A101418 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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}]