A101418 Floor of the area of a lens constructed using circular arcs of radius n.

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

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Jan 16 2005

Keywords

• nonn

Examples

			a(2) = 4 because a lens given by the intersection of two circles of radius two has an area of approximately 4.91347...
		

Links

• Eric Weisstein's World of Mathematics, Lens

Crossrefs

Cf. A093731.

Programs

Mathematica

Table[Floor[(4*Pi - 3*Sqrt[3])/6*r^2], {r, 1, 60}]

PARI

a(n)=(4*Pi-sqrt(27))*n^2\6 \\ Charles R Greathouse IV, Nov 27 2016

Formula

a(n) = floor((4*Pi - 3*sqrt(3))/6*n^2).