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Search: id:A064313
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| A064313 |
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Integer part of area of a regular polygon with n sides each of length 1. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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2,5
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COMMENT
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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).
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LINKS
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Harry J. Smith, Table of n, a(n) for n=2,...,1000
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FORMULA
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a(n) = floor[n/(4*tan(pi/n))].
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EXAMPLE
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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.
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MAPLE
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A064313 := proc(n) RETURN(floor((n/4)*cot(Pi/n))) end:
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MATHEMATICA
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Table[ Floor[(n/4)*Cot[Pi/n]], {n, 2, 75} ]
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PROGRAM
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(PARI) { for (n=2, 1000, if (n>2, a=n\(4*tan(Pi/n)), a=0); write("b064313.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 11 2009]
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CROSSREFS
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Sequence in context: A022825 A160138 A062413 this_sequence A011865 A085680 A047872
Adjacent sequences: A064310 A064311 A064312 this_sequence A064314 A064315 A064316
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Oct 15 2001
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