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

%I A341426 #9 Feb 11 2021 21:45:00
%S A341426 1,71,491,2522,9263,27723,71480,163908,345657,679802,1252185,2203724,
%T A341426 3715206,6041979,9510283,14591324,21788606,31894205,45741815,64467383,
%U A341426 89363919,122254946,164721244,219526449,289133792,377013829,486522424,622759365
%N A341426 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n^2.
%H A341426 Alois P. Heinz, <a href="/A341426/b341426.txt">Table of n, a(n) for n = 3..1000</a>
%H A341426 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341426 a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^7 / (128 * (1 - x)).
%p A341426 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
%p A341426       add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
%p A341426     end:
%p A341426 a:= n-> b(n^2, 7):
%p A341426 seq(a(n), n=3..30);  # _Alois P. Heinz_, Feb 11 2021
%t A341426 Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^7/(128 (1 - x)), {x, 0, n^2}], {n, 3, 30}]
%Y A341426 Cf. A000122, A001182, A055406, A055413, A253663, A302995, A340906, A341396, A341402, A341423, A341424, A341425, A341427, A341428, A341429.
%K A341426 nonn
%O A341426 3,2
%A A341426 _Ilya Gutkovskiy_, Feb 11 2021