%I #9 Feb 11 2021 19:26:18

%S 6,51,177,547,1348,2958,5574,10084,16974,27450,41970,62671,90216,

%T 128082,175867,238018,316373,414998,534094,682144,859705,1075165,

%U 1326551,1627896,1976582,2390057,2862607,3411273,4039483,4760419,5571729,6500650,7541560,8722096

%N Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_5)^2 <= n^2.

%H Alois P. Heinz, <a href="/A341424/b341424.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)^5 / (32 * (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, 5):

%p seq(a(n), n=3..36); # _Alois P. Heinz_, Feb 11 2021

%t Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^5/(32 (1 - x)), {x, 0, n^2}], {n, 3, 36}]

%Y Cf. A000122, A001182, A055404, A055411, A175360, A253663, A302995, A340481, A341400, A341423, A341425, A341426, A341427, A341428, A341429.

%K nonn

%O 3,1

%A _Ilya Gutkovskiy_, Feb 11 2021