A361695 Number of ways of writing n^2 as a sum of seven squares.

1, 14, 574, 3542, 18494, 43414, 145222, 235998, 591934, 860846, 1779974, 2256422, 4678982, 5195750, 9675918, 10983742, 18942014, 19873966, 35294686, 34670454, 57349894, 59707494, 92513302, 90116222, 149759302, 135668414, 213025750, 209185718, 311753358, 287144326, 450333422

Offset: 0

Author

Alois P. Heinz, Mar 22 2023

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000
• Index entries for sequences related to sums of squares

Crossrefs

Column k=7 of A302996.

Cf. A008451, A065461.

Programs

Maple

a:= n-> coeff((sum(x^(j^2), j=-n..n))^7, x, n^2):
seq(a(n), n=0..30);
# second Maple program:
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, 7):
seq(a(n), n=0..30);

Mathematica

SquaresR[7, Range[0, 30]^2] (* Paolo Xausa, Aug 21 2025 *)

Formula

a(n) = [x^(n^2)] (Sum_{j=-n..n} x^(j^2))^7.

a(n) = A008451(n^2).

a(n) = A302996(n,7).