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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).
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
0,2
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
PROG
(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
CROSSREFS
Sequence in context: A356490 A336462 A116728 * A333558 A095306 A356649
KEYWORD
nonn
AUTHOR
Christina Steffan, Sep 05 2016
EXTENSIONS
More terms from Franz Vrabec, Oct 02 2016
STATUS
approved