawn on the perimeter of a square lattice with side length n. a(n) is the number of regions inside the square after drawing unit circles centered at each interior lattice point of the square.
- A339661 (program): Number of factorizations of n into distinct squarefree semiprimes.
- A339684 (program): a(n) = Sum_{d|n} 4^(d-1).
- A339685 (program): a(n) = Sum_{d|n} 5^(d-1).
- A339686 (program): a(n) = Sum_{d|n} 6^(d-1).
- A339687 (program): a(n) = Sum_{d|n} 7^(d-1).
- A339688 (program): a(n) = Sum_{d|n} 8^(d-1).
- A339689 (program): a(n) = Sum_{d|n} 9^(d-1).
- A339710 (program): a(n) = Sum_{k=0..n} binomial(n, k)*binomial(2*n + k, k)*2^k.
- A339711 (program): a(n) = A178901(n)/n.
- A339747 (program): a(n) = (5^(valuation(n, 5) + 1) - 1) / 4.
- A339748 (program): a(n) = (6^(valuation(n, 6) + 1) - 1) / 5.
- A339749 (program): a(n) is the greatest k > 0 such that 1+n, 1+2*n, …, 1+n*k are pairwise coprime.
- A339760 (program): Number of (undirected) Hamiltonian paths in the 2 X n king graph.
- A339765 (program): a(n) = 2*floor(n*phi) - 3*n, where phi = (1+sqrt(5))/2.
- A339771 (program): a(n) = Sum_{i=0..n} Sum_{j=0..n} 2^max(i,j).
- A339804 (program): a(n) = Sum_{k=1..floor(n/2)} k * (n-k) * floor((n-k)/k).
- A339824 (program): Even bisection of the infinite Fibonacci word A003849.
- A339825 (program): Odd bisection of the infinite Fibonacci word A003849.
- A339828 (program): a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - 4*a(n-4) + a(n-5) for n >= 6, where a(1) = 1, a(2) = 3, a(3) = 5, a(4) = 16, a(5) = 53.
- A339850 (program): Number of Hamiltonian circuits within parallelograms of size 3 X n on the triangular lattice.
- A339903 (program): Fully multiplicative with a(p) = A000265(q-1), where q = A151800(p), the next prime > p.
- A339904 (program): The odd part of {Euler totient function phi applied to the prime shifted n}: a(n) = A000265(A000010(A003961(n))).
- A339905 (program): Fully multiplicative with a(prime(k)) = prime(k+1) - 1.
- A339916 (program): The sum of 2^((d-1)/2) over all divisors of 2n+1.
- A339918 (program): a(n) = Sum_{k=1..n} floor(3*n/k).
- A339919 (program): a(n) = Sum_{k=1..n} (floor(3*n/k) - 3*floor(n/k)).
- A339950 (program): Numbers k such that all k-sections of the infinite Fibonacci word A014675 have just two different run-lengths.
- A339964 (program): a(n) = gcd(sigma(n), n+1).
- A339965 (program): a(n) = sigma(n) / gcd(sigma(n),n+1).
- A339966 (program): a(n) = (n+1) / gcd(sigma(n),n+1).
- A339967 (program): a(n) = gcd(sigma(n), n+2).
- A340051 (program): Mixed-radix representation of n where the least significant digit is in base 3 and other digits are in base 2.
- A340068 (program): a(n) is the number of integers in the set {n+1,n+2, . . . ,2n} whose representation in base 2 contain exactly three digits 1’s.
- A340071 (program): a(n) = gcd(A003961(n)-1, phi(A003961(n))), where A003961 shifts the prime factorization of n one step towards larger primes.
- A340073 (program): a(n) = (x-1) / gcd(x-1, phi(x)), where x = A003961(n), i.e., n with its prime factorization shifted one step towards larger primes.
- A340074 (program): a(n) = gcd(A003961(n)-1, A339904(n)).
- A340078 (program): a(n) = gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).
- A340079 (program): a(n) = n / gcd(n, 1+A018804(n)), where A018804(n) = Sum_{k=1..n} gcd(k, n).
- A340081 (program): a(n) = gcd(n-1, A003958(n)).
- A340082 (program): a(n) = A003958(n) / gcd(n-1, A003958(n)).
- A340083 (program): a(n) = (n-1) / gcd(n-1, A003958(n)).
- A340084 (program): a(n) = gcd(n-1, A336466(n)); Odd part of A340081(n).
- A340085 (program): a(n) = A336466(n) / gcd(n-1, A336466(n)); Odd part of A340082(n).
- A340086 (program): a(1) = 0, for n > 1, a(n) = A000265(n-1) / gcd(n-1, A336466(n)).
- A340087 (program): a(n) = gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler’s phi function.
- A340089 (program): a(n) = (n-1) / gcd(n-1, A091732(n)), where A091732 is an infinitary analog of Euler’s phi function.
- A340128 (program): a(n) = (n*prime(n)) mod prime(n+1).
- A340134 (program): a(n+1) = a(n-2*a(n)) + 1, starting with a(1) = a(2) = 0.
- A340161 (program): a(n) is the smallest number k for which the set {k + 1, k + 2, …, k + k} contains exactly n elements with exactly three 1-bits (A014311).
- A340163 (program): For n>=1, smallest integer k such that for all m>=k: m^(1/n)+(m+1)^(1/n) >= (2^n*m+2^(n-1)-1)^(1/n).
- A340172 (program): List of Y-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340171 gives X-coordinates.
- A340184 (program): n with the rightmost occurrence of the smallest digit of n deleted.
- A340199 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 3) missing two edges, where the two removed edges are not incident to the same vertex in the 3-point set and are also not incident to the same vertex in the other set.
- A340215 (program): Consider constructing binary words that begin with 0 such that the subword 00, whenever it appears, is followed by 111. Then a(n) counts such words at length n (including those where the string 111 is yet being completed - see Example).
- A340216 (program): Decimal expansion of the sum of the reciprocals of the squares of the positive triangular numbers.
- A340217 (program): Consider binary words that begin with 1 such that the subword 00, whenever it appears, is followed by 111. Then a(n) counts such words at length n (including those where the string 111 is yet being completed - see Example).
- A340227 (program): Number of pairs of divisors of n, (d1,d2), such that d1 < d2 and d1*d2 is squarefree.
- A340228 (program): a(n) is the sum of the lengths of all the segments used to draw a rectangle of height 2^(n-1) and width n divided into 2^(n-1) rectangles of unit height, in turn, divided into rectangles of unit height and lengths corresponding to the parts of the compositions of n.
- A340234 (program): Number of harmonious graphs with n edges and at most n vertices, allowing self-loops.
- A340251 (program): a(n) is the index of the bit that was inverted in A340250(n) to get A340250(n+1).
- A340257 (program): a(n) = 2^n * (1+n*(n+1)/2).
- A340262 (program): T(n, k) = multinomial(n + k/2; n, k/2) if k is even else 0. Triangle read by rows, for 0 <= k <= n.
- A340266 (program): The number of degrees of freedom in a quadrilateral cell for a serendipity finite element space of order n.
- A340301 (program): a(n) = n * floor(log_2(n)).
- A340309 (program): Number of ordered pairs of vertices which have two different shortest paths between them in the n-Hanoi graph (3 pegs, n discs).
- A340317 (program): (Product of primes <= n) read modulo n.
- A340323 (program): Multiplicative with a(p^e) = (p + 1) * (p - 1)^(e - 1).
- A340332 (program): E.g.f.: Sum_{n>=0} x^n * exp(3*2^n*x) / n!.
- A340335 (program): E.g.f.: Sum_{n>=0} x^n * exp(2^n*x).
- A340336 (program): E.g.f.: Sum_{n>=0} x^n * cosh(2^n*x).
- A340337 (program): E.g.f.: Sum_{n>=0} x^n * sinh(2^n*x).
- A340346 (program): The largest divisor of n that is a term of A055932 (numbers divisible by all primes smaller than their largest prime factor).
- A340363 (program): a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime and i, j >= 0, otherwise 0.
- A340368 (program): Multiplicative with a(p^e) = (p - 1) * (p + 1)^(e-1).
- A340369 (program): a(n) = 1 if n has at most 3 prime factors when counted with multiplicity, 0 otherwise.
- A340371 (program): a(n) = 1 if the odd part of n is noncomposite, 0 otherwise.
- A340373 (program): a(n) = 1 if n is of the form of 2^i * p^j, with p an odd prime, and i>=0, j>=1, otherwise 0.
- A340375 (program): a(n) = 1 if n is of the form 2^i - 2^j with i >= j, and 0 otherwise.
- A340378 (program): Number of 1-digits in the ternary representation of A048673(n).
- A340379 (program): Number of 2-digits in the ternary representation of A048673(n).
- A340395 (program): a(n) = A340131(A001006(n)).
- A340436 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where exactly two of the removed edges are incident to the same vertex in the 3-point set but none of the removed edges are incident to the same vertex in the other set.
- A340445 (program): Number of partitions of n into 3 parts that are not all the same.
- A340448 (program): Radio number of the cycle graph C_n.
- A340461 (program): a(n) = 2*sigma(phi(n)) - n.
- A340479 (program): a(n) = R(n) + digsum(n).
- A340494 (program): Index where n first appears in A340488.
- A340495 (program): Records in first differences of A340494.
- A340497 (program): Index where 2*n first appears in A340488.
- A340498 (program): Where 2^n appears in A340488 for the first time.
- A340503 (program): Fixed under 0 -> 02, 1 -> 32, 2 -> 01, 3 -> 31.
- A340504 (program): Fixed under 0 -> 03, 1 -> 23, 2 -> 21, 3 -> 01.
- A340507 (program): a(n) = floor(sqrt(2*n)) - A003056(n).
- A340519 (program): Smallest order of a non-abelian group with a center of order n.
- A340520 (program): a(n) = 2*A006463(n) + 1.
- A340528 (program): Radio number of the path graph P_n.
- A340536 (program): Digital root of 2*n^2.
- A340550 (program): Number of main classes of doubly symmetric diagonal Latin squares of order n.
- A340554 (program): T(n, k) = [x^k] hypergeom([-2^n/2, -2^n/2 - 1/2], [1/2], x). Triangle read by rows, T(n, k) for n >= 0.
- A340567 (program): Total number of ascents in all faro permutations of length n.
- A340568 (program): Total number of consecutive triples matching the pattern 132 in all faro permutations of length n.
- A340615 (program): a(n) = k/2 if k is even, otherwise (3k+1)/2, where k = n+floor((n+1)/5).
- A340619 (program): n appears A006519(n) times.
- A340627 (program): a(n) = (11*2^n - 2*(-1)^n)/3 for n >= 0.
- A340631 (program): a(n) is the minimum number of pebbles such that any assignment of those pebbles on a complete graph with n vertices is a next-player winning game in the two-player impartial pebbling game.
- A340632 (program): a(n) in binary is a run of 1-bits from the most significant 1-bit of n down to the least significant 1-bit of n, inclusive.
- A340646 (program): a(n) = (prime(n)^n) mod prime(n+1).
- A340648 (program): a(n) is the maximum number of nonzero entries in an n X n sign-restricted matrix.
- A340649 (program): a(n) = (n*prime(n+1)) mod prime(n).
- A340679 (program): If n is a power of prime then a(n) = 1, otherwise a(n) = product of the distinct prime factors of n.
- A340683 (program): a(n) = A007949((A003961(A003961(n))+1)/2), where A003961 shifts the prime factorization of n one step towards larger primes, and A007949(x) gives the exponent of largest power of 3 dividing x.
- A340709 (program): Let k = n/2+floor(n/4) if n is even, otherwise (3n+1)/2; then a(n) = A093545(k).
- A340714 (program): a(n) is the sum of (n-2*j) for j < n/2 coprime to n.
- A340740 (program): a(n) is the sum of all the remainders when n is divided by positive integers less than n/2 and coprime to n.
- A340745 (program): a(n) is the number of “add the square” iterations required to reach or exceed 1 starting at 1/n.
- A340757 (program): Counterexamples to a conjecture of Ramanujan about congruences related to the partition function.
- A340760 (program): Number of partitions of n into 4 parts whose largest 3 parts have the same parity.
- A340761 (program): Number of partitions of n into 4 parts whose ‘middle’ two parts have the same parity.
- A340763 (program): Number of primes p <= n that are congruent to 1 modulo 3.
- A340764 (program): Number of primes p <= n that are congruent to 2 modulo 3.
- A340767 (program): Number of primes p <= 6*n + 5 that are congruent to 2 modulo 3.
- A340768 (program): Third-smallest divisor of n-th composite number.
- A340774 (program): Dirichlet g.f.: Sum_{n>0} a(n)/n^s = zeta(s-1) * zeta(2*s-1).
- A340781 (program): a(n) = (n - 1)*prime(n + 1) mod prime(n).
- A340789 (program): a(n) = (n!)^2 * Sum_{k=1..n} (-1)^(k+1) / (k!)^2.
- A340793 (program): Sequence whose partial sums give A000203.
- A340804 (program): Triangle read by rows: T(n, k) = 1 + k*(n - 1) + (2*k - n - 1)*(k mod 2) with 0 < k <= n.
- A340806 (program): a(n) = Sum_{k=1..n-1} (k^n mod n).
- A340837 (program): a(n) = (1/2) * Sum_{k>=0} (k*(k - 1))^n / 2^k.
- A340849 (program): a(n) = A001045(n) + A052928(n).
- A340850 (program): Dirichlet g.f.: Sum_{n>0} a(n)/n^s = zeta(s) * zeta(s-2) / (zeta(s-1))^2.
- A340863 (program): a(n) = n!*LaguerreL(n, -n^2).
- A340867 (program): a(n) = (prime(n) - a(n-1)) mod 4; a(0)=0.
- A340881 (program): Row sums of A340880.
- A340883 (program): Row sums of A340882.
- A340898 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to the same vertex in the 3-point set.
- A340901 (program): Additive with a(p^e) = (-p)^e.
- A340971 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k) * binomial(2*k,k).
- A340972 (program): a(n) = Sum_{k=0..n} (-n)^k * binomial(n,k) * binomial(2*k,k).
- A340973 (program): Generating function Sum_{n >= 0} a(n)*x^n = 1/sqrt((1-x)*(1-13*x)).
- A341016 (program): Numbers k such that A124440(k) is a multiple of A066840(k).
- A341036 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(k-2).
- A341042 (program): Multiplicative projection of odd part of n.
- A341043 (program): a(n) = 16*n^3 - 36*n^2 + 30*n - 9.
- A341055 (program): Inverse permutation to A341054.
- A341062 (program): Sequence whose partial sums give A000005.
- A341104 (program): a(n) = [x^n] (x - 1)^4/((1 - 2*x)*(x^2 - 3*x + 1)).
- A341185 (program): a(n) = Sum_{k=0..n} k^n * k! * binomial(n,k)^2.
- A341196 (program): a(n) = Sum_{k=0..n} k^4 * (n-k)! * binomial(n,k)^2.
- A341197 (program): a(n) = Sum_{k=0..n} k^n * (n-k)! * binomial(n,k)^2.
- A341208 (program): a(n) = F(n+4) * F(n+1) - 4 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
- A341209 (program): a(n) = (n^3 + 6*n^2 + 17*n + 6)/6.
- A341239 (program): a(n) = floor(r*floor(s*n)), where r = 1 + sqrt(2) and s = sqrt(2).
- A341240 (program): a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) - 4*a(n-4) + 2*a(n-5) for n >= 7, where a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 12, a(5) = 38, a(6) = 127.
- A341248 (program): a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 4, a(3) = 18.
- A341249 (program): a(n) = floor(r*floor(s*n)), where r = 2 + sqrt(2) and s = sqrt(2).
- A341250 (program): a(n) = 5*a(n-1) - 4*a(n-3) for n >= 4, where a(1) = 1, a(2) = 3, a(3) = 13.
- A341255 (program): Let f(n) = floor(r*floor(r*n)) = A341254(n), where r = (2 + sqrt(5))/2). Let a(1) = 1. Then a(n) = f(a(n-1)) for n >= 2.
- A341259 (program): Number of 0’s in n-th word defined at A341258.
- A341276 (program): a(n) = 1 + 3*n*(n+1) - Sum_{k=1..n} d(k), where d(k) is the number of divisors of k.
- A341282 (program): Numbers k such that there is no k-digit number m with the property that the binary expansion of m begins with the base-10 digits of m.
- A341301 (program): a(n) = ceiling(n^2 - 7*n/3 + 19/3).
- A341302 (program): a(n) = n! + (n-1)! + n-2.
- A341307 (program): Expansion of (x^9+x^8+2*x^7+x^6+2*x^5+2*x^4+x^3+x^2+1)/(1-x^6)^2.
- A341309 (program): Sum of odd divisors of n that are <= A003056(n).
- A341311 (program): G.f. = (1+x^2+2*x^3+3*x^4+4*x^5+3*x^6+4*x^7+3*x^8+2*x^9+x^10)/(1-x^6)^2.
- A341314 (program): Array read by antidiagonals: T(n,k) = (n+k)/gcd(n,k), n>=0, k>=0.
- A341315 (program): Triangle read by rows: T(n,k) = (n+k)/gcd(n,k), n>=0, 0<=k<=n.
- A341316 (program): Row sums in A341315.
- A341330 (program): a(n) = Sum_{k=1..n} (-k)^(k+1).
- A341331 (program): a(n) = n^n - (n-1)^n - (n-2)^n - … - 1^n.
- A341345 (program): a(n) = A048673(n) mod 3.
- A341346 (program): a(n) = A048673(2n-1) mod 3.
- A341347 (program): a(n) = (1+A003961(A003961(n)))/2 mod 3, where A003961 shifts the prime factorization of n one step towards larger primes.
- A341356 (program): The most significant digit in A097801-base.
- A341361 (program): a(n) is the smallest abundant number of the form 2^e * prime(n).
- A341389 (program): Characteristic function of A158705, nonnegative integers with an odd number of even powers of 2 in their base-2 representation.
- A341397 (program): Number of integer solutions to (x_1)^2 + (x_2)^2 + … + (x_8)^2 <= n.
- A341409 (program): a(n) = (Sum_{k=1..3} k^n) mod n.
- A341410 (program): a(n) = (Sum_{k=1..4} k^n) mod n.
- A341411 (program): a(n) = (Sum_{k=1..5} k^n) mod n.
- A341412 (program): a(n) = (Sum_{k=1..6} k^n) mod n.
- A341413 (program): a(n) = (Sum_{k=1..7} k^n) mod n.
- A341414 (program): a(n) = (Fibonacci(n)*Lucas(n)) mod 10.
- A341441 (program): Total number of triangles visible in a regular (2n+1)-gon with all diagonals drawn.
- A341463 (program): a(n) = (-1)^(n+1) * (3^n+1)/2.
- A341491 (program): a(n) = binomial(6*n, n) * hypergeom([-5*n, -n], [-6*n], -1).
- A341509 (program): a(n) = 2^j if n is of the form 2^i - 2^j with i > j, and 0 otherwise.
- A341513 (program): Sum of digits in A097801-base.
- A341514 (program): Number of trailing zeros in A097801-base.
- A341522 (program): a(n) = A156552(3*A005940(1+n)).
- A341523 (program): Number of prime factors (with multiplicity) shared by n and sigma(n): a(n) = bigomega(gcd(n, sigma(n))).
- A341525 (program): Numerator of A003973(n) / A003961(n).
- A341528 (program): a(n) = n * sigma(A003961(n)), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of the divisors of n.
- A341529 (program): a(n) = sigma(n) * A003961(n), where A003961 shifts the prime factorization of n one step towards larger primes, and sigma is the sum of the divisors of n.
- A341543 (program): a(n) = sqrt( Product_{j=1..n} Product_{k=1..2} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/2)^2) ).
- A341544 (program): a(n) = sqrt( Product_{j=1..n} Product_{k=1..4} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/4)^2) ).
- A341549 (program): a(n) = Sum_{k=1..n} (-1)^(n+k)*A087322(n,k).
- A341552 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 3 point set but exactly two removed edges are incident to the same vertex in the other set.
- A341579 (program): Number of steps needed to solve the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
- A341580 (program): Number of steps needed to reach position “YZ^(n-1)” in the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
- A341581 (program): Number of steps needed to move the largest disk out from a stack of n disks in the Towers of Hanoi exchanging disks puzzle with 3 pegs.
- A341582 (program): Number of simple moves of the smallest disk in the solution to the Towers of Hanoi exchanging disks puzzle with 3 pegs and n disks.
- A341590 (program): a(n) = (Sum_{j=1..3} StirlingS1(3,j)*(2^j-1)^n)/3!.
- A341591 (program): Number of superior prime divisors of n.
- A341625 (program): a(n) = 1 if the arithmetic derivative of n is less than n, otherwise 0.
- A341629 (program): Characteristic function of A055932: a(n) = 1 if n is a number all of whose prime divisors are consecutive primes starting at 2, otherwise 0.
- A341635 (program): a(n) = Sum_{d|n} phi(d) * mu(d) * mu(n/d).
- A341636 (program): a(n) = Sum_{d|n} phi(d) * tau(d) * tau(n/d).
- A341642 (program): Number of strictly superior prime divisors of n.
- A341655 (program): a(n) is the number of divisors of prime(n)^2 - 1.
- A341656 (program): a(n) is the number of divisors of prime(n)^4 - 1.
- A341657 (program): a(n) is the number of divisors of prime(n)^6 - 1.
- A341663 (program): a(n) is the number of divisors of prime(n)^3 - 1.
- A341671 (program): Solutions y of the Diophantine equation 3*(x^2+x+1) = y^2.
- A341675 (program): Number of superior odd divisors of n.
- A341691 (program): a(0) = 0, and for any n > 0, a(n) = n - a(k) where k is the greatest number < n such that n AND a(k) = a(k) (where AND denotes the bitwise AND operator).
- A341703 (program): a(n) = 6*binomial(n,4) + 2*binomial(n,2) + 1.
- A341704 (program): a(n) = 20*binomial(n,6) + 2*binomial(n,3) + 1.
- A341705 (program): a(n) = 70*binomial(n,8) + 2*binomial(n,4) + 1.
- A341706 (program): Row 2 of semigroup multiplication table shown in A341317 and A341318.
- A341718 (program): Subtract 1 from each term of A004094 (the powers of 2 written backwards).
- A341735 (program): a(n) = A007678(2*n+1).
- A341740 (program): a(n) is the maximum value of the magic constant in a normal magic triangle of order n.
- A341744 (program): a(0)=1, a(1)=2; for n > 1, a(n) = a(n - a(n-2)) + n.
- A341765 (program): Let b(2*m) be the number of even gaps 2*m between successive odd primes from 3 up to prime(n). Let k1 = sum of all b(2*m) when m == 1 (mod 3) and let k2 = sum of all b(2*m) when m == 2 (mod 3). Then a(n) = k1 - k2.
- A341768 (program): a(n) = n * (binomial(n,2) - 2).
- A341772 (program): a(n) = Sum_{d|n} phi(d) * J_2(n/d).
- A341815 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k^n.
- A341854 (program): Number of triangulations of a fixed hexagon with n internal nodes.
- A341859 (program): Decimal expansion of 4 - (8/5)*sqrt(5).
- A341861 (program): Number of primes among the (p-1)/2 numbers {2*p+1, 4*p+1, …, (p-1)*p+1}, p = prime(n).
- A341865 (program): The cardinality of the largest multiset of positive integers whose product and sum equals n.
- A341866 (program): The cardinality of the smallest (nontrivial, except for prime n) multiset of positive integers whose product and sum equal n.
- A341885 (program): a(n) is the sum of A000217(p) over the prime factors p of n, counted with multiplicity.
- A341896 (program): a(n) is the number of words of length n over the alphabet {a,b,c} with an even number of appearances of the letter ‘a’ and the sum of appearances of the letters ‘b’ and ‘c’ add up to at most 3.
- A341900 (program): Partial sums of A005165.
- A341905 (program): a(n) = a(n-1) + a(n-2) + 2*a(n-3) with a(0) = 3, a(1) = 0, a(2) = 2.
- A341915 (program): For any nonnegative number n with runs in binary expansion (r_1, …, r_w), a(n) = Sum_{k = 1..w} 2^(r_1 + … + r_k - 1).
- A341916 (program): Inverse permutation to A341915.
- A341927 (program): Bisection of the numerators of the convergents of cf(1,4,1,6,1,6,…,6,1).
- A341928 (program): a(n) = F(n+4) * F(n+2) + 7 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
- A341929 (program): Bisection of the numerators of the convergents of cf (1,1,6,1,6,1,…,6,1).
- A341943 (program): Fixed points of A341915.
- A341952 (program): Let x = (prime(n+1) - prime(n))/2 modulo 3 for n >= 2, then a(n) = -1 if x = 2, otherwise a(n) = x.
- A341995 (program): a(n) = 1 if the arithmetic derivative (A003415) of n is a prime, otherwise 0.
- A341997 (program): a(n) = A327936(A003415(n)).
- A341998 (program): Arithmetic derivative of n divided by its largest squarefree divisor: a(n) = A003557(A003415(n)).
- A341999 (program): a(n) = 1 if the k-th arithmetic derivative is nonzero for all k >= 0, otherwise 0.
- A342001 (program): Arithmetic derivative of n divided by {n / the largest squarefree divisor of n}: a(n) = A003415(n) / A003557(n).
- A342002 (program): a(n) = A327860(n) / A328572(n) = A003415(A276086(n)) / A003557(A276086(n)).
- A342003 (program): Maximal exponent in the prime factorization of the arithmetic derivative of n: a(n) = A051903(A003415(n)).
- A342014 (program): Arithmetic derivative of n, taken modulo n: a(n) = A003415(n) mod n.
- A342023 (program): a(n) = 1 if there is a prime p such that p^p divides n, otherwise 0.
- A342025 (program): a(n) = 1 if n has the same numbers of prime factors of forms 4*k+1 and 4*k+3 when counted with multiplicity, otherwise 0.
- A342036 (program): Palindromes of even length only using 0 or 1.
- A342040 (program): Binary palindromes of odd length.
- A342089 (program): Numbers that have two representations as the sum of distinct non-consecutive Lucas numbers (A000032).
- A342107 (program): a(n) = Sum_{k=0..n} (4*k)!/k!^4.
- A342112 (program): Drop the final digit of n^5.
- A342122 (program): a(n) is the remainder when the binary reverse of n is divided by n.
- A342126 (program): The binary expansion of a(n) corresponds to that of n where all the 1’s have been replaced by 0’s except in the first run of 1’s.
- A342131 (program): a(n) = n/2 + floor(n/4) if n is even, otherwise (3*n+1)/2.
- A342138 (program): Array T(n,k) = (n+k)*(3*n+3*k-5)/2 + (3*k+1), read by ascending antidiagonals.
- A342159 (program): Number of words of length n, over the alphabet {a,b,c}, which have an odd number of a’s and the number of b’s plus the number of c’s is less than or equal to 3.
- A342165 (program): A fractal-like sequence: erase the terms that have a prime index, the non-erased terms rebuild the original sequence.
- A342166 (program): Product of first n Fubini numbers.
- A342167 (program): a(n) = U(n, (n+2)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
- A342168 (program): a(n) = U(n, (n+3)/2) where U(n, x) is a Chebyshev polynomial of the 2nd kind.
- A342170 (program): Product of first n little Schröder numbers.
- A342173 (program): a(n) = Sum_{j=1..n-1} floor(prime(n)/prime(j)).
- A342177 (program): Product of first n Motzkin numbers.
- A342178 (program): Product of first n central Delannoy numbers.
- A342205 (program): a(n) = T(n,n+1) where T(n,x) is a Chebyshev polynomial of the first kind.
- A342206 (program): a(n) = T(n,n+2) where T(n,x) is a Chebyshev polynomial of the first kind.
- A342207 (program): a(n) = U(n,n+1) where U(n,x) is a Chebyshev polynomial of the second kind.
- A342213 (program): Largest number of maximal planar node-induced subgraphs of an n-node graph.
- A342235 (program): Coordination sequence of David Eppstein’s “Tetrastix” graph.
- A342253 (program): a(n) = (n-6)*sqrt((n-5)^2) + 2*n + 31.
- A342279 (program): A bisection of A000201: a(n) = A000201(2*n+1).
- A342280 (program): a(n) = A001952(2*n+1).
- A342281 (program): A bisection of A001951: a(n) = A001951(2*n+1).
- A342286 (program): a(n) = number of n-variable nondegenerate self-reflecting truth-tables.
- A342287 (program): a(n) = number of n-variable nondegenerate self-dual truth-tables.
- A342288 (program): C(n)*C(n+2), where C(n) is the n-th Catalan number A000108(n).
- A342294 (program): a(n) = Sum_{k = 0..n} binomial(n,k)^11.
- A342295 (program): a(n) = Sum_{k = 0..n} binomial(n,k)^12.
- A342311 (program): T(n, k) = (n - k + 2)*binomial(2*n, n + k - 2). Triangle read by rows, T(n, k) for 0 <= k <= n.
- A342350 (program): Numbers k such that lcm(1,2,3,…,k)/21 equals the denominator of the k-th harmonic number H(k).
- A342352 (program): Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^2/2 - x - 1).
- A342354 (program): M(n,k) = 2*n^2 + 2*k + 1 for 0 <= k <= n and M(n,k) = 2*k^2 + 4*k - 2*n + 1 for 0 <= n <= k; square array M(n,k) read by ascending antidiagonals (n, k >= 0).
- A342362 (program): Expansion of the o.g.f. (1 + 8*x + 10*x^2 + 8*x^3 + x^4)/((1 - x)^4*(1 + x)^2).
- A342363 (program): First differences of A341282.
- A342369 (program): If n is congruent to 2 (mod 3), then a(n) = (2*n - 1)/3; otherwise, a(n) = 2*n.
- A342370 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(k-1).
- A342371 (program): Partial sums of A051697.
- A342379 (program): Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^3/6 - x^2/2 - x - 1).
- A342380 (program): Expansion of e.g.f. (exp(x)-1)*(exp(x) - x^4/24 - x^3/6 - x^2/2 - x - 1).
- A342385 (program): Triangle with n>=0 as first column and main diagonal. The (n+2)-th column is (n+1)*A028310(n).
- A342389 (program): a(n) = Sum_{k=1..n} k^gcd(k,n).
- A342394 (program): a(n) = Sum_{k=1..n} k^(gcd(k,n) - 1).
- A342395 (program): a(n) = Sum_{k=1..n} k^(n/gcd(k,n)).
- A342396 (program): a(n) = Sum_{k=1..n} k^(n/gcd(k,n) - 1).
- A342397 (program): Expansion of the o.g.f. (2*x^2 + 3*x + 2)*x/((x + 1)^2*(x - 1)^4).
- A342404 (program): a(n) = binomial(n,2)*(2^(n-2) - n + 1).
- A342410 (program): The binary expansion of a(n) corresponds to that of n where all the 1’s have been replaced by 0’s except in the last run of 1’s.
- A342411 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n) - 2).
- A342412 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n-2).
- A342413 (program): a(n) = gcd(phi(n), A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
- A342414 (program): a(n) = A003415(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
- A342415 (program): a(n) = phi(n) / gcd(phi(n),A003415(n)), where A003415(n) is the arithmetic derivative of n, and phi is Euler totient function.
- A342416 (program): a(n) = gcd(A173557(n), A342001(n)).
- A342420 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(n/gcd(k,n)).
- A342421 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^(gcd(k,n) - 1).
- A342422 (program): a(n) = Sum_{k=1..n} (n/gcd(k,n))^gcd(k,n).
- A342423 (program): a(n) = Sum_{k=1..n} gcd(k,n)^gcd(k,n).
- A342424 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n)).
- A342432 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n-2).
- A342433 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n-1).
- A342435 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 2).
- A342436 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(gcd(k,n) - 1).
- A342437 (program): a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n) - 1).
- A342448 (program): Partial sums of A066194.
- A342449 (program): a(n) = Sum_{k=1..n} gcd(k,n)^k.
- A342455 (program): The fifth powers of primorials: a(n) = A002110(n)^5.
- A342460 (program): a(n) = 1 if n > 1 and is divisible by the sum of its prime factors (with repetition), otherwise 0.
- A342482 (program): a(n) = n*(2^(n-1) - n - 1).
- A342483 (program): a(n) = binomial(n,2)*(2^(n-2) - n).
- A342527 (program): Number of compositions of n with alternating parts equal.
- A342534 (program): a(n) = Sum_{k=1..n} phi(gcd(k, n))^2.
- A342553 (program): Least integer m > 2*n such that m-2*n and m+2*n are both squares, for n>1.
- A342568 (program): 1/a(n) is the current through the resistor at the central rung of an electrical ladder network made of 6*n+1 one-ohm resistors, fed by 1 volt at diametrically opposite ends of the ladder.
- A342573 (program): The number of ordered n-tuples consisting of n permutations (not necessarily distinct) such that the first element of each of them is the same.
- A342603 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 6*a(n) + a(n+1).
- A342610 (program): a(0) = 0, a(1) = 1; a(2*n) = 5*a(n), a(2*n+1) = a(n) + a(n+1).
- A342611 (program): a(0) = 0, a(1) = 1; a(2*n) = 7*a(n), a(2*n+1) = a(n) + a(n+1).
- A342614 (program): a(0) = 0, a(1) = 1; a(2*n) = 8*a(n), a(2*n+1) = a(n) + a(n+1).
- A342615 (program): a(0) = 0, a(1) = 1; a(2*n) = 9*a(n), a(2*n+1) = a(n) + a(n+1).
- A342628 (program): a(n) = Sum_{d|n} d^(n-d).
- A342629 (program): a(n) = Sum_{d|n} (n/d)^(n-d).
- A342633 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 3*a(n) + a(n+1).
- A342634 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 4*a(n) + a(n+1).
- A342635 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 5*a(n) + a(n+1).
- A342636 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 7*a(n) + a(n+1).
- A342637 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 8*a(n) + a(n+1).
- A342638 (program): a(0) = 0, a(1) = 1; a(2*n) = a(n), a(2*n+1) = 9*a(n) + a(n+1).
- A342661 (program): a(n) = n * sigma(A064989(n)), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma gives the sum of the divisors of its argument.
- A342662 (program): a(n) = sigma(n) * A064989(n), where A064989 is multiplicative with a(2^e) = 1 and a(p^e) = prevprime(p)^e for odd primes p, and sigma is the sum of the divisors of n.
- A342671 (program): a(n) = gcd(sigma(n), A003961(n)), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
- A342672 (program): a(n) = lcm(sigma(n), A003961(n)), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
- A342673 (program): a(n) = gcd(n, sigma(A003961(n))), where A003961 is fully multiplicative with a(prime(k)) = prime(k+1), and sigma is the sum of divisors of n.
- A342675 (program): a(n) = Sum_{d|n} d^(n-d+1).
- A342676 (program): a(n) is the number of lunar primes less than or equal to n.
- A342696 (program): a(n) = floor(n/12).
- A342709 (program): 12-gonal (dodecagonal) square numbers.
- A342710 (program): Solutions x to the Pell-Fermat equation x^2 - 5*y^2 = 4.
- A342711 (program): Partial sums of A000267.
- A342712 (program): Partial sums of A248333.
- A342719 (program): Array read by ascending antidiagonals: T(k, n) is the sum of the consecutive positive integers from 1 to (n - 1)*k placed along the perimeter of a n-th order perimeter-magic k-gon.
- A342730 (program): a(n) = floor((frac(e*n) + 1) * prime(n+1)).
- A342737 (program): Number of wedged n-spheres in the homotopy type of the neighborhood complex of Kneser graph KG_{3,n}.
- A342748 (program): a(n) = sum of digits in the n-th word in A341334.
- A342761 (program): Fold a square sheet of paper alternately vertically to the left and horizontally downwards; after each fold, draw a line along each inward crease; after n folds, the resulting graph has a(n) edges.
- A342768 (program): a(n) = A342767(n, n).
- A342769 (program): Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < s <= t ordered by increasing values of s and where k = 1,2,… .
- A342774 (program): Length of n-th word in the ordering A342753 of all binary words.
- A342802 (program): Replace 2^k with (-3)^k in binary expansion of n.
- A342831 (program): a(n) is the smallest positive integer k such that the n-dimensional cube [0,k]^n contains at least as many internal lattice points as external lattice points.
- A342850 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where all three removed edges are incident to different vertices in the 3-point set and none of the removed edges are incident to the same vertex in the other set.
- A342851 (program): Remove duplicates in the decimal digit-reversal of n.
- A342856 (program): Factorial numbers n that are sqrt(n)-smooth.
- A342871 (program): a(n) = Sum_{k=1..n} floor(n^(1/k)), n >= 1.
- A342873 (program): Numbers whose distance to the nearest cube equals the distance to the nearest product of 3 consecutive integers (three-dimensional oblong).
- A342892 (program): a(n) is the complement of the bit two places to the left of the least significant “1” in the binary expansion of n.
- A342903 (program): a(n) is the smallest number that is the sum of n positive squares in two ways.
- A342905 (program): Array read by antidiagonals: T(n,k) = product of all distinct primes dividing n*k (n>=1, k>=1).
- A342906 (program): a(n) = 2^(2*n-2) - Catalan(n).
- A342912 (program): a(n) = [x^n] (1 - 2*x - sqrt((1 - 3*x)/(1 + x)))/(2*x^3).
- A342913 (program): Pairwise listing of the partitions of 2k into two parts, (s,t), with 0 < t <= s ordered by decreasing values of s and where k = 1,2,… .
- A342914 (program): Number of grid points covered by a truncated triangle drawn on the hexagonal lattice with the short sides having length n and the long sides length 2*n.
- A342915 (program): a(n) = gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
- A342916 (program): a(n) = (1+n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
- A342917 (program): a(n) = A001615(n) / gcd(1+n, A001615(n)), where A001615 is Dedekind psi, n * Product_{p|n, p prime} (1 + 1/p).
- A342925 (program): a(n) = A003415(sigma(n)), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
- A342926 (program): a(n) = A003415(sigma(n)) - n, where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
- A342939 (program): a(n) is the Skolem number of the triangular grid graph T_n.
- A342940 (program): Triangle read by rows: T(n, k) is the Skolem number of the parallelogram graph P_{n, k}, with 1 < k <= n.
- A342959 (program): Number of 1’s within a sample word of length 10^n of the infinite Fibonacci word A003842 where n is the sequence index.
- A342975 (program): Cubes composed of digits {0, 1, 3}.
- A342977 (program): Decimal expansion of (Pi - 2) / 4.
- A342983 (program): Number of tree-rooted planar maps with n+1 vertices and n+1 faces.
- A342994 (program): a(n) = (1000^n - 1)*(220/333).
- A343005 (program): a(n) is the number of dihedral symmetries D_{2m} (m >= 3) that configurations of n non-overlapping equal circles can possess.
- A343007 (program): Relative position of the average value between two consecutive partial sums of the Leibniz formula for Pi.
- A343008 (program): a(n) = F(n+5) * F(n+2) - 12 * (-1)^n where F(n) = A000045(n) are the Fibonacci numbers.
- A343009 (program): a(n) = (n^(2n)-1)/(n^2-1) for n > 1.
- A343010 (program): Integers k for which there exist three consecutive Fibonacci numbers a, b, and c such that a*b*c = k*(a+b+c).
- A343028 (program): a(n) = floor(11*n / 3).
- A343029 (program): Number of 1-bits in the binary expansion of n which have an even number of 0-bits at less significant bit positions.
- A343030 (program): Number of 1-bits in the binary expansion of n which have an odd number of 0-bits at less significant bit positions.
- A343037 (program): Triangle T(n,k), n >= 2, 1 <= k <= n-1, read by rows, where T(n,k) is the difference between smallest square >= binomial(n,k) and binomial(n,k).
- A343041 (program): a(0) = 0 and for any n > 0, a(n) = A343040(a(n-1), n).
- A343048 (program): a(n) is the least number whose sum of digits in primorial base equals n.
- A343069 (program): Decimal expansion of 2*(1+5*sqrt(2))/7.
- A343093 (program): Number of rooted toroidal maps with n edges and no isthmuses.
- A343114 (program): a(n) = Sum_{i=1..n} gcd(n^i,i).
- A343122 (program): Consider the longest arithmetic progressions of primes from among the first n primes; a(n) is the smallest constant difference of these arithmetic progressions.
- A343125 (program): Triangle T(k, n) = (n+3)*(k-n) - 4, k >= 2, 1 <= n <= k-1, read by rows.
- A343173 (program): First differences of paper-folding sequence A014577.
- A343174 (program): Partial sums of paper-folding sequence A014577.
- A343175 (program): a(0)=2; for n > 0, a(n) = 2^(2*n-1) + 2^n + 1.
- A343176 (program): a(0)=3; for n > 0, a(n) = 2^(2*n) + 3*2^(n-1) + 1.
- A343177 (program): a(0)=4; if n >0 is even then a(n) = 2^(n/2+1)+3, otherwise a(n) = 3*(2^((n-1)/2)+1).
- A343180 (program): Trajectory of 1 under the morphism 1 -> 12, 2 -> 32, 3 -> 14, 4 -> 34.
- A343199 (program): Decimal expansion of 6+2*sqrt(3).
- A343206 (program): Numerators of Daehee numbers.
- A343219 (program): a(n) = 1 if A003415(sigma(k)) > k, otherwise 0.
- A343223 (program): a(n) = gcd(A003415(n), A003415(sigma(n))-n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
- A343228 (program): A binary encoding of the digits “+1” in balanced ternary representation of n.
- A343229 (program): A binary encoding of the digits “-1” in balanced ternary representation of n.
- A343230 (program): A binary encoding of the digits “0” in balanced ternary representation of n.
- A343231 (program): A binary encoding of the nonzero digits in balanced ternary representation of n.
- A343233 (program): Triangle read by rows: Riordan triangle T = (1 - x*c(x), x), with the generating function c of A000108 (Catalan).
- A343241 (program): Primes congruent to 2 or 8 modulo 15.
- A343259 (program): a(n) = 2 * T(n,n/2) where T(n,x) is a Chebyshev polynomial of the first kind.
- A343260 (program): a(n) = 2 * T(n,(n+1)/2) where T(n,x) is a Chebyshev polynomial of the first kind.
- A343261 (program): a(n) = 2 * T(n,(n+2)/2) where T(n,x) is a Chebyshev polynomial of the first kind.
- A343265 (program): a(n) is the number of ways n can be reached starting from 0 and using only two operations: adding one or, once n > 1, squaring.
- A343275 (program): a(n) = |2*n - 10^length(n)|.
- A343276 (program): a(n) = n! * [x^n] -x*(x + 1)*exp(x)/(x - 1)^3.
- A343291 (program): a(n) = (n-2)*2^(n-1) + n + 2.
- A343299 (program): a(n) = n + A000120(a(n-1)) - a(n-1), with n > 1, a(1) = 1, where A000120(x) is the binary weight of x.
- A343317 (program): a(n) is the least k >= 0 such that A343316(n, k) = n.
- A343318 (program): a(n) = (2^n + 1)^3.
- A343372 (program): Number of sets in the geometry determined by the Hausdorff metric at each location between two sets defined by a complete bipartite graph K(3,n) (with n at least 4) missing three edges, where exactly two removed edges are incident to the same vertex in the 3-point set and exactly two removed edges are incident to the same vertex in the other set.
- A343386 (program): Number of odd Motzkin n-paths, i.e., Motzkin n-paths with an odd number of up steps.
- A343395 (program): a(n) = Sum_{i=1..n} gcd(n^(n-i),n-i).
- A343407 (program): Number of proper divisors of n that are triangular numbers.
- A343408 (program): Sum of proper divisors of n that are triangular numbers.
- A343430 (program): Part of n composed of prime factors of the form 3k-1.
- A343442 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j + 2), with a(1) = 1.
- A343443 (program): If n = Product (p_j^k_j) then a(n) = Product (k_j + 2), with a(1) = 1.
- A343445 (program): Coefficients of the series S(p, q) for which (-sqrt(p))*S converges to the largest real root of x^3 - p*x + q for 0 < p and 0 < q < 2*(p/3)^(3/2).
- A343446 (program): Coefficients of the series S(p, q) for which -(p^(1/3))*S converges to the largest real root of x^4 - p*x + q, where 0 < p and 0 < q < 3*(p/4)^(4/3).
- A343461 (program): a(n) is the maximal number of congruent n-gons that can be arranged around a vertex without overlapping.
- A343490 (program): a(n) = Sum_{k=1..n} 4^(gcd(k, n) - 1).
- A343492 (program): a(n) = Sum_{k=1..n} 5^(gcd(k, n) - 1).
- A343497 (program): a(n) = Sum_{k=1..n} gcd(k, n)^3.
- A343498 (program): a(n) = Sum_{k=1..n} gcd(k, n)^4.
- A343499 (program): a(n) = Sum_{k=1..n} gcd(k, n)^5.
- A343508 (program): a(n) = Sum_{k=1..n} gcd(k, n)^6.
- A343509 (program): a(n) = Sum_{k=1..n} gcd(k, n)^7.
- A343513 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^3.
- A343514 (program): a(n) = Sum_{k=1..n} (k/gcd(n, k))^4.
- A343525 (program): If n = Product (p_j^k_j) then a(n) = Product (2*p_j^k_j + 1), with a(1) = 1.
- A343526 (program): Number of divisors of n^7.
- A343539 (program): a(n) = (2*n+1)*Lucas(2*n+1).
- A343543 (program): a(n) = n*Lucas(2*n).
- A343545 (program): a(n) = n * Sum_{d|n} binomial(d+3,4)/d.
- A343560 (program): a(n) = (n-1)*(4*n+1).
- A343561 (program): 2nd row of A341867: a(n) = (n^2+15*n+32)*2^(n-3).
- A343569 (program): If n = Product (p_j^k_j) then a(n) = Product (2*(p_j^k_j + 1)), with a(1) = 1.
- A343570 (program): If n = Product (p_j^k_j) then a(n) = Product (p_j^k_j + 3), with a(1) = 1.
- A343572 (program): a(n) = ceiling((16^n)*Sum_{k=0..n+1} (4/(8k+1)-2/(8k+4)-1/(8k+5)-1/(8k+6))/16^k).
- A343578 (program): a(n) = 32*n^2 - 40*n + 10.
- A343580 (program): a(n) = abs(A021009(n, floor(n/2))).
- A343581 (program): a(n) = binomial(n, floor(n/2))*FallingFactorial(n - 1, n - floor(n/2)).
- A343582 (program): a(n) = (-1)^n*n!*[x^n] exp(-3*x)/(1 - 2*x).
- A343584 (program): a(n) = Sum_{j=0..n}(-1)^(n-j)*binomial(n, j)*A028246(n+1, j+1).
- A343586 (program): a(n) = the sum of all the multiples of 2 or 5 less than or equal to 10^n.
- A343607 (program): Minimal number of colors required for an edge-coloring of the complete graph K_n with no monochromatic triangle.
- A343608 (program): a(n) = [n/5]*[n/5 - 1]*(3n - 10[n/5 + 1])/6, where [.] = floor: upper bound for minimum number of monochromatic triangles in a 3-edge-colored complete graph K_n.
- A343609 (program): a(n) = floor(n/9).
- A343638 (program): a(n) = (Sum of decimal digits of 3*n) / 3.
- A343639 (program): a(n) = (Sum of digits of 9*n) / 9.
- A343655 (program): Number of pairwise coprime sets of divisors of n, where a singleton is not considered pairwise coprime unless it is {1}.
- A343688 (program): a(1)=1, a(2)=0, a(n) = (4*n-2)*a(n-1) + a(n-2), n > 2.
- A343689 (program): a(1)=0, a(2)=1, a(n) = (4*n-2)*a(n-1) + a(n-2), n > 2.
- A343694 (program): a(n) is the number of men’s preference profiles in the stable marriage problem with n men and n women, such that all men prefer different women as their first choices.
- A343720 (program): Triangle read by rows: T(n,k) = k^2 mod n for k = 0..n-1, n >= 1.
- A343752 (program): a(1) = 1; for n > 1, a(n) = n if a(n-1) is divisible by n, otherwise a(n) = a(n-1)+n.
- A343754 (program): a(n) = 0, and for any n > 0, a(n+1) = a(n) - A065363(n) + 1.
- A343766 (program): Lexicographically earliest sequence of distinct integers such that a(0) = 0 and the balanced ternary expansions of two consecutive terms differ by a single digit, as far to the right as possible.
- A343773 (program): Excess of the number of even Motzkin n-paths (A107587) over the odd ones (A343386).
- A343785 (program): a(n) is completely multiplicative with a(p^e) = (-1)^e if p == 2 (mod 3) and a(p^e) = 1 otherwise.
- A343794 (program): Numbers k such that 630*k + 315 is not an abundant number (A005101).
- A343803 (program): a(n) = Sum_{k=1..n} k * (number of divisors of n<=k).
- A343808 (program): Partial sums of A062074.
- A343810 (program): Numbers that contain only the digits 0,4,8. Permutable multiples of 4: numbers k such that every permutation of the digits of k is a multiple of 4.
- A343823 (program): Numbers k > 10 such that every permutation of the digits of k is congruent to 3 (mod 4).
- A343824 (program): Sum of the elements in all pairs (d1, d2) of divisors of n such that d1<=d2, d1|n, d2|n, and d1 + d2 <= n.
- A343832 (program): a(n) = Sum_{k=0..n} k! * binomial(n,k) * binomial(2*n+1,k).
- A343840 (program): a(n) = Sum_{k=0..n}(-1)^(n-k)*binomial(n, k)*|A021009(n, k)|.
- A343842 (program): Series expansion of 1/sqrt(8*x^2 + 1), even powers only.
- A343859 (program): Partial sums of the primes excluding 3.
- A343877 (program): Number of pairs (d1, d2) of divisors of n such that d1<d2, d1|n, d2|n, and d1 + d2 <= n.
- A343885 (program): a(n) = a(n-1) - a(n-2) + a(n-3) + a(n-4), with a(1) = a(2) = a(3) = a(4) = 1.
- A343896 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * binomial(n,k) * binomial(2*n+1,k).
- A343898 (program): a(n) = Sum_{k=0..n} (k!)^3 * binomial(n,k).
- A343906 (program): Decimal expansion of 6*sqrt(6).
- A343910 (program): a(n) = mu(phi(n)), where mu is the Möbius function and phi is the Euler totient function.
- A343911 (program): a(n) = Omega(phi(n)), where Omega is the number of prime factors of n with multiplicity and phi is the Euler totient function.
- A343928 (program): a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).
- A343929 (program): a(n) = Sum_{k=0..n} (k!)^(n+1) * binomial(n,k).
- A343932 (program): a(n) = (Sum_{k=1..n} k^k) mod n.
- A343933 (program): a(n) = (Sum_{k=1..n} (-k)^k) mod n.
- A343935 (program): Number of ways to choose a multiset of n divisors of n.
- A343936 (program): Number of ways to choose a multiset of n divisors of n - 1.
- A343943 (program): Number of distinct possible alternating sums of permutations of the multiset of prime factors of n.
- A343948 (program): Decimal expansion of -(1 + (5/9)^(1/3)*((9+4*sqrt(6))^(1/3) - (4*sqrt(6)-9)^(1/3)))/4 (negated).
- A343949 (program): Shortest distance from curve start to end along the segments of dragon curve expansion level n, and which is the diameter of the curve as a graph.
- A343963 (program): a(0) = 0, and for any n > 0, the binary expansion of n has n digits and starts with the binary expansion of n, say of w digits, and in case n > w, the remaining binary digits in a(n) are those of a(n-w).
- A343964 (program): Decimal expansion of 18 + 2*sqrt(3).
- A343965 (program): Decimal expansion of 4 + 10*sqrt(2)/3.
- A343966 (program): Decimal expansion of (4/3)*(4*sqrt(2)-5).
- A343974 (program): Even numbers k such that the two sets of primes in the Goldbach representation of k and k+2 as the sum of two odd primes do not intersect.
- A343994 (program): Number of nodes in graph BC(n,2) when the internal nodes are counted with multiplicity.
- A343996 (program): a(n) = A011772(n) if that number is odd, otherwise A011772(n)+1.
- A343997 (program): a(n) = A011772(n) if that number is even, otherwise A011772(n)+1.
- A343998 (program): a(n) = A343997(n)/2.
- A343999 (program): a(n) = A011772(n) mod 2.
- A344001 (program): Indices k such that A011772(k) is odd.
- A344004 (program): Number of ordered subsequences of {1,…,n} containing at least three elements and such that the first differences contain only odd numbers.
- A344005 (program): a(n) = smallest positive m such that n divides the oblong number m*(m+1).
- A344006 (program): a(n) = m*(m+1)/n, where A344005(n) is the smallest number m such that n divides m*(m+1).
- A344019 (program): A tight upper bound on the order of a finite subgroup of the collineation group of the free projective plane F_n.
- A344024 (program): a(n) = A003415(A001615(n)).
- A344041 (program): Decimal expansion of Sum_{k>=1} F(k)/(k*2^k), where F(k) is the k-th Fibonacci number (A000045).
- A344042 (program): a(n) = n * Sum_{d|n} sigma(d)^2 / d.
- A344049 (program): a(n) = KummerU(-2*n, 1, -n).
- A344050 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*|Lah(n, k)|. Inverse binomial convolution of the unsigned Lah numbers A271703.
- A344051 (program): a(n) = Sum_{k=0..n} binomial(n, k)*|Lah(n, k)|. Binomial convolution of the unsigned Lah numbers A271703.
- A344053 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*Stirling2(n, k)*k!.
- A344055 (program): a(n) = 2^n * n! * x^n.
- A344057 (program): a(n) = (2*n)! / CatalanNumber(n - 1) for n >= 1 and a(0) = 1.
- A344069 (program): Decimal expansion of sqrt(13)/3.
- A344106 (program): a(n) = n! * LaguerreL(n, -n+1).
- A344107 (program): a(n) = n! * LaguerreL(n, -n+2).
- A344109 (program): a(n) = (5*2^n + 7*(-1)^n)/3.
- A344110 (program): Triangle read by rows: T(n,k) = 2^(n*k), n >= 0, 0 <= k <= n.
- A344111 (program): Decimal expansion of 4 + sqrt(3).
- A344113 (program): a(n) = 2^(n^2) - n^n.
- A344114 (program): a(n) = 2^(n^2) - n!.
- A344121 (program): a(n) is the multiplicative inverse of 24 (mod 7^n).
- A344128 (program): a(n) = Sum_{k=1..n} k * floor(n/k^2).
- A344131 (program): a(n+1) = (8*n^2+8*n+3)*a(n) - 16*n^4*a(n-1), with a(0)=0, a(1)=1.
- A344136 (program): Number of linear intervals in the Tamari lattices.
- A344150 (program): Length of the n-th word in A342910.
- A344171 (program): Decimal expansion of 12*sqrt(5).
- A344191 (program): a(n) = Catalan(n) * (n^2 + 2) / (n + 2).
- A344212 (program): Decimal expansion of 1 + 1/sqrt(5).
- A344215 (program): a(n) = n*(3^(n-1) - 2^(n-1)).
- A344221 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^3), where tau(n) is the number of divisors of n.
- A344222 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^4), where tau(n) is the number of divisors of n.
- A344223 (program): a(n) = Sum_{k=1..n} tau(gcd(k,n)^n), where tau(n) is the number of divisors of n.
- A344226 (program): a(n) = Sum_{d|n} n^omega(d) / d.
- A344236 (program): Number of n-step walks from a universal vertex to the other on the diamond graph.
- A344259 (program): For any number n with binary expansion (b(1), …, b(k)), the binary expansion of a(n) is (b(1), …, b(ceiling(k/2))).
- A344260 (program): a(n) is the number of relations from an n-element set into a set of at most n elements.
- A344261 (program): Number of n-step walks from one of the vertices with degree 3 to itself on the four-vertex diamond graph.
- A344262 (program): a(0)=1; for n>0, a(n) = a(n-1)*n+1 if n is even, (a(n-1)+1)*n otherwise.
- A344299 (program): Expansion of Sum_{k>=1} (-1)^(k+1) * x^(k^2) / (1 - x^(k^2)).
- A344300 (program): Expansion of Sum_{k>=1} (-1)^(k+1) * k^2 * x^(k^2) / (1 - x^(k^2)).
- A344317 (program): a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 1.
- A344326 (program): Dirichlet g.f.: zeta(s)^2/zeta(2*s-1).
- A344327 (program): Number of divisors of n^4.
- A344328 (program): Number of divisors of n^5.
- A344329 (program): Number of divisors of n^6.
- A344335 (program): Number of divisors of n^8.
- A344336 (program): Number of divisors of n^9.
- A344337 (program): a(n) = 9^omega(n), where omega(n) is the number of distinct primes dividing n.
- A344346 (program): Numbers k which have an odd number of trailing zeros in their binary reflected Gray code A014550(k).
- A344349 (program): Number of primes along the main antidiagonal of the n X n square array whose elements are the numbers from 1..n^2, listed in increasing order by rows.
- A344350 (program): a(n) = Sum_{k=1..n} mu(n*k-k-1)^2, where mu is the Möbius function.
- A344362 (program): Decimal expansion of (5^(1/4) + 5^(-1/4))/2.
- A344363 (program): Decimal expansion of (5^(1/4) + 5^(3/4))/2.
- A344370 (program): Dirichlet g.f.: Product_{k>=2} (1 + k^(1-s)).
- A344371 (program): a(n) = Sum_{k=1..n} (-1)^(n-k) gcd(k,n).
- A344372 (program): a(n) = Sum_{k=1..2n} (-1)^k gcd(k,2n).
- A344373 (program): a(n) = Sum_{k=1..n-1} (-1)^k gcd(k, n).
- A344382 (program): Decimal expansion of sqrt(29)/5.
- A344386 (program): Decimal expansion of sqrt(53)/7.
- A344387 (program): Decimal expansion of sqrt(17)/4.
- A344389 (program): a(n) is the number of nonnegative numbers < 10^n with all digits distinct.
- A344395 (program): a(n) = binomial(4*n - 1, 2*n - 1)*hypergeom([-n, -n + 1/2], [2*n + 1], 4).
- A344396 (program): a(n) = binomial(2*n + 1, n)*hypergeom([-(n + 1)/2, -n/2], [n + 2], 4).
- A344399 (program): a(n) = 4^n*binomial(n - 1/2, -1/2)*(n^2 + 1).
- A344402 (program): a(n) = denominator(R(n,3)), where R(n,d) = (Product_{j prime to d)} Pochhammer(j/d, n)) / n!.
- A344403 (program): a(n) = Sum_{d|n} d * floor(n/d^2).
- A344404 (program): a(n) = Sum_{d|n} floor(n/d^2).
- A344405 (program): a(n) = Sum_{d|n} (n/d) * floor(n/d^2).
- A344418 (program): a(n) = n*a(n-1) + n^(1+n mod 2), a(0) = 0.
- A344419 (program): a(n) = n*a(n-1) + n^(n mod 2), a(0) = 0.
- A344420 (program): a(n) = floor(n/11).
- A344423 (program): a(n) = 10^(2*n+2) + 111*10^n + 1.
- A344425 (program): Decimal expansion of sqrt(85)/9.
- A344426 (program): Decimal expansion of sqrt(26)/5.
- A344428 (program): Decimal expansion of exp(-2/5).
- A344439 (program): a(n) = n - A206369(n).
- A344440 (program): a(n) = n + A061020(n).
- A344441 (program): a(n) = A061020(n) + abs(A061020(n)).
- A344442 (program): a(n) = A332844(n) - n.
- A344444 (program): Completely additive with a(2) = 12, a(3) = 19; for prime p > 3, a(p) = ceiling((a(p-1) + a(p+1))/2).
- A344461 (program): a(n) = Sum_{d|n} d^gcd(d,n/d).
- A344478 (program): Number of unitary prime divisors p of n such that n/p is squarefree.
- A344483 (program): a(n) = n^2 + sigma(n) - n*d(n).
- A344485 (program): a(n) = Sum_{d|n} (n-d) * phi(n/d).
- A344496 (program): a(0)=0; for n > 0, a(n) = a(n-1)*n + n if n is odd, (a(n-1) + n)*n otherwise.
- A344501 (program): a(n) = Sum_{k=0..n} binomial(n, k)*HT(n, k) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*HT(n, k), where HT(n, k) is the Hermite triangle A099174.
- A344508 (program): a(n) = Sum_{k=1..n} k * lcm(k,n).
- A344509 (program): a(n) = (1/n) * Sum_{k=1..n} k * lcm(k,n).
- A344510 (program): a(n) = Sum_{k=1..n} k * gcd(k,n).
- A344511 (program): a(n) = Sum_{k >= 0} sign(d_k) * 2^k for any number n with decimal expansion Sum_{k >= 0} d_k * 10^k.
- A344517 (program): Minimum diameter of 4-regular circulant graphs of order n.
- A344520 (program): Decimal expansion of 2*(1+sqrt(10))/3.
- A344521 (program): a(n) = Sum_{1 <= i <= j <= k <= n} gcd(i,j,k).
- A344526 (program): a(n) = Sum_{k=1..n} k^3 * phi(k).
- A344543 (program): Lexicographically earliest sequence S of distinct positive terms such that the product of the last k digits of S is even, k being the rightmost digit of a(n).
- A344551 (program): a(n) = Sum_{k=1..n} k^floor((n-k)/k).
- A344552 (program): a(n) = Sum_{k=1..n} floor(k*(n-k)/n).
- A344553 (program): Number of lattice paths from (0,0) to (2n-1,n) using steps E=(1,0), N=(0,1), and D=(1,1) which stay weakly above the line through (0,0) and (2n-1,n).
- A344554 (program): Decimal expansion of 2*(1+sqrt(26))/5.
- A344564 (program): a(n) = [x^n] -3/(2*x - 1)^5.
- A344565 (program): Triangle read by rows, for 0 <= k <= n: T(n, k) = binomial(n, k) * binomial(binomial(n + 3, 2), 2).
- A344568 (program): Decimal expansion of 2*(1+sqrt(82))/9.
- A344569 (program): Decimal expansion of 2*(1+sqrt(290))/17.
- A344587 (program): a(n) = 2*A003961(n) - sigma(A003961(n)).
- A344596 (program): a(n) = Sum_{k=1..n} mu(k) * (floor(n/k)^3 - floor((n-1)/k)^3).
- A344598 (program): a(n) = Sum_{k=1..n} phi(k) * (floor(n/k)^2 - floor((n-1)/k)^2).
- A344617 (program): Sign of the alternating sum of the prime indices of n.
- A344618 (program): Reverse-alternating sums of standard compositions (A066099). Alternating sums of the compositions ranked by A228351.
- A344622 (program): a(n) = n*(n+1)/2 - sigma(n) + d(n).
- A344624 (program): a(n) = Sum_{k=1..n} k^c(k), where c(n) is the characteristic function of squares.
- A344674 (program): a(n) is the maximum value such that there is an n X n binary orthogonal matrix with every row having at least a(n) ones.
- A344679 (program): Number of 2-matchings of the n-th centered square grid graph.
- A344684 (program): Sum of two consecutive products of Fibonacci and Pell numbers: F(n)*P(n) + F(n+1)*P(n+1).
- A344685 (program): Triangle T(n, k) obtained from the array N1(a, b) = a^2 + a*b - b^2, for a >= 0 and b >= 0, read by upwards antidiagonals.
- A344686 (program): Triangle T(n, k) obtained from the array N2(a, b) = a^2 - a*b - b^2, for a >= 0 and b >= 0, read by upwards antidiagonals.
- A344687 (program): a(n) is the lowest nonnegative exponent k such that n!^k is the product of the divisors of n!.
- A344690 (program): a(n) is the number of multisets of size n consisting of permutations of n elements.
- A344695 (program): a(n) = gcd(sigma(n), psi(n)), where sigma is the sum of divisors function, A000203, and psi is the Dedekind psi function, A001615.
- A344705 (program): a(n) = n + A001615(n) - sigma(n), where A001615 is the Dedekind psi-function, and sigma(n) gives the sum of divisors of n; difference between psi and the sum of proper divisors.
- A344713 (program): a(n) is the number of iterations needed for n to reach 0 under the mapping x -> A055212(x).
- A344717 (program): a(n) = (3n - 9/2 - 1/n + 6/(n+1))*binomial(2n-2,n-1).
- A344720 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^2.
- A344721 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^3.
- A344722 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^4.
- A344723 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^5.
- A344724 (program): a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^n.
- A344747 (program): a(n) = (1/6)*(3^n + (-2)^n - 1).
- A344763 (program): a(n) = n - A011772(n).
- A344764 (program): a(n) = gcd(n, A011772(n)).
- A344765 (program): a(n) = sigma(n) - A011772(n).
- A344766 (program): a(n) = gcd(sigma(n), A011772(n)).
- A344791 (program): a(n) is the number of 2-point antichains in the poset D_{2n+1} of type D, whose elements are compositions of 2n+1.
- A344805 (program): Numbers that are the sum of six second powers in one or more ways.
- A344814 (program): a(n) = Sum_{k=1..n} floor(n/k) * 3^(k-1).
- A344815 (program): a(n) = Sum_{k=1..n} floor(n/k) * 4^(k-1).
- A344816 (program): a(n) = Sum_{k=1..n} floor(n/k) * 5^(k-1).
- A344817 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-2)^(k-1).
- A344818 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-3)^(k-1).
- A344819 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-4)^(k-1).
- A344820 (program): a(n) = Sum_{k=1..n} floor(n/k) * (-n)^(k-1).
- A344851 (program): a(n) = (n^2) mod (2^A070939(n)).
- A344853 (program): a(n) = n minus (sum of digits of n in base 3).
- A344863 (program): a(n) = mu(sigma(n)).
- A344864 (program): a(n) = mu(d(n)).
- A344866 (program): Number of polygons formed when every pair of vertices of a regular (2n-1)-gon are joined by an infinite line.
- A344872 (program): Semiprimes of the form 3m+2.
- A344875 (program): Multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e - 1 for odd primes p.
- A344877 (program): a(n) = gcd(n, A344875(n)), where A344875 is multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e -1 for odd primes p.
- A344907 (program): Number of polygon edges formed when every pair of vertices of a regular (2n-1)-gon are joined by an infinite line.
- A344919 (program): a(n) = n^n - n*(n + 1) / 2.
- A344920 (program): The Worpitzky transform of the squares.
- A344935 (program): a(0)=1; for n > 0, a(n) = n*(a(n-1) + i^(n-1)) if n is odd, n*a(n-1) + i^n otherwise, where i = sqrt(-1).
- A344947 (program): Number of open tours by a biased rook on a specific A070941(n) X 1 board, which ends on a black cell, where cells are colored white or black according to the binary representation of 2n.
- A344953 (program): Positions of words in A341258 that end with 1.
- A344956 (program): Positions of words in A341258 starting with 0 and ending with 0.
- A344957 (program): Positions of words in A341258 starting with 0 and ending with 1.
- A344958 (program): Positions of words in A344953 starting with 1 and ending with 0.
- A345013 (program): Triangle read by rows, related to clusters of type D.
- A345018 (program): For each n, append to the sequence n^2 consecutive integers, starting from n.
- A345019 (program): Numbers whose last digit is refactorable.
- A345021 (program): a(n) is the result of replacing 2’s by 0’s in the hereditary base-2 expansion of n.
- A345028 (program): a(n) = Sum_{k=1..n} 2^(floor(n/k) - 1).
- A345029 (program): a(n) = Sum_{k=1..n} 3^(floor(n/k) - 1).
- A345030 (program): a(n) = Sum_{k=1..n} n^(floor(n/k) - 1).
- A345031 (program): a(n) = 6*a(n-1) - 7*a(n-2) - 2*a(n-3) for n >= 3, with a(0) = a(1) = 0, a(2) = 1.
- A345034 (program): a(n) = Sum_{k=1..n} (-2)^(floor(n/k) - 1).
- A345035 (program): a(n) = Sum_{k=1..n} (-3)^(floor(n/k) - 1).
- A345036 (program): a(n) = Sum_{k=1..n} (-n)^(floor(n/k) - 1).
- A345037 (program): a(n) = Sum_{k=1..n} (-k)^(floor(n/k) - 1).
- A345052 (program): a(n) = A003557(n) * A048250(n) * A173557(n).
- A345069 (program): Sums of two consecutive even-indexed primes.
- A345070 (program): Averages of two consecutive even-indexed primes.
- A345071 (program): Sums of two consecutive odd-indexed primes.
- A345082 (program): Number of elements of order n in R/Z X Z/2Z.
- A345089 (program): Averages of two consecutive odd-indexed odd primes.
- A345090 (program): a(n) = Sum_{k=1..n} k^floor(1/gcd(k,2*n-k)).
- A345091 (program): a(n) = Sum_{k=1..n} k^floor(1/gcd(n,k)).
- A345094 (program): a(n) = Sum_{k=1..n} floor(n/k)^(floor(n/k) - 1).
- A345098 (program): a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).
- A345100 (program): a(n) = Sum_{k=1..n} k^floor(n/k).
- A345108 (program): a(n) = Sum_{k=1..n} 2^(n - floor(n/k)).
- A345109 (program): a(n) = Sum_{k=1..n} (-2)^(n - floor(n/k)).
- A345110 (program): a(n) is n rotated one place to the left or, equivalently, n with the most significant digit moved to the least significant place, omitting leading zeros.
- A345111 (program): a(n) = n + A345110(n).
- A345132 (program): Number of (n+2) X (n+2) symmetric matrices with nonnegative integer entries, trace 0, with n rows that sum to 2, and 2 rows that sum to 1.
- A345135 (program): Number of ordered rooted binary trees with n leaves and with minimal Sackin tree balance index.
- A345160 (program): a(n) = Product_{k=1..n} sigma_3(k).
- A345176 (program): a(n) = Sum_{k=1..n} floor(n/k)^k.
- A345211 (program): Numbers with the same number of odd / even, refactorable divisors.
- A345222 (program): Number of divisors of n with a prime number of divisors.
- A345261 (program): a(n) = Sum_{d|n} d * rad(d).
- A345264 (program): a(n) = Sum_{d|n} rad(d) * mu(n/d)^2.
- A345266 (program): a(n) = Sum_{p|n, p prime} gcd(p,n/p).
- A345277 (program): Sums of 3 consecutive even-indexed primes.
- A345280 (program): a(n) = Sum_{p|n} nextprime(p), where nextprime(n) is the smallest prime > n.
- A345303 (program): a(n) = Sum_{p|n, p prime} p * gcd(p,n/p).
- A345305 (program): a(n) = n * Sum_{p|n, p prime} gcd(p,n/p) / p.
- A345320 (program): Sum of the divisors of n whose square does not divide n.
- A345339 (program): a(n) = 18*n + 20.
- A345340 (program): The number of squares with vertices from the vertices of the n-dimensional hypercube.
- A345345 (program): a(n) = Sum_{d^2|n} omega(n/d^2).
- A345347 (program): Find the largest k with F(k) <= n, where F(k) is the k-th Fibonacci number. a(n) = F(k+2) + n.
- A345360 (program): a(n) = n^n*n - n.
- A345366 (program): a(n) = (p*q+1) mod (p+q) where p=prime(n) and q=prime(n+1).
- A345367 (program): a(n) = Sum_{k=0..n} binomial(4*k,k) / (3*k + 1).
- A345368 (program): a(n) = Sum_{k=0..n} binomial(5*k,k) / (4*k + 1).
- A345380 (program): Number of Jacobsthal-Lucas numbers m <= n.
- A345401 (program): a(n) is the unique odd number h such that BCR(h*2^m-1) = 2n (except for BCR(0) = 1) where BCR is bit complement and reverse per A036044.
- A345444 (program): a(n) = A344005(2*n+1).
- A345445 (program): a(n) = n^n - (n+1)!/2.
- A345448 (program): Number of tilings of a 2 X n rectangle with dominos and long L-shaped 4-minos.
- A345451 (program): Sum of the unitary divisors of n whose square does not divide n.
- A345455 (program): a(n) = Sum_{k=0..n} binomial(5*n+1,5*k).
- A345456 (program): a(n) = Sum_{k=0..n} binomial(5*n+2,5*k).
- A345457 (program): a(n) = Sum_{k=0..n} binomial(5*n+3,5*k).
- A345458 (program): a(n) = Sum_{k=0..n} binomial(5*n+4,5*k).
- A345478 (program): Numbers that are the sum of seven squares in one or more ways.
- A345480 (program): Numbers that are the sum of seven squares in three or more ways.
- A345482 (program): Numbers that are the sum of seven squares in five or more ways.
- A345483 (program): Numbers that are the sum of seven squares in six or more ways.
- A345487 (program): Numbers that are the sum of seven squares in ten or more ways.
- A345488 (program): Numbers that are the sum of eight squares in one or more ways.
- A345490 (program): Numbers that are the sum of eight squares in three or more ways.
- A345493 (program): Numbers that are the sum of eight squares in six or more ways.
- A345494 (program): Numbers that are the sum of eight squares in seven or more ways.
- A345495 (program): Numbers that are the sum of eight squares in eight or more ways.
- A345496 (program): Numbers that are the sum of eight squares in nine or more ways.
- A345497 (program): Numbers that are the sum of eight squares in ten or more ways.
- A345498 (program): Numbers that are the sum of nine squares in one or more ways.
- A345499 (program): Numbers that are the sum of nine squares in two or more ways.
- A345500 (program): Numbers that are the sum of nine squares in three or more ways.
- A345501 (program): Numbers that are the sum of nine squares in four or more ways.
- A345502 (program): Numbers that are the sum of nine squares in five or more ways.
- A345503 (program): Numbers that are the sum of nine squares in six or more ways.
- A345504 (program): Numbers that are the sum of nine squares in seven or more ways.
- A345505 (program): Numbers that are the sum of nine squares in eight or more ways.
- A345508 (program): Numbers that are the sum of ten squares in one or more ways.
- A345509 (program): Numbers that are the sum of ten squares in two or more ways.
- A345510 (program): Numbers that are the sum of ten squares in three or more ways.
- A345531 (program): Smallest prime power greater than the n-th prime.
- A345632 (program): Sum of terms of even index in the binomial decomposition of n^(n-1).
- A345633 (program): Sum of terms of odd index in the binomial decomposition of n^(n-1).
- A345668 (program): Last prime minus distance to last prime.
- A345685 (program): a(n) is the smallest cardinality of all covering sets associated with Riesel number A101036(n).
- A345701 (program): a(n) = 3*n^3 - 1.
- A345702 (program): Numbers that can be written as 2*a^2 - 1 and 3*b^3 - 1.
- A345727 (program): a(n) = (prime(n)+1) * prime(n+1).
- A345735 (program): A prime-generating quasipolynomial: a(n) = 6*floor(n^2/4) + 17.
- A345741 (program): a(n) = n + (n - 1) * d(n).
- A345743 (program): a(n) = Sum_{k=1..n} n^abs(mu(k)).
- A345745 (program): a(n) = Sum_{k=1..n} n^(1 - mu(k)^2).
- A345754 (program): Number of 2 X 2 matrices over Z_n such that their permanent equals their determinant.
- A345867 (program): Total number of 0’s in the binary expansions of the first n primes.
- A345876 (program): a(n) = Sum_{k=0..n} binomial(2*n, n-k) * k^n.
- A345887 (program): Number of tilings of an n-cell circular array with rectangular tiles of any size, and where the number of possible colors of a tile is given by the largest cell covered.
- A345888 (program): a(n) = n + (n - 1) * pi(n).
- A345889 (program): Number of tilings of an n-cell circular array with rectangular tiles of any size, and where the number of possible colors of a tile is given by the smallest cell covered.
- A345890 (program): a(n) = n + (n - 1) * (n - pi(n)).
- A345891 (program): a(n) = n + (n - 1) * phi(n).
- A345892 (program): a(n) = n + (n - 1) * (n - phi(n)).
- A345897 (program): a(n) = 2*n^4/3 - 4*n^3/3 + 11*n^2/6 - 13*n/6 + 1.
- A345927 (program): Alternating sum of the binary expansion of n (row n of A030190). Replace 2^k with (-1)^(A070939(n)-k) in the binary expansion of n (compare to the definition of A065359).
- A345931 (program): a(n) = gcd(n, A002034(n)), where A002034(n) gives the smallest positive integer k such that n divides k!.
- A345937 (program): a(n) = gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
- A345938 (program): a(n) = uphi(n) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
- A345939 (program): a(n) = (n-1) / gcd(n-1, uphi(n)), where uphi is unitary totient (or unitary phi) function, A047994.
- A345940 (program): Factorial of the largest prime factor of n, read modulo n: a(n) = A006530(n)! mod n.
- A345952 (program): a(n) = 1 if the largest prime power divisor of n (A034699) is greater than the largest prime divisor of n (A006530).
- A345954 (program): a(n) is the number of ternary strings of length n with at least three 0’s.
- A345963 (program): a(n) = (q^2-q+1)/3 where q = 2^(2*n+1) = A004171(n).
- A345980 (program): a(n) = spum of a path P_n.
- A345981 (program): a(n) = integral spum of a path P_n.
- A345983 (program): Partial sums of A344005.
- A345984 (program): Partial sums of A011772.
- A345988 (program): Smallest oblong number m*(m+1) that is divisible by n.
- A345993 (program): Let m = A344005(n) = smallest m such that n divides m*(m+1); a(n) = gcd(n,m+1).
- A346004 (program): If n even then n otherwise ((n+1)/2)^2.
- A346035 (program): a(1) = 1; if a(n) is not divisible by 3, a(n+1) = 4*a(n) + 1, otherwise a(n+1) = a(n)/3.
- A346054 (program): Number of ways to tile a 3 X n strip with dominos, and L-shaped 5-minos.
- A346065 (program): a(n) = Sum_{k=0..n} binomial(6*k,k) / (5*k + 1).
- A346070 (program): Symbolic code for the corner turns in the Lévy dragon curve.
- A346122 (program): n times the n-th digit of the decimal expansion of Pi.
- A346145 (program): Primes of the form k^2 + 25.
- A346152 (program): a(n) is the least prime divisor p_j of n such that if n = Product_{i=1..k} p_i^e_i and p_1 < p_2 < … < p_k, then Product_{i=1..j-1} p_i^e_i <= sqrt(n) < Product_{i=j..k} p_i^e_i. a(1) = 1.
- A346155 (program): Partial sums of A007978.
- A346174 (program): Inverse binomial transform of A317614.
- A346178 (program): Expansion of (1-2*x)/(1-10*x).
- A346180 (program): a(n) = prime(n) + n if n is prime, a(n) = prime(n) otherwise.
- A346181 (program): a(n) = Sum_{k=0..n} binomial(n,k) * k^n * (k+1)^(n-1), with a(0)=1.
- A346183 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial((k+1)^2, n).
- A346184 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(k^2, n).
- A346197 (program): a(n) is the minimum number of pebbles such that any assignment of those pebbles on K_5 is a next-player winning game in the two-player impartial (n+1,n) pebbling game.
- A346202 (program): a(n) = L(n)^2, where L is Liouville’s function.
- A346224 (program): a(n) = (n!)^2 * Sum_{k=0..floor(n/2)} 1 / ((n-2*k)! * 4^k * k!).
- A346232 (program): Maximum number of squares in a square grid whose interiors can be touched by a (possibly skew) line segment of length n.
- A346234 (program): Dirichlet inverse of A003961, where A003961(n) is fully multiplicative with a(prime(k)) = prime(k+1).
- A346244 (program): a(n) = n - A342001(n).
- A346258 (program): E.g.f.: exp(x) / (1 - 3 * x)^(1/3).
- A346295 (program): a(n) = Sum_{k=0..n} (2^k + 1) * (2^k + 2) / 2.
- A346301 (program): Positions of words in A076478 such that first digit = last digit.
- A346302 (program): Positions of words in A076478 such that first digit != last digit.
- A346303 (program): Positions of words in A076478 that start with 0 and end with 0.
- A346304 (program): Positions of words in A076478 that start with 1 and end with 0.
- A346305 (program): Positions of words in A076478 that start with 1 and end with 1.
- A346306 (program): Position in A076478 of the binary complement of the n-th word in A076478.
- A346307 (program): Number of runs in the n-th word in A076478.
- A346309 (program): Positions of words in A076478 such that #0’s - #1’s is odd.
- A346310 (program): Positions of words in A076478 such that #0’s - #1’s is even.
- A346311 (program): Maximum number of edges a single edge crosses in a drawing of the complete graph K_n where every vertex lies on the outer face.
- A346317 (program): Number of permutations of [n] having two cycles of the form (c1, c2, …, c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.
- A346370 (program): Upper bound for the number of solutions of the TRINTUM cube puzzle n X 1 X 1 (cuboid formed by 4n + 2 parts) different by the set of parts, which are distinguished by the amount of surface area they contribute to the assembled cuboid.
- A346375 (program): a(n) = Sum_{k=0..n} (2^k + 2) * (2^k + 3) / 2.
- A346376 (program): a(n) = n^4 + 14*n^3 + 63*n^2 + 98*n + 28.
- A346388 (program): a(n) is the number of proper divisors of A053742(n) ending with 5.
- A346394 (program): E.g.f.: -log(1 - x) * exp(2*x).
- A346395 (program): E.g.f.: -log(1 - x) * exp(3*x).
- A346396 (program): E.g.f.: -log(1 - x) * exp(4*x).
- A346397 (program): E.g.f.: -log(1 - x) * exp(-2*x).
- A346398 (program): E.g.f.: -log(1 - x) * exp(-3*x).
- A346401 (program): a(n) is the minimum number of pebbles such that any assignment of those pebbles on a complete graph with n vertices is a next-player winning game in the two-player impartial (3, 2) pebbling game.
- A346403 (program): a(1)=1; for n>1, a(n) gives the sum of the exponents in the different ways to write n as n = x^y, 2 <= x, 1 <= y.
- A346405 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k)^2 * k!).
- A346409 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k)^2 * k!).
- A346410 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} 1 / ((n-k) * k!)^2.
- A346411 (program): a(n) = (n!)^2 * Sum_{k=0..n-1} (-1)^k / ((n-k) * k!)^2.
- A346425 (program): a(n) is the greatest number k such that k! <= prime(n).
- A346432 (program): a(0) = 1; a(n) = n! * Sum_{k=0..n-1} (n-k+1) * a(k) / k!.
- A346434 (program): Triangle read by rows of numbers with n 1’s and n 0’s in their representation in base of Fibonacci numbers (A210619), written as those 1’s and 0’s.
- A346461 (program): a(n) = 2^A042965(n+1).
- A346470 (program): a(n) = psi(A276086(n)), where psi is Dedekind psi function A001615, and A276086 is the prime product form of primorial base expansion of n.
- A346471 (program): a(n) = A344695(A276086(n)), where A344695(x) = gcd(psi(x), sigma(x)), and A276086 gives the prime product form of primorial base expansion of n.
- A346474 (program): a(n) = A342414(A276086(n)).
- A346475 (program): a(n) = A342919(A276086(n)).
- A346494 (program): Heptagonal numbers (A000566) with prime indices (A000040).
- A346502 (program): a(n) = 3n - (sum of digits of 3n in base 3).
- A346503 (program): G.f. A(x) satisfies: A(x) = 1 + x^3 * A(x)^2 / (1 - x).
- A346513 (program): a(n) = Fibonacci(n+1)^3 - Fibonacci(n)^3.
- A346514 (program): a(n) = n^4 + 28*n^3 + 252*n^2 + 784*n + 448.
- A346515 (program): a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14).
- A346550 (program): Expansion of Sum_{k>=0} k! * x^k * (1 + x)^(k+1).
- A346558 (program): a(n) = Sum_{d|n} phi(n/d) * (2^d - 1).
- A346563 (program): a(n) = n + A007978(n).
- A346573 (program): Decimal expansion of 2 - Pi/3.
- A346597 (program): Partial sums of A019554.
- A346618 (program): Triangle read by rows: T(n,k) = 1 iff 2 divides binomial(n,k) but 4 does not (0 <= k <= n).
- A346626 (program): G.f. A(x) satisfies: A(x) = (1 + x * A(x)^3) / (1 - x).
- A346627 (program): G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * A(x)^3.
- A346628 (program): G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x) * A(x)^3.
- A346629 (program): Number of n-digit positive integers that are the product of two integers ending with 2.
- A346633 (program): Sum of even-indexed parts (even bisection) of the n-th composition in standard order.
- A346636 (program): a(n) is the number of quadruples (a_1, a_2, a_3, a_4) having all terms in {1,…,n} such that there exists a quadrilateral with these side lengths.
- A346642 (program): a(n) = Sum_{j=1..n} Sum_{i=1..j} j^3*i^3.
- A346646 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(4*k,k) / (3*k + 1).
- A346647 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(5*k,k) / (4*k + 1).
- A346648 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(6*k,k) / (5*k + 1).
- A346649 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(7*k,k) / (6*k + 1).
- A346650 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(8*k,k) / (7*k + 1).
- A346651 (program): a(n) is the number of divisors of A139245(n) ending with 2.
- A346663 (program): The number of nonreal roots of Sum_{k=0..n} prime(k+1)*x^k.
- A346664 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(4*k,k) / (3*k + 1).
- A346665 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(5*k,k) / (4*k + 1).
- A346666 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(6*k,k) / (5*k + 1).
- A346667 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(7*k,k) / (6*k + 1).
- A346668 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(8*k,k) / (7*k + 1).
- A346671 (program): a(n) = Sum_{k=0..n} binomial(7*k,k) / (6*k + 1).
- A346672 (program): a(n) = Sum_{k=0..n} binomial(8*k,k) / (7*k + 1).
- A346680 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(4*k,k) / (3*k + 1).
- A346681 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*k,k) / (4*k + 1).
- A346682 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(6*k,k) / (5*k + 1).
- A346683 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(7*k,k) / (6*k + 1).
- A346684 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(8*k,k) / (7*k + 1).
- A346688 (program): Replace 4^k with (-1)^k in base-4 expansion of n.
- A346689 (program): Replace 5^k with (-1)^k in base-5 expansion of n.
- A346690 (program): Replace 6^k with (-1)^k in base-6 expansion of n.
- A346691 (program): Replace 7^k with (-1)^k in base-7 expansion of n.
- A346693 (program): Minimum integer length of a segment that touches the interior of n squares on a unit square grid.
- A346731 (program): Replace 8^k with (-1)^k in base-8 expansion of n.
- A346732 (program): Replace 9^k with (-1)^k in base-9 expansion of n.
- A346758 (program): a(n) = Sum_{d|n} mu(n/d) * floor(d^2/4).
- A346759 (program): a(n) = Sum_{d|n} floor(d^2/4).
- A346762 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 2*x) + x * (1 - 2*x) * A(x)^3.
- A346763 (program): G.f. A(x) satisfies: A(x) = 1 / (1 - 3*x) + x * (1 - 3*x) * A(x)^3.
- A346773 (program): a(n) = Sum_{d|n} möbius(d)^n.
- A346796 (program): Number of equivalence classes of triangles in an n-dimensional hypercube, equivalent up to translation of difference vectors corresponding to edges.
- A346803 (program): Numbers that are the sum of nine squares in ten or more ways.
- A346804 (program): Numbers that are the sum of ten squares in five or more ways.
- A346805 (program): Numbers that are the sum of ten squares in six or more ways.
- A346806 (program): Numbers that are the sum of ten squares in seven or more ways.
- A346807 (program): Numbers that are the sum of ten squares in eight or more ways.
- A346808 (program): Numbers that are the sum of ten squares in ten or more ways.
- A346811 (program): Square array read by antidiagonals upwards in which T(n, k) is the number of essentially different relations from the first proportional segment theorem for n lines, k parallel and n-k intersecting in a common point.
- A346839 (program): Decimal expansion of Sum_{n>=0} A346838(n) / n!.
- A346865 (program): Sum of divisors of the n-th hexagonal number.
- A346866 (program): Sum of divisors of the n-th second hexagonal number.
- A346869 (program): Sum of all divisors, except the smallest and the largest of every number, of the first n odd numbers.
- A346870 (program): Sum of all divisors, except the smallest and the largest of every number, of the first n positive even numbers.
- A346877 (program): Sum of the divisors, except the largest, of the n-th odd number.
- A346878 (program): Sum of the divisors, except the largest, of the n-th positive even number.
- A346879 (program): Sum of the divisors, except the smallest and the largest, of the n-th odd number.
- A346880 (program): Sum of the divisors, except the smallest and the largest, of the n-th positive even number.
- A346896 (program): Expansion of e.g.f.: (1-12*x)^(-11/12).
- A346912 (program): a(0) = 1; a(n) = a(n-1) + a(floor(n/2)) + 1.
- A346933 (program): Decimal expansion of 2 * Pi^2 / 27.
- A346943 (program): a(n) = a(n-1) + n*(n+1)*a(n-2) with a(0)=1, a(1)=1.
- A346949 (program): Value of the permanent of the matrix [1-zeta^{j-k}]_{1<=j,k<=2n}, where zeta is any primitive 2n-th root of unity.
- A346958 (program): a(n) is the minimal number of cubes required to make a void of volume n.
- A346960 (program): a(0) = 0, a(1) = 1; a(n) = n * (n+1) * a(n-1) + a(n-2).
- A346965 (program): a(n) is the number of ascending subsequences in reducing n to 1 using the Collatz reduction, or -1 if n refutes the Collatz conjecture.
- A347012 (program): E.g.f.: exp(x) / (1 - 4 * x)^(1/4).
- A347013 (program): E.g.f.: exp(x) / (1 - 5 * x)^(1/5).
- A347014 (program): E.g.f.: exp(x) / (1 - 6 * x)^(1/6).
- A347017 (program): a(n) = floor(2^(n-1)) - binomial(n,3) + binomial(n,2) - n + 1.
- A347026 (program): Irregular triangle read by rows in which row n lists the first n odd numbers, followed by the first n odd numbers in decreasing order.
- A347030 (program): a(n) = 1 + Sum_{k=2..n} (-1)^k * a(floor(n/k)).
- A347036 (program): Number of Motzkin paths of length n avoiding UHHD.
- A347047 (program): Smallest squarefree semiprime whose prime indices sum to n.
- A347051 (program): a(0) = 1, a(1) = 2; a(n) = n * (n+1) * a(n-1) + a(n-2).
- A347056 (program): Triangle read by rows: T(n,k) = (n+1)*(n+2)*(k+3)*binomial(n,k)/6, 0 <= k <= n.
- A347092 (program): Dirichlet inverse of A322577, which is the convolution of Dedekind psi with Euler phi.
- A347107 (program): a(n) = Sum_{1 <= i < j <= n} j^3*i^3.
- A347112 (program): a(n) = concat(prime(n+1),n) mod prime(n).
- A347127 (program): a(n) = A327251(n) / A003557(n).
- A347128 (program): a(n) = A018804(n) / A003557(n), where A018804 is Pillai’s arithmetical function.
- A347129 (program): a(n) = A347130(n) / A003557(n), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n.
- A347142 (program): Sum of 4th powers of divisors of n that are < sqrt(n).
- A347143 (program): Sum of 4th powers of divisors of n that are <= sqrt(n).
- A347149 (program): Dirichlet g.f.: Product_{primes p} (1 + 3/p^s).
- A347152 (program): Decimal expansion of 7 * Pi / 2.
- A347153 (program): Sum of all divisors, except the largest of every number, of the first n odd numbers.
- A347154 (program): Sum of all divisors, except the largest of every number, of the first n positive even numbers.
- A347157 (program): Sum of cubes of distinct prime divisors of n that are < sqrt(n).
- A347158 (program): Sum of 4th powers of distinct prime divisors of n that are < sqrt(n).
- A347159 (program): Sum of cubes of distinct prime divisors of n that are <= sqrt(n).
- A347160 (program): Sum of 4th powers of distinct prime divisors of n that are <= sqrt(n).
- A347167 (program): Numbers k such that phi(binomial(k,2)) is a power of 2.
- A347173 (program): Sum of squares of odd divisors of n that are <= sqrt(n).
- A347174 (program): Sum of cubes of odd divisors of n that are <= sqrt(n).
- A347175 (program): Sum of 4th powers of odd divisors of n that are <= sqrt(n).
- A347178 (program): Decimal expansion of imaginary part of (i + (i + (i + (i + …)^(1/3))^(1/3))^(1/3))^(1/3), where i is the imaginary unit.
- A347191 (program): Number of divisors of n^2-1.
- A347263 (program): Irregular triangle read by rows: T(n,k) is the sum of the subparts of the ziggurat diagram of n (described in A347186) that arise from the (2*k-1)-th double-staircase of the double-staircases diagram of n (described in A335616), n >= 1, k >= 1, and the first element of column k is in row A000384(k).
- A347266 (program): a(n) is the number whose binary representation is the concatenation of terms in the n-th row of A237048.
- A347272 (program): Main diagonal of the square array A347270.
- A347274 (program): a(n) = Sum_{j=1..n} j*n^(n+1-j).
- A347275 (program): a(n) is the number of nonnegative ordered pairs (a,b) satisfying (a+b <= n) and (a*b <= n).
- A347286 (program): a(n) is n minus the number of odd divisors of n.
- A347289 (program): Number of independent sets in the binomial tree of order n.
- A347291 (program): Multiplicative function defined by a(p) = 2 and a(p^k) = p^(k-1) for k >= 2.
- A347302 (program): a(n) = 3^n - lcm{1..n}, with a(0) = 0.
- A347303 (program): a(n) = 3^(n-1) - lcm{1..n}.
- A347319 (program): a(n) = (2*n+1)*(n^3-2*n^2+n+1).
- A347325 (program): Solution to the spectator-first Tantalizer problem.
- A347342 (program): a(n) = prime(n) mod floor(prime(n) / n).
- A347350 (program): Sequence obtained by writing the first 4 integers and skipping 1, then writing the next 5 integers and skipping 2, then writing the next 6 and skipping 3, etc.
- A347365 (program): a(n) = n * (2-(-1)^n), or zero together with first differences of even triangular numbers halved (A074378).
- A347385 (program): Dedekind psi function applied to the odd part of n: a(n) = A001615(A000265(n)).
- A347397 (program): a(n) = Sum_{k=1..n} k^k * floor(n/k^k).
- A347398 (program): Expansion of g.f. Sum_{k>=1} k^k * x^(k^k)/(1 - x^(k^k)).
- A347399 (program): a(n) = A347398(n^n).
- A347400 (program): Lexicographically earliest sequence of distinct terms > 0 such that concatenating n to a(n) forms a palindrome in base 10.
- A347429 (program): a(n) is the alternating sum of the n-th row of A047920.
- A347433 (program): Irregular triangle read by rows: T(n,k) is the difference between the total arch lengths of a semi-meander multiplied by its number of exterior arches and total arch lengths of the semi-meanders with n + 1 top arches generated by the exterior arch splitting algorithm on the given semi-meander.
- A347477 (program): Number of total dominating sets in the complement graph of the n-cycle.
- A347478 (program): Number of total dominating sets in the n-alkane graph.
- A347493 (program): a(0) = 1, a(1) = 0, a(2) = a(3) = 1; thereafter, a(n) = a(n-1) + a(n-2) + a(n-4).
- A347501 (program): Number of dominating sets in the n-alkane graph.
- A347502 (program): Number of dominating sets in the n-cycle complement graph.
- A347503 (program): Number of dominating sets in the n-dipyramidal graph.
- A347512 (program): Number of minimal dominating sets in the n-book graph.
- A347513 (program): Number of minimal dominating sets in the n-cycle complement graph.
- A347516 (program): Number of divisors of n that are at most n^(1/3).
- A347517 (program): Partial sums of A347516.
- A347523 (program): Characteristic function of nonpowers of 2.
- A347525 (program): Number of minimum dominating sets in the n-Andrásfai graph.
- A347532 (program): a(n) is the sum of the nonpowers of 2 in the 3x+1 sequence that starts at n.
- A347535 (program): Number of minimum dominating sets in the complete bipartite graph K_n,n.
- A347536 (program): Number of minimum dominating sets in the complete tripartite graph K_n,n,n.
- A347553 (program): Number of minimum dominating sets in the n-cycle complement graph.
- A347581 (program): The Barnyard sequence: a(n) is the minimum number of unit length line segments required to enclose areas of 1 through n on a square grid.