OFFSET
1,6
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=1} x^(4*k^2)/Product_{j=1..4*k-1} (1-x^j).
a(n) ~ c * exp(Pi*sqrt(2*n/5)) / n^(3/4), where c = (3 - sqrt(5))^(1/4) / (8*sqrt(5)) = 0.05226232058... - Vaclav Kotesovec, Jan 25 2022, updated Oct 13 2024
EXAMPLE
For n=7 there are a(7)=3 such partitions: [1,2,2,2], [1,1,2,3] and [1,1,1,4]. - R. J. Mathar, Jun 20 2022
MATHEMATICA
CoefficientList[Series[Sum[x^(4k^2)/Product[1-x^j, {j, 4k-1}], {k, 63}], {x, 0, 63}], x] (* Stefano Spezia, Jan 22 2022 *)
PROG
(PARI) my(N=66, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, sqrtint(N\4), x^(4*k^2)/prod(j=1, 4*k-1, 1-x^j))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 21 2022
STATUS
approved