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Number of partitions of n^2 into consecutive positive squares.
2

%I #5 Apr 18 2019 16:51:48

%S 1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1

%N Number of partitions of n^2 into consecutive positive squares.

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%F a(n) = [x^(n^2)] Sum_{i>=1} Sum_{j>=i} Product_{k=i..j} x^(k^2).

%F a(n) = A296338(A000290(n)).

%F a(n) >= 2 for n in A097812.

%e 29^2 = 20^2 + 21^2, so a(29) = 2.

%Y Cf. A000290, A030273, A034705, A037444, A097812, A151557, A296338.

%K nonn

%O 1,5

%A _Ilya Gutkovskiy_, Apr 18 2019