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

%I A341427 #8 Feb 12 2021 09:20:06
%S A341427 1,45,767,4452,21178,74452,224313,586035,1387583,2999430,6102276,
%T A341427 11656386,21282969,37159993,62687904,102213426,162345824,251064745,
%U A341427 379922217,562833191,819351646,1171991382,1651937498,2294227971,3147090871,4263499419
%N A341427 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_8)^2 <= n^2.
%H A341427 Alois P. Heinz, <a href="/A341427/b341427.txt">Table of n, a(n) for n = 3..1000</a>
%H A341427 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341427 a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^8 / (256 * (1 - x)).
%p A341427 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
%p A341427       add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
%p A341427     end:
%p A341427 a:= n-> b(n^2, 8):
%p A341427 seq(a(n), n=3..28);  # _Alois P. Heinz_, Feb 11 2021
%t A341427 Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^8/(256 (1 - x)), {x, 0, n^2}], {n, 3, 28}]
%Y A341427 Cf. A000122, A001182, A055407, A055414, A253663, A302995, A340915, A341397, A341403, A341423, A341424, A341425, A341426, A341428, A341429.
%K A341427 nonn
%O A341427 3,2
%A A341427 _Ilya Gutkovskiy_, Feb 11 2021