A035444 Number of partitions of n into parts 4k.

1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 5, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 15, 0, 0, 0, 22, 0, 0, 0, 30, 0, 0, 0, 42, 0, 0, 0, 56, 0, 0, 0, 77, 0, 0, 0, 101, 0, 0, 0, 135, 0, 0, 0, 176, 0, 0, 0, 231, 0, 0, 0, 297, 0, 0, 0, 385, 0, 0, 0, 490, 0, 0, 0, 627, 0, 0, 0, 792, 0, 0, 0, 1002, 0

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A000041, A114099.

Programs

Maple

seq(coeff(series(mul(1/(1-x^(4*k)),k=1..n), x,n+1),x,n),n=0..105); # Muniru A Asiru, Jul 22 2018

Mathematica

nmax=100; CoefficientList[Series[Product[1/(1 - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vincenzo Librandi, Jul 04 2018 *)
nmax = 50; kmax = nmax/4; s = Range[0, kmax]*4;
Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Aug 03 2020 *)

PARI

A035444(n) = if((n%4),0,numbpart(n/4)); \\ Antti Karttunen, Jul 03 2018

Formula

a(4*n) = A000041(n). a(4*n + 1) = a(4*n + 2) = a(4*n + 3) = 0. - Michael Somos, Jun 02 2012

G.f.: 1 / Product_{n>=1} 1 - q^(4*n). - Joerg Arndt, Aug 26 2015

Extensions

Error in offset corrected by Vaclav Kotesovec, Aug 26 2015

Name simplified, Joerg Arndt, Aug 26 2015