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A341428 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n^2.

%I A341428 #9 Feb 12 2021 09:51:49
%S A341428 1,46,760,7751,43910,186098,652710,1943742,5178030,12411211,27773308,
%T A341428 57798904,114152429,214399664,387571706,673189698,1135916808,
%U A341428 1857320784,2966816950,4623984661,7066527283,10577150039,15589368584,22580091614,32256768126
%N A341428 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n^2.
%H A341428 Alois P. Heinz, <a href="/A341428/b341428.txt">Table of n, a(n) for n = 3..1000</a>
%H A341428 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341428 a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^9 / (512 * (1 - x)).
%p A341428 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
%p A341428       add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
%p A341428     end:
%p A341428 a:= n-> b(n^2, 9):
%p A341428 seq(a(n), n=3..27);  # _Alois P. Heinz_, Feb 11 2021
%t A341428 Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^9/(512 (1 - x)), {x, 0, n^2}], {n, 3, 27}]
%Y A341428 Cf. A000122, A001182, A055408, A055415, A253663, A302995, A340946, A341398, A341404, A341423, A341424, A341425, A341426, A341427, A341429.
%K A341428 nonn
%O A341428 3,2
%A A341428 _Ilya Gutkovskiy_, Feb 11 2021