13396

Properties

Appears in sequences

• Generalized Stirling numbers, [n+2,n]_2.at n=16A001701
• Number of "long curves", i.e., topological types of smooth embeddings of the oriented real line into the oriented plane that coincide with the standard immersion x -> (x,0) in the neighborhood of -infinity and +infinity.at n=6A054993
• Triangular array T(n,k) giving number of alternating link diagrams with n >= 0 crossings, k = 0..[n/2] connected components and two external legs.at n=12A062038
• Table T(n,k) giving number of two-legged knot diagrams with n >= 0 self-intersections and k >= 0 tangencies, read by antidiagonals.at n=21A067640
• Numbers n such that zero is never reached by iterating the mapping k -> abs(reverse(lpd(k))-reverse(gpf(k))). lpd(k) is the largest proper divisor and gpf(k) is the largest prime factor of k.at n=37A076425
• G.f. = { 1+sum(4*n*q^n, n=1..infinity)} / { theta series for square lattice }.at n=18A079902
• Expansion of q^(-1/6) * eta(q^2)^3 / eta(q)^2 in powers of q.at n=50A085140
• Coefficients of partition Hermite-MacMahon polynomials: p(x,n)= If[n == 0, 1, HermiteH[n, x]*Sum[MacMahon[n-1, k-1]*x^(k - 1), {k, 1, n}]/2^Floor[n/2]].at n=40A171533
• Number of strings of numbers x(i=1..n) in 0..4 with sum i*x(i)^2 equal to n*16.at n=9A184436
• Number of partitions p of n such that the number of numbers p having multiplicity 1 in p is not a part and the number of numbers having multiplicity > 1 is not a part.at n=45A241417
• Zeroless numbers n with digits d_1, d_2, ... d_k such that d_1^3 + ... + d_k^3 is a cube.at n=46A254960
• Numbers m such that A166133(m+1) = A166133(m)^2 - 1.at n=22A256703
• Number of active (ON, black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by "Rule 249", based on the 5-celled von Neumann neighborhood.at n=6A271013
• Numbers k such that prime(k) divides primorial(j) + 1 for exactly three integers j.at n=2A283928
• Number of n X 3 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.at n=8A297219
• Number of n X 3 0..1 arrays with every element unequal to 0, 1 or 5 king-move adjacent elements, with upper left element zero.at n=17A303714
• Number of integer partitions of n whose second differences sum to 0, meaning either there is only one part, or the first two parts have the same difference as the last two parts.at n=45A360683
• Least k such that there are exactly A003586(n) ways to choose a binary index of each binary index of k.at n=29A368111
• Sorted positions of first appearances in A368109 (number of ways to choose a binary index of each binary index).at n=30A368112
• Place a point on the integer coordinates, up to |n|, along all four axial directions on a Cartesian plane, and then join an infinite straight line between every pair of points: a(n) is the number of finite edges created in the resulting graph.at n=5A386561