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A265260 Number of partitions of n into even squares.

%I A265260 #25 Nov 21 2017 19:46:31
%S A265260 1,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,2,0,0,0,2,0,0,0,2,0,0,0,2,0,0,0,3,0,
%T A265260 0,0,4,0,0,0,4,0,0,0,4,0,0,0,5,0,0,0,6,0,0,0,6,0,0,0,6,0,0,0,8,0,0,0,
%U A265260 9,0,0,0,10,0,0,0,10,0,0,0,12,0,0,0,13,0,0,0,14,0,0,0,14,0,0,0,16,0,0,0,19,0,0,0,20,0
%N A265260 Number of partitions of n into even squares.
%C A265260 a(n) = 0 if and only if n is not divisible by 4 (sequence A042968).
%H A265260 Hans Havermann, <a href="/A265260/b265260.txt">Table of n, a(n) for n = 0..831</a>
%F A265260 G.f.: 1/Product_{i>=1} (1 - x^{4i^2}).
%F A265260 a(4n) = A001156(n). - _Alois P. Heinz_, Jan 27 2016
%e A265260 a(28) = 2 because we have [4,4,4,4,4,4,4] and [4,4,4,16].
%e A265260 a(32) = 3 because we have [4,4,4,4,4,4,4,4], [4,4,4,4,16], and [16,16].
%p A265260 g := 1/mul(1-x^(4*i^2), i = 1 .. 150): gser := series(g, x = 0, 105): seq(coeff(gser, x, n), n = 0 .. 100);
%p A265260 # second Maple program:
%p A265260 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A265260       b(n, i-1)+ `if`(i^2>n, 0, b(n-i^2, i))))
%p A265260     end:
%p A265260 a:= n-> `if`(irem(n, 4, 'm')=0, b(m, isqrt(m)), 0):
%p A265260 seq(a(n), n=0..120);  # _Alois P. Heinz_, Jan 27 2016
%t A265260 a[n_] := If[n==0, 1, If[Divisible[n, 4], PowersRepresentations[n/4, n/4, 2] // Length, 0]]; Array[a, 100, 0] (* _Jean-François Alcover_, Feb 19 2016, after _Alois P. Heinz_ *)
%Y A265260 Cf. A001156, A042968, A167661.
%K A265260 nonn
%O A265260 0,17
%A A265260 _Emeric Deutsch_, Jan 26 2016
%E A265260 Data-section extended up to a(105) by _Antti Karttunen_, Nov 21 2017, from the b-file provided by _Hans Havermann_