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%I #5 Dec 02 2020 01:01:00
%S 0,1,0,1,1,1,1,1,1,3,1,3,2,3,3,3,4,5,4,6,5,7,7,7,8,10,9,12,10,14,13,
%T 14,15,18,17,21,20,24,24,25,27,31,30,35,34,40,40,42,45,50,50,56,55,64,
%U 65,68,72,78,79,88,85,99,99,105,110,118,122,131,132,146,149
%N Number of partitions of n into an odd 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(9) = 3 because we have [9], [4, 4, 1] and [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, A027193, A292520, A339364, A339366, A339367.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Dec 01 2020
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