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%I #25 Jan 25 2024 08:03:10
%S 1,1,0,0,0,0,0,0,2,3,0,0,5,15,0,0,127,184,0,0,819,1382,0,0,9441,18176,
%T 0,0,96562,172371,0,0,1192142,2252342,0,0,13869696,25741462,0,0,
%U 177056022,334176492,0,0,2207693292,4182801839,0,0,28966597122,55125154468
%N Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = n^2.
%F a(n) = [x^(n^2)] Product_{k=1..n} (x^(k^2) + 1/x^(k^2)).
%p b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
%p b(abs(n-i^2), i-1) +b(n+i^2, i-1))))((1+(3+2*i)*i)*i/6)
%p end:
%p a:= n-> `if`(irem(n, 4)>1, 0, b(n^2, n)):
%p seq(a(n), n=0..49); # _Alois P. Heinz_, Jan 22 2024
%Y Cf. A063890, A158092, A348165.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Jan 22 2024
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