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A101418
Floor of the area of a lens constructed using circular arcs of radius n.
0
1, 4, 11, 19, 30, 44, 60, 78, 99, 122, 148, 176, 207, 240, 276, 314, 354, 397, 443, 491, 541, 594, 649, 707, 767, 830, 895, 963, 1033, 1105, 1180, 1257, 1337, 1419, 1504, 1591, 1681, 1773, 1868, 1965, 2064, 2166, 2271, 2378, 2487, 2599, 2713, 2830, 2949
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Lens
FORMULA
a(n) = floor((4*Pi - 3*sqrt(3))/6*n^2).
EXAMPLE
a(2) = 4 because a lens given by the intersection of two circles of radius two has an area of approximately 4.91347...
MATHEMATICA
Table[Floor[(4*Pi - 3*Sqrt[3])/6*r^2], {r, 1, 60}]
PROG
(PARI) a(n)=(4*Pi-sqrt(27))*n^2\6 \\ Charles R Greathouse IV, Nov 27 2016
CROSSREFS
Cf. A093731.
Sequence in context: A162996 A348913 A037262 * A213395 A185873 A009874
KEYWORD
nonn
AUTHOR
Joseph Biberstine (jrbibers(AT)indiana.edu), Jan 16 2005
STATUS
approved