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A064313
Integer part of area of a regular polygon with n sides each of length 1.
5
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
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 15 2001
STATUS
approved