A341428 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n^2.

1, 46, 760, 7751, 43910, 186098, 652710, 1943742, 5178030, 12411211, 27773308, 57798904, 114152429, 214399664, 387571706, 673189698, 1135916808, 1857320784, 2966816950, 4623984661, 7066527283, 10577150039, 15589368584, 22580091614, 32256768126

Offset: 3

Author

Ilya Gutkovskiy, Feb 11 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000122, A001182, A055408, A055415, A253663, A302995, A340946, A341398, A341404, A341423, A341424, A341425, A341426, A341427, A341429.

Programs

Maple

b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
      add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
    end:
a:= n-> b(n^2, 9):
seq(a(n), n=3..27);  # Alois P. Heinz, Feb 11 2021

Mathematica

Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^9/(512 (1 - x)), {x, 0, n^2}], {n, 3, 27}]

Formula

a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^9 / (512 * (1 - x)).