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%I #5 Dec 02 2020 01:00:54
%S 1,0,1,0,1,1,1,1,2,1,3,1,3,3,3,3,4,4,6,4,7,6,7,7,8,9,11,9,13,12,14,14,
%T 16,16,20,17,23,22,25,25,28,29,33,31,37,38,41,42,45,48,54,51,61,60,67,
%U 67,72,76,84,81,93,93,102,104,110,117,125,125,139,140,153
%N Number of partitions of n into an even number of squares.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F G.f.: (1/2) * (Product_{k>=1} 1 / (1 - x^(k^2)) + Product_{k>=1} 1 / (1 + x^(k^2))).
%F a(n) = (A001156(n) + A292520(n)) / 2.
%e a(10) = 3 because we have [9, 1], [4, 4, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1, 1, 1].
%t nmax = 70; CoefficientList[Series[(1/2) (Product[1/(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}] + Product[1/(1 + x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]), {x, 0, nmax}], x]
%Y Cf. A000290, A001156, A027187, A292520, A339365, A339366, A339367.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Dec 01 2020
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