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A341426 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n^2. 7
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 (list; graph; refs; listen; history; text; internal format)
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)^7 / (128 * (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, 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}]

CROSSREFS

Cf. A000122, A001182, A055406, A055413, A253663, A302995, A340906, A341396, A341402, A341423, A341424, A341425, A341427, A341428, A341429.

Sequence in context: A057541 A268889 A142432 * A250982 A250975 A209960

Adjacent sequences:  A341423 A341424 A341425 * A341427 A341428 A341429

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 11 2021

STATUS

approved

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Last modified September 22 18:56 EDT 2021. Contains 347608 sequences. (Running on oeis4.)