A298330 Number of ordered ways of writing n^2 as a sum of n squares of positive integers.

1, 1, 0, 3, 1, 5, 141, 742, 6120, 43888, 300232, 3074478, 28901797, 290411147, 3175037698, 34951274416, 399750066121, 4814421349467, 59532792202344, 768079420764884, 10247011240209066, 140144002390928732, 1978092111496441512, 28633995987157024399

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..100

Index entries for sequences related to sums of squares

Formula

a(n) = [x^(n^2)] (Sum_{k>=1} x^(k^2))^n.

Example

a(3) = 3 because we have [4, 4, 1], [4, 1, 4] and [1, 4, 4].

Maple

G:= (JacobiTheta3(0, x)-1)/2:
f:= proc(n) local S; S:= series(G^n, x, n^2+1); coeff(S, x, n^2) end proc:
map(f, [$0..25]); # Robert Israel, Dec 16 2024

Mathematica

Table[SeriesCoefficient[(-1 + EllipticTheta[3, 0, x])^n/2^n, {x, 0, n^2}], {n, 0, 23}]

Crossrefs

Cf. A037444, A066535, A232173, A287617, A298329.

Sequence in context: A370333 A370433 A174424 * A210621 A226771 A096614

Adjacent sequences: A298327 A298328 A298329 * A298331 A298332 A298333

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Jan 17 2018

Status

approved