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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.
1
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
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
KEYWORD
nonn
AUTHOR
Thomas Otten, Jul 10 2024
STATUS
approved