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

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Index entries for sequences related to sums of squares

Formula

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

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

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

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);

Crossrefs

Column k=7 of A302996.

Cf. A008451, A065461.

Sequence in context: A217582 A002010 A166185 * A349766 A269478 A269645

Adjacent sequences: A361692 A361693 A361694 * A361696 A361697 A361698

Keyword

nonn

Author

Alois P. Heinz, Mar 22 2023

Status

approved