A374493 Number of ways of writing n^2 as a sum of 8 squares.

1, 16, 1136, 12112, 74864, 252016, 859952, 1887888, 4793456, 8830096, 17893136, 28366288, 56672048, 77264112, 134040048, 190776112, 306783344, 386279728, 626936816, 752843856, 1179182864, 1429131216, 2014006448, 2368768912, 3628646192, 3937752016, 5485751952

Offset: 0

Author

Seiichi Manyama, Jul 12 2024

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to sums of squares

Crossrefs

Column k=8 of A302996.

Cf. A000143.

Programs

Mathematica

SquaresR[8, Range[0,30]^2] (* Paolo Xausa, Aug 21 2025 *)

PARI

a000143(n) = if(n==0, 1, 16*sumdiv(n, d, (-1)^(n+d)*d^3));
a(n) = a000143(n^2);

Formula

a(n) = [x^(n^2)] (Sum_{j=-n..n} x^(j^2))^8.

a(n) = A000143(n^2).

a(n) is divisible by 16 for n > 0.