A349609 Number of solutions to x^2 + y^2 <= n^2, where x, y are positive odd integers.

0, 0, 1, 1, 3, 4, 8, 8, 13, 15, 20, 22, 28, 31, 39, 43, 52, 54, 64, 69, 79, 83, 96, 102, 112, 121, 135, 140, 154, 162, 179, 185, 203, 212, 228, 238, 255, 265, 281, 296, 316, 326, 349, 359, 382, 394, 416, 429, 451, 469, 494, 508, 532, 547, 573, 587

Offset

0,5

Links

Table of n, a(n) for n=0..55.

Index entries for sequences related to sums of squares

Formula

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

a(n) = Sum_{k=0..n^2} A290081(k).

a(n) = A053415(n) / 4.

Example

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

Mathematica

Table[SeriesCoefficient[EllipticTheta[2, 0, x^4]^2/(4 (1 - x)), {x, 0, n^2}], {n, 0, 55}]

Crossrefs

Cf. A000328, A000603, A001182, A008442, A053415, A290081, A349610, A349611.

Sequence in context: A197138 A065309 A097689 * A258326 A308769 A002246

Adjacent sequences: A349606 A349607 A349608 * A349610 A349611 A349612

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2021

Status

approved