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.

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

0,2

Links

Table of n, a(n) for n=0..48.

Thomas Otten, Illustration of initial terms.

Formula

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

Prog

(PARI) a(n) = my(s=n^2+1); 4*sum(k=1, sqrtint(s), sqrtint(s-k^2)) \\ Andrew Howroyd, Jul 11 2024
(Python)
def A374532(n): return sum(isqrt(k*((n<<1)-k)+1) for k in range(n))<<2 # Chai Wah Wu, Jul 18 2024

Crossrefs

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

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

Sequence in context: A008216 A008074 A008190 * A008193 A010897 A301048

Adjacent sequences: A374529 A374530 A374531 * A374533 A374534 A374535

Keyword

nonn

Author

Thomas Otten, Jul 10 2024

Status

approved