A361431 Number of ways to write n^2 as an ordered sum of n^2 squares of integers.

1, 2, 24, 34802, 509145568, 142743029326162, 715761543475698773496, 63014651062141097287201438690, 96683719664587866428237173383906926464, 2573179910450886540215919614478751310457090316706, 1184101051443285881265166362742300236491599013268534224381864

Offset: 0

Author

Alois P. Heinz, Mar 11 2023

Keywords

• nonn

Examples

			a(2) = 24: 4 = x^2 + y^2 + z^2 + u^2 has 24 solutions (x,y,z,u): 16 permutations of (+/-1,+/-1,+/-1,+/-1) and 8 permutations of (+/-2,0,0,0).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..40

Crossrefs

Cf. A000290, A066535.

Programs

Maple

b:= proc(n, t) option remember; `if`(n=0, 1, `if`(n<0 or t<1, 0,
      b(n, t-1) +2*add(b(n-j^2, t-1), j=1..isqrt(n))))
    end:
a:= n-> b(n^2$2):
seq(a(n), n=0..10);

Formula

a(n) = [x^(n^2)] (Sum_{j=-oo..oo} x^(j^2))^(n^2).

a(n) = A066535(n^2).