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%I #7 Jan 30 2024 16:01:12
%S 0,1,0,0,0,0,2,0,0,5,2,0,0,13,43,0,0,193,274,0,0,1552,3245,0,0,18628,
%T 31048,0,0,188536,372710,0,0,2376996,4197425,0,0,27465147,53072709,0,
%U 0,351329160,650125358,0,0,4398613111,8429649875,0,0,57629346805,108986428106
%N Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = 1.
%F a(n) = [x^1] Product_{k=1..n} (x^(k^2) + 1/x^(k^2)).
%p b:= proc(n, i) option remember; `if`(n>i*(i+1)*(2*i+1)/6, 0,
%p `if`(i=0, 1, b(n+i^2, i-1)+b(abs(n-i^2), i-1)))
%p end:
%p a:=n-> b(1, n):
%p seq(a(n), n=0..50); # _Alois P. Heinz_, Jan 30 2024
%t Table[Coefficient[Product[(x^(k^2) + 1/x^(k^2)), {k, 1, n}], x, 1], {n, 0, 48}]
%Y Cf. A000290, A063866, A158092, A348165, A350403, A369731, A369732.
%K nonn
%O 0,7
%A _Ilya Gutkovskiy_, Jan 30 2024
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