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A368243
Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = n^2.
4
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, 0, 0, 96562, 172371, 0, 0, 1192142, 2252342, 0, 0, 13869696, 25741462, 0, 0, 177056022, 334176492, 0, 0, 2207693292, 4182801839, 0, 0, 28966597122, 55125154468
OFFSET
0,9
FORMULA
a(n) = [x^(n^2)] Product_{k=1..n} (x^(k^2) + 1/x^(k^2)).
MAPLE
b:= proc(n, i) option remember; (m-> `if`(n>m, 0, `if`(n=m, 1,
b(abs(n-i^2), i-1) +b(n+i^2, i-1))))((1+(3+2*i)*i)*i/6)
end:
a:= n-> `if`(irem(n, 4)>1, 0, b(n^2, n)):
seq(a(n), n=0..49); # Alois P. Heinz, Jan 22 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 22 2024
STATUS
approved