login
Number of solutions to x^2 + y^2 + z^2 + w^2 <= n, where x, y, z, w are positive odd integers.
0

%I #11 May 11 2024 21:51:21

%S 0,0,0,0,1,1,1,1,1,1,1,1,5,5,5,5,5,5,5,5,11,11,11,11,11,11,11,11,19,

%T 19,19,19,19,19,19,19,32,32,32,32,32,32,32,32,44,44,44,44,44,44,44,44,

%U 58,58,58,58,58,58,58,58,82,82,82,82,82,82,82,82,100,100,100,100,100,100,100,100

%N Number of solutions to x^2 + y^2 + z^2 + w^2 <= n, where x, y, z, w are positive odd integers.

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%t nmax = 75; CoefficientList[Series[EllipticTheta[2, 0, x^4]^4/(16 (1 - x)), {x, 0, nmax}], x]

%Y Cf. A008438, A046895, A224213, A349611, A372511, A372512.

%K nonn

%O 0,13

%A _Ilya Gutkovskiy_, May 07 2024