OFFSET
1,3
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Product_{k>=0} 1/((1-x^(8*k+1))*(1-x^(8*k+3))). - Robert Israel, Aug 29 2018
a(n) ~ exp(Pi*sqrt(n/6)) * Gamma(3/8) * Gamma(1/8) / (8 * Pi^(3/2) * sqrt(2*n)). - Vaclav Kotesovec, Aug 26 2015
MAPLE
N:= 100: # for a(1)..a(N)
P:= 1/mul((1-x^(8*k+1))*(1-x^(8*k+3)), k=0..floor((N-1)/8)):
S:= series(P, x, N+1):
seq(coeff(S, x, j), j=1..N); # Robert Israel, Aug 28 2018
MATHEMATICA
nmax = 100; Rest[CoefficientList[Series[Product[1/((1 - x^(8k+1))*(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 + 1}~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