A341426 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n^2.

1, 71, 491, 2522, 9263, 27723, 71480, 163908, 345657, 679802, 1252185, 2203724, 3715206, 6041979, 9510283, 14591324, 21788606, 31894205, 45741815, 64467383, 89363919, 122254946, 164721244, 219526449, 289133792, 377013829, 486522424, 622759365

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, A055406, A055413, A253663, A302995, A340906, A341396, A341402, A341423, A341424, A341425, A341427, A341428, 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, 7):
seq(a(n), n=3..30);  # Alois P. Heinz, Feb 11 2021

Mathematica

Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^7/(128 (1 - x)), {x, 0, n^2}], {n, 3, 30}]

Formula

a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^7 / (128 * (1 - x)).