A237526 -id:A237526 - cp's OEIS frontend

A372511 Number of solutions to x^2 + y^2 <= n, where x, y are positive odd integers.

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17

Offset: 0

Ilya Gutkovskiy, May 04 2024

nonn

Index entries for sequences related to sums of squares

Cf. A008442, A057655, A224212, A237526, A290081, A349609, A372512.

nmax = 85; CoefficientList[Series[EllipticTheta[2, 0, x^4]^2/(4 (1 - x)), {x, 0, nmax}], x]

A374532 Number of complete unit squares that fit inside a circle of radius sqrt(n^2+1) centered at the origin of a square lattice.

Original entry on oeis.org

0, 4, 12, 24, 40, 68, 96, 132, 180, 224, 284, 340, 408, 492, 564, 656, 740, 848, 960, 1060, 1184, 1304, 1444, 1576, 1704, 1868, 2024, 2196, 2356, 2520, 2716, 2892, 3104, 3292, 3504, 3720, 3916, 4160, 4384, 4628, 4872, 5108, 5372, 5640, 5916, 6188, 6456, 6764, 7036

Offset: 0

Thomas Otten, Jul 10 2024

nonn

Thomas Otten, Illustration of initial terms.

Cf. A119677 (case for radius of n), A237526.

Cf. A046092, A000328 (quadrant width 1 cell).

a(n) = my(s=n^2+1); 4*sum(k=1, sqrtint(s), sqrtint(s-k^2)) \\ Andrew Howroyd, Jul 11 2024

def A374532(n): return sum(isqrt(k*((n<<1)-k)+1) for k in range(n))<<2 # Chai Wah Wu, Jul 18 2024

a(n) = 4*A237526(n^2 + 1).

cp's OEIS Frontend

A372511 Number of solutions to x^2 + y^2 <= n, where x, y are positive odd integers.

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