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

2,5

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).

Links

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

Formula

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

Example

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.

Maple

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A134030.

Sequence in context: A022825 A225086 A062413 * A011865 A085680 A253186

Adjacent sequences: A064310 A064311 A064312 * A064314 A064315 A064316

Keyword

nonn

Author

Henry Bottomley, Oct 15 2001

Status

approved