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A341425 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n^2.

%I A341425 #9 Feb 11 2021 20:14:32
%S A341425 7,48,331,1269,3698,9382,20927,42683,79844,142173,238810,387615,
%T A341425 603589,915324,1345294,1939221,2729723,3783313,5138567,6895632,
%U A341425 9108626,11909496,15362753,19642539,24832744,31179476,38757032,47877886,58647957,71447776,86391220
%N A341425 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n^2.
%H A341425 Alois P. Heinz, <a href="/A341425/b341425.txt">Table of n, a(n) for n = 3..1000</a>
%H A341425 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341425 a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^6 / (64 * (1 - x)).
%p A341425 b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
%p A341425       add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
%p A341425     end:
%p A341425 a:= n-> b(n^2, 6):
%p A341425 seq(a(n), n=3..33);  # _Alois P. Heinz_, Feb 11 2021
%t A341425 Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^6/(64 (1 - x)), {x, 0, n^2}], {n, 3, 33}]
%Y A341425 Cf. A000122, A001182, A055405, A055412, A175361, A253663, A302995, A340905, A341401, A341423, A341424, A341426, A341427, A341428, A341429.
%K A341425 nonn
%O A341425 3,1
%A A341425 _Ilya Gutkovskiy_, Feb 11 2021