A275820 Expansion of Product_{k>=1} (1 + x^(2*k) + x^(3*k)).

1, 0, 1, 1, 1, 0, 3, 1, 3, 3, 3, 2, 7, 3, 8, 7, 10, 7, 16, 8, 17, 17, 21, 17, 35, 22, 37, 36, 46, 37, 69, 46, 74, 71, 91, 81, 128, 96, 144, 139, 173, 154, 236, 185, 263, 257, 314, 286, 417, 345, 470, 462, 557, 517, 719, 617, 815, 802, 960, 904, 1211, 1068

Offset

0,7

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Formula

a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2*sqrt(3*Pi)*n^(3/4)), where c = Integral_{0..infinity} log(1 + exp(-2*x) + exp(-3*x)) dx = 0.60248650631158778882474716370201988195290074160793967143564...

Mathematica

nmax = 100; CoefficientList[Series[Product[1+x^(2*k)+x^(3*k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; p = ConstantArray[0, nmax + 1]; p[[1]] = 1; p[[3]] = 1; p[[4]] = 1; Do[Do[p[[j+1]] = p[[j+1]] + If[j < 2*k, 0, p[[j - 2*k + 1]]] + If[j < 3*k, 0, p[[j - 3*k + 1]]], {j, nmax, k, -1}]; , {k, 2, nmax}]; p (* Vaclav Kotesovec, May 10 2018 *)

Crossrefs

Cf. A000726, A263401, A264905, A266686, A275821.

Sequence in context: A337333 A348665 A152774 * A210146 A354198 A233654

Adjacent sequences: A275817 A275818 A275819 * A275821 A275822 A275823

Keyword

nonn

Author

Vaclav Kotesovec, Nov 15 2016

Status

approved