A035449 Number of partitions of n into parts 8k+1 or 8k+3.

1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 6, 8, 8, 9, 11, 11, 13, 16, 17, 20, 23, 25, 28, 31, 34, 38, 43, 48, 53, 59, 65, 70, 78, 86, 93, 105, 115, 125, 139, 150, 162, 179, 193, 211, 233, 251, 274, 298, 320, 348, 377, 407, 443, 480, 519, 561, 604, 651, 700, 755, 815, 876, 946

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

Cf. A035679.

Sequence in context: A328796 A247049 A029059 * A161555 A029058 A046026

Adjacent sequences: A035446 A035447 A035448 * A035450 A035451 A035452

Keyword

nonn

Author

Olivier Gérard

Status

approved