OFFSET
1,6
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(k*(3*k+5)/2).
a(n) = p(n-4) - p(n-11) + p(n-21) - ... + (-1)^(k-1) * p(n-k*(3*k+5)/2) + ..., where p() is A000041().
a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*n*sqrt(3)) * (1 - (1/(2*Pi) + 31*Pi/144) / sqrt(n/6)). - Vaclav Kotesovec, May 26 2023
EXAMPLE
a(6) = 2 counts these partitions: 6, 5+1.
PROG
(PARI) a(n) = sum(k=1, sqrtint(n), (-1)^(k-1)*numbpart(n-k*(3*k+5)/2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 22 2023
STATUS
approved