OFFSET
0,4
COMMENTS
a(n) is the number of partitions of n into distinct parts where no part is a multiple of 6. - Joerg Arndt, Aug 31 2015
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 12.
FORMULA
a(n) ~ exp(Pi*sqrt(5*n/2)/3) * 5^(1/4) / (2^(7/4) * sqrt(3) * n^(3/4)) * (1 - (9/(4*Pi*sqrt(10)) + 5*Pi*sqrt(5/2)/144) / sqrt(n)). - Vaclav Kotesovec, Aug 31 2015, extended Jan 21 2017
G.f.: Product_{k>=1} (1 - x^(12*k-6))/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 07 2017
MAPLE
b:= proc(n, i) option remember; local r;
`if`(2*n>i*(i+1)-(j-> 6*j*(j+1))(iquo(i, 6, 'r')), 0,
`if`(n=0, 1, b(n, i-1)+`if`(i>n or r=0, 0, b(n-i, i-1))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..80); # Alois P. Heinz, Aug 31 2015
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + x^k) / (1 + x^(6*k)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 31 2015
STATUS
approved