OFFSET
0,12
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(Pi*sqrt(n)/3) / (2^(4/3) * sqrt(3) * n^(3/4)) * (1 - (Pi/144 + 9/(8*Pi)) / sqrt(n)). - Vaclav Kotesovec, Aug 26 2015, extended Jan 16 2017
G.f.: Sum_{k>=0} x^(k*(3*k - 1)/2) / Product_{j=1..k} (1 - x^(3*j)). - Ilya Gutkovskiy, Nov 24 2020
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1 + x^(3*k+1)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[If[Mod[k, 3] == 1, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Jan 13 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 26 2015
STATUS
approved