A064313 Integer part of area of a regular polygon with n sides each of length 1.

0, 0, 1, 1, 2, 3, 4, 6, 7, 9, 11, 13, 15, 17, 20, 22, 25, 28, 31, 34, 38, 41, 45, 49, 53, 57, 62, 66, 71, 76, 81, 86, 91, 97, 102, 108, 114, 120, 127, 133, 140, 146, 153, 160, 168, 175, 183, 190, 198, 206, 214, 223, 231, 240, 249, 258, 267, 276, 286, 295, 305, 315

Offset: 2

Author

Henry Bottomley, Oct 15 2001

Keywords

• nonn

Comments

Usually (perhaps always?) floor(n^2/(4*Pi) - Pi/12) for a polygon of circumference n. Note that the area of a circle with circumference C is C^2/(4*Pi).

Examples

			Areas (starting from n=2) are: 0, 0.433... (equilateral triangle), 1 (square), 1.720... (pentagon), 2.598... (hexagon), 3.633... (heptagon), 4.828... (octagon), etc., so sequence starts 0, 0, 1, 1, 2, 3, 4, etc.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A134030.

Programs

Maple

A064313 := proc(n) RETURN(floor((n/4)*cot(Pi/n))) end:

Mathematica

Table[ Floor[(n/4)*Cot[Pi/n]], {n, 2, 75} ]

PARI

{ for (n=2, 1000, if (n>2, a=n\(4*tan(Pi/n)), a=0); write("b064313.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 11 2009

Formula

a(n) = floor(n/(4*tan(Pi/n))).