OFFSET
1,6
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(1/4) * Gamma(3/8) / (8 * 2^(5/16) * 3^(1/16) * Pi^(11/8) * n^(9/16)). - Vaclav Kotesovec, Aug 26 2015
G.f.: Product_{k>=0} 1/((1-x^(8*k+2))*(1-x^(8*k+3))). - Robert Israel, Dec 11 2018
MAPLE
nmax:= 100:
g:= mul(1/(1-x^(8*k+2))/(1-x^(8*k+3)), k=0..(nmax-2)/8):
S:= series(g, x, nmax+1):
seq(coeff(S, x, j), j=1..nmax); # Robert Israel, Dec 11 2018
MATHEMATICA
nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+2))*(1 - x^(8k+3))), {k, 0, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Aug 26 2015 *)
nmax = 60; kmax = nmax/8;
s = Flatten[{Range[0, kmax]*8 + 2}~Join~{Range[0, kmax]*8 + 3}];
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 1, nmax}] (* Robert Price, Aug 03 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved