OFFSET
0,11
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
Vaclav Kotesovec, Graph - The asymptotic ratio (100000 terms)
FORMULA
a(n) ~ (-1)^n * c^(1/4) * exp(sqrt(c*n)) / (2^(3/2)*sqrt(Pi)*n^(3/4)), where c = Integral_{0..infinity} log(1 + 2*exp(-x) + exp(-2*x) - exp(-3*x)) dx = 1.522848148277623680909526566...
MATHEMATICA
nmax=100; CoefficientList[Series[Product[1+x^(2*k)-x^(3*k), {k, 1, nmax}], {x, 0, nmax}], x]
RootReduce[QPochhammer[Root[-1 + # + #^3 &, 1], x] QPochhammer[Root[-1 + # + #^3 &, 2], x] QPochhammer[Root[-1 + # + #^3 &, 3], x] + O[x]^70][[3]] (* Vladimir Reshetnikov, Nov 20 2016 *)
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 06 2018 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Nov 15 2016
STATUS
approved