A341429 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n^2.

56, 1108, 12098, 84624, 439371, 1785368, 6078048, 18139393, 48586117, 118929400, 270250734, 578320470, 1169522013, 2261784392, 4193751331, 7509793133, 13008356489, 21921125415, 35951569269, 57666975238, 90464266824, 139295784464, 210514511189, 313228848537

Offset: 4

Author

Ilya Gutkovskiy, Feb 11 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000122, A001182, A055409, A055416, A253663, A302995, A340947, A341399, A341405, A341423, A341424, A341425, A341426, A341427, A341428.

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, 10):
seq(a(n), n=4..27);  # Alois P. Heinz, Feb 11 2021

Mathematica

Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^10/(1024 (1 - x)), {x, 0, n^2}], {n, 4, 27}]

Formula

a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^10 / (1024 * (1 - x)).