A349610 Number of solutions to x^2 + y^2 + z^2 <= n^2, where x, y, z are positive odd integers.

0, 0, 1, 1, 4, 7, 17, 20, 35, 45, 69, 84, 114, 136, 184, 217, 272, 314, 389, 443, 528, 597, 702, 784, 901, 1018, 1166, 1268, 1442, 1589, 1791, 1926, 2157, 2332, 2584, 2800, 3058, 3293, 3596, 3872, 4194, 4485, 4878, 5184, 5590, 5950, 6388, 6761, 7232

Offset

0,5

Links

David A. Corneth, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

Formula

a(n) = [x^(n^2)] theta_2(x^4)^3 / (8 * (1 - x)).

a(n) = Sum_{k=0..n^2} A008437(k).

a(n) = A053596(n) / 8.

Example

a(4) = 4 since there are solutions (1,1,1), (3,1,1), (1,3,1), (1,1,3).

Mathematica

Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^3/(8 (1 - x)), {x, 0, n^2}], {n, 0, 48}]

Crossrefs

Cf. A000604, A000605, A008437, A053596, A085121, A253663, A349609, A349611.

Sequence in context: A367744 A363642 A124402 * A216552 A034736 A236564

Adjacent sequences: A349607 A349608 A349609 * A349611 A349612 A349613

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2021

Status

approved