A341423 - OEIS

%I #9 Feb 11 2021 18:44:21

%S 1,5,32,94,219,437,804,1362,2177,3271,4768,6708,9227,12381,16254,

%T 20954,26707,33461,41480,50884,61703,74183,88606,104862,123481,144241,

%U 167604,193648,222799,254731,290244,329512,372545,419661,470822,526646,587481,653505

%N Number of positive solutions to (x_1)^2 + (x_2)^2 + (x_3)^2 + (x_4)^2 <= n^2.

%H Alois P. Heinz, <a href="/A341423/b341423.txt">Table of n, a(n) for n = 2..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)^4 / (16 * (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, 4):

%p seq(a(n), n=2..39);  # _Alois P. Heinz_, Feb 11 2021

%t Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^4/(16 (1 - x)), {x, 0, n^2}], {n, 2, 39}]

%Y Cf. A000122, A001182, A046895, A055403, A055410, A063730, A224213, A253663, A302995, A341424, A341425, A341426, A341427, A341428, A341429.

%K nonn

%O 2,2

%A _Ilya Gutkovskiy_, Feb 11 2021