A339366 - OEIS

%I #5 Dec 02 2020 01:01:06

%S 1,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,0,0,0,1,1,0,0,1,1,0,0,0,

%T 1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,0,2,1,1,1,1,0,0,1,1,0,0,1,1,1,0,3,1,0,

%U 1,0,1,1,0,1,2,1,0,0,3,1,1,1,1,0,1,3,1,1,0,1,3

%N Number of partitions of n into an even number of distinct 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 + x^(k^2)) + Product_{k>=1} (1 - x^(k^2))).

%F a(n) = (A033461(n) + A276516(n)) / 2.

%e a(50) = 2 because we have [49, 1] and [36, 9, 4, 1].

%t nmax = 90; CoefficientList[Series[(1/2) (Product[(1 + x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}] + Product[(1 - x^(k^2)), {k, 1, Floor[nmax^(1/2)] + 1}]), {x, 0, nmax}], x]

%Y Cf. A000290, A033461, A067661, A276516, A339364, A339365, A339367.

%K nonn

%O 0,51

%A _Ilya Gutkovskiy_, Dec 01 2020