19090

Appears in sequences

• Denominators of convergents to Pi by Farey fractions.at n=36A063673
• Triangle Q, read by rows, where column k of Q equals column 0 of Q^(k+1) and Q is equal to the matrix square of integer triangle P = A135880 such that column 0 of Q equals column 0 of P shift left.at n=40A135885
• Triangle, read by rows equal to the matrix product P*R^-1*P, where P = A135880 and R = A135894; P*R^-1*P equals triangle Q=A135885 shifted down one row.at n=49A135899
• a(n) = 36*n^2 + 2*n.at n=22A158064
• Totally multiplicative sequence with a(p) = a(p-1) + 9 for prime p.at n=25A166706
• Number of lower triangles of a 4 X 4 0..n array with each element differing from all of its diagonal, vertical, antidiagonal and horizontal neighbors by one or less.at n=8A195234
• Number of unlabeled 6-trees on n nodes.at n=14A202037
• Numbers n such that both n*Pi and n*e are within 1/sqrt(n) of integers.at n=37A208530
• Numbers k such that (2^64 - 189)*10^k + 1 is prime.at n=8A209250
• Number of (w,x,y,z) with all terms in {1,...,n} and w*x>3*y*z.at n=17A211918
• Words of length n over the alphabet {0,...,n-1} that are 112-avoiding.at n=6A239296
• A triple of positive integers (n,p,k) is admissible if there exist at least two different multisets of k positive integers, {x_1,x_2,...,x_k} and {y_1,y_2,...,y_k}, such that x_1+x_2+...+x_k = y_1+y_2+...+y_k = n and x_1x_2...x_k = y_1y_2...y_k = p. For each n, let A(n) = {(p,k):(n,p,k) is admissible for some k}; then a(n) = |A(n)|.at n=45A334246
• Number of ways to write n as an ordered sum of 10 primes (counting 1 as a prime).at n=9A341989
• Triangle read by rows: T(n,k) is the number of pairs (c,m), where c is a covering of the 1 X (2n) grid with 1 X 2 rectangles and equal numbers of red and blue 1 X 1 squares and m is a matching between red squares and blue squares, such that exactly k matched pairs are adjacent.at n=16A360441
• Expansion of g.f. A(x,y) satisfying y/x = Sum_{n=-oo..+oo} x^(n*(3*n+1)/2) * (A(x,y)^(3*n) - 1/A(x,y)^(3*n+1)), as a triangle read by rows.at n=24A361050
• Central terms of triangle A361050.at n=3A361538