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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 15 2001
STATUS
approved