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A035444 Number of partitions of n into parts 4k.

%I A035444 #35 Aug 03 2020 18:27:52
%S A035444 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,
%T A035444 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,
%U A035444 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
%N A035444 Number of partitions of n into parts 4k.
%H A035444 Antti Karttunen, <a href="/A035444/b035444.txt">Table of n, a(n) for n = 0..16384</a>
%F A035444 a(4*n) = A000041(n). a(4*n + 1) = a(4*n + 2) = a(4*n + 3) = 0. - _Michael Somos_, Jun 02 2012
%F A035444 G.f.: 1 / Product_{n>=1} 1 - q^(4*n). - _Joerg Arndt_, Aug 26 2015
%p A035444 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
%t A035444 nmax=100; CoefficientList[Series[Product[1/(1 - x^(4 k)), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vincenzo Librandi_, Jul 04 2018 *)
%t A035444 nmax = 50; kmax = nmax/4; s = Range[0, kmax]*4;
%t A035444 Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* _Robert Price_, Aug 03 2020 *)
%o A035444 (PARI) A035444(n) = if((n%4),0,numbpart(n/4)); \\ _Antti Karttunen_, Jul 03 2018
%Y A035444 Cf. A000041, A114099.
%K A035444 nonn
%O A035444 0,9
%A A035444 _Olivier Gérard_
%E A035444 Error in offset corrected by _Vaclav Kotesovec_, Aug 26 2015
%E A035444 Name simplified, _Joerg Arndt_, Aug 26 2015