A341427 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_8)^2 <= n^2.

1, 45, 767, 4452, 21178, 74452, 224313, 586035, 1387583, 2999430, 6102276, 11656386, 21282969, 37159993, 62687904, 102213426, 162345824, 251064745, 379922217, 562833191, 819351646, 1171991382, 1651937498, 2294227971, 3147090871, 4263499419

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Index entries for sequences related to sums of squares

Formula

a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^8 / (256 * (1 - x)).

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, 8):
seq(a(n), n=3..28);  # Alois P. Heinz, Feb 11 2021

Mathematica

Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^8/(256 (1 - x)), {x, 0, n^2}], {n, 3, 28}]

Crossrefs

Cf. A000122, A001182, A055407, A055414, A253663, A302995, A340915, A341397, A341403, A341423, A341424, A341425, A341426, A341428, A341429.

Sequence in context: A099632 A264138 A293971 * A024379 A134290 A359933

Adjacent sequences: A341424 A341425 A341426 * A341428 A341429 A341430

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 11 2021

Status

approved