A035444 - OEIS

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

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OFFSET

0,9

LINKS

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

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

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 *)

PROG

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

CROSSREFS

Cf. A000041, A114099.

Sequence in context: A244140 A091227 A300715 * A376417 A376418 A244141

Adjacent sequences: A035441 A035442 A035443 * A035445 A035446 A035447

KEYWORD

nonn

AUTHOR

Olivier Gérard

EXTENSIONS

Error in offset corrected by Vaclav Kotesovec, Aug 26 2015

Name simplified, Joerg Arndt, Aug 26 2015

STATUS

approved