A368243 Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = n^2.

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

Links

Table of n, a(n) for n=0..49.

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

Cf. A063890, A158092, A348165.

Sequence in context: A213714 A242011 A353612 * A259657 A332672 A184362

Adjacent sequences: A368240 A368241 A368242 * A368244 A368245 A368246

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 22 2024

Status

approved