Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #9 Feb 11 2021 21:45:00
%S 1,71,491,2522,9263,27723,71480,163908,345657,679802,1252185,2203724,
%T 3715206,6041979,9510283,14591324,21788606,31894205,45741815,64467383,
%U 89363919,122254946,164721244,219526449,289133792,377013829,486522424,622759365
%N Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n^2.
%H Alois P. Heinz, <a href="/A341426/b341426.txt">Table of n, a(n) for n = 3..1000</a>
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^7 / (128 * (1 - x)).
%p b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
%p add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
%p end:
%p a:= n-> b(n^2, 7):
%p seq(a(n), n=3..30); # _Alois P. Heinz_, Feb 11 2021
%t Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^7/(128 (1 - x)), {x, 0, n^2}], {n, 3, 30}]
%Y Cf. A000122, A001182, A055406, A055413, A253663, A302995, A340906, A341396, A341402, A341423, A341424, A341425, A341427, A341428, A341429.
%K nonn
%O 3,2
%A _Ilya Gutkovskiy_, Feb 11 2021