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A341429 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n^2.

%I A341429 #8 Feb 12 2021 10:42:10
%S A341429 56,1108,12098,84624,439371,1785368,6078048,18139393,48586117,
%T A341429 118929400,270250734,578320470,1169522013,2261784392,4193751331,
%U A341429 7509793133,13008356489,21921125415,35951569269,57666975238,90464266824,139295784464,210514511189,313228848537
%N A341429 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n^2.
%H A341429 Alois P. Heinz, <a href="/A341429/b341429.txt">Table of n, a(n) for n = 4..1000</a>
%H A341429 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341429 a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^10 / (1024 * (1 - x)).
%p A341429 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
%p A341429       add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
%p A341429     end:
%p A341429 a:= n-> b(n^2, 10):
%p A341429 seq(a(n), n=4..27);  # _Alois P. Heinz_, Feb 11 2021
%t A341429 Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^10/(1024 (1 - x)), {x, 0, n^2}], {n, 4, 27}]
%Y A341429 Cf. A000122, A001182, A055409, A055416, A253663, A302995, A340947, A341399, A341405, A341423, A341424, A341425, A341426, A341427, A341428.
%K A341429 nonn
%O A341429 4,1
%A A341429 _Ilya Gutkovskiy_, Feb 11 2021