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A035444 Number of partitions of n into parts 4k. 17
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
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
Sequence in context: A244140 A091227 A300715 * A244141 A152489 A143655
KEYWORD
nonn
AUTHOR
EXTENSIONS
Error in offset corrected by Vaclav Kotesovec, Aug 26 2015
Name simplified, Joerg Arndt, Aug 26 2015
STATUS
approved

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)