A292496 Number of solutions to +- 1^2 +- 3^2 +- 5^2 +- 7^2 +- ... +- (4*n-1)^2 = 0.

1, 0, 0, 0, 2, 0, 12, 0, 40, 10, 516, 124, 5020, 1828, 48570, 32806, 527890, 444480, 6137942, 6482314, 70573856, 93276044, 853480374, 1300190254, 10660384742, 18371629260, 134129890382, 259804151324, 1728886287134, 3667061002286, 22672130669968

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..100

Formula

Constant term in the expansion of Product_{k=1..2*n} (x^(2*k-1)^2+1/x^(2*k-1)^2).

Example

For n=4 the 2 solutions are +1^2-3^2-5^2+7^2-9^2+11^2+13^2-15^2 = 0 and -1^2+3^2+5^2-7^2+9^2-11^2-13^2+15^2 = 0.

Prog

(PARI) a(n) = polcoeff(prod(k=1, 2*n, x^(2*k-1)^2+1/x^(2*k-1)^2), 0); \\ Michel Marcus, Sep 18 2017

Crossrefs

Cf. A158092, A292476, A292497.

Sequence in context: A293260 A095238 A167345 * A285480 A156431 A067994

Adjacent sequences: A292493 A292494 A292495 * A292497 A292498 A292499

Keyword

nonn

Author

Seiichi Manyama, Sep 17 2017

Status

approved