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

Author

Ilya Gutkovskiy, Nov 23 2021

Keywords

• nonn

Examples

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

Links

• Index entries for sequences related to sums of squares

Crossrefs

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

Programs

Mathematica

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

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.