A276478 Number of points in square lattice in and on the boundary of the area encompassed by two arcs of radius n and centers at (0,0) and (n,0).
1, 2, 5, 12, 19, 34, 45, 56, 77, 98, 127, 148, 169, 206, 239, 280, 311, 350, 393, 440, 495, 534, 593, 644, 697, 770, 827, 896, 957, 1026, 1105, 1168, 1255, 1330, 1417, 1512, 1579, 1678, 1759, 1868, 1969, 2050, 2159, 2256, 2377, 2490, 2585, 2704, 2811, 2942
Offset: 0
Keywords
Links
- Wikipedia, Vesica piscis
Programs
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PARI
a(n) = my(m = floor(n*sqrt(3)/2)); 1 - 3*n - 2*(n-1)*m + 4*sum(k=0, m, sqrtint(n^2-k^2)); \\ Michel Marcus, Mar 07 2021
Formula
a(n) = 1 - 3*n - 2*(n-1)*m(n) + 4 * Sum_{k=0..m(n)} floor(sqrt(n^2-k^2)) where m(n) = floor(n*sqrt(3)/2). - Franz Vrabec, Oct 02 2016
a(n)/n^2 tends to A093731 as n tends to infinity. - Rémy Sigrist, Mar 07 2021
Extensions
More terms from Franz Vrabec, Oct 02 2016