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

1,2

Links

Table of n, a(n) for n=1..49.

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

Adjacent sequences: A101415 A101416 A101417 * A101419 A101420 A101421

Keyword

nonn

Author

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

Status

approved