OFFSET
0,4
COMMENTS
a(n) is the number of partitions of n into distinct parts where no part is a multiple of 8.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ exp(Pi*sqrt(7*n/6)/2) * 7^(1/4) / (4 * 6^(1/4) * n^(3/4)) * (1 - (3*sqrt(3)/ (2*Pi*sqrt(14)) + 7*Pi*sqrt(7)/(96*sqrt(6))) / sqrt(n)). - Vaclav Kotesovec, Aug 31 2015, extended Jan 21 2017
G.f.: Product_{k>=1} (1 - x^(16*k-8))/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 07 2017
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
[0, 1, 0, 1, 0, 1, 0, 1, -1, 1, 0, 1, 0, 1, 0, 1]
[1+irem(d, 16)], d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..80); # Alois P. Heinz, Aug 31 2015
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + x^k) / (1 + x^(8*k)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 31 2015
STATUS
approved