A369730 Number of solutions to +- 1^2 +- 2^2 +- 3^2 +- ... +- n^2 = 1.

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, 31048, 0, 0, 188536, 372710, 0, 0, 2376996, 4197425, 0, 0, 27465147, 53072709, 0, 0, 351329160, 650125358, 0, 0, 4398613111, 8429649875, 0, 0, 57629346805, 108986428106

Offset

0,7

Links

Table of n, a(n) for n=0..50.

Formula

a(n) = [x^1] Product_{k=1..n} (x^(k^2) + 1/x^(k^2)).

Maple

b:= proc(n, i) option remember; `if`(n>i*(i+1)*(2*i+1)/6, 0,
      `if`(i=0, 1, b(n+i^2, i-1)+b(abs(n-i^2), i-1)))
    end:
a:=n-> b(1, n):
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 30 2024

Mathematica

Table[Coefficient[Product[(x^(k^2) + 1/x^(k^2)), {k, 1, n}], x, 1], {n, 0, 48}]

Crossrefs

Cf. A000290, A063866, A158092, A348165, A350403, A369731, A369732.

Sequence in context: A290321 A145430 A143160 * A156387 A370065 A324040

Adjacent sequences: A369727 A369728 A369729 * A369731 A369732 A369733

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2024

Status

approved