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A360792
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Integer portion of area of inscribed circle in a regular polygon having n sides of unit length.
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0
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0, 0, 1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 17, 19, 22, 25, 28, 31, 34, 37, 41, 45, 49, 53, 57, 61, 66, 71, 75, 80, 86, 91, 96, 102, 108, 114, 120, 126, 133, 139, 146, 153, 160, 167, 175, 182, 190, 198, 206, 214, 223, 231, 240, 249, 258, 267, 276, 285, 295, 305
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OFFSET
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3,4
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LINKS
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FORMULA
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a(n) = floor((Pi/4)*(cot(Pi/n)^2)).
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EXAMPLE
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For n = 5, the circle inscribed in a regular pentagon with sides of unit length has area (Pi/4)*cot(Pi/5)^2 = 1.4878796365..., so a(5) = floor(1.4878796365...) = 1.
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MAPLE
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a:= n-> floor(Pi/(2*tan(Pi/n))^2):
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MATHEMATICA
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a[n_] := Floor[(Pi/4)*Cot[Pi/n]^2]; Array[a, 60, 3] (* Amiram Eldar, Feb 24 2023 *)
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PROG
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(PARI) a(n) = floor((Pi/4)/tan(Pi/n)^2) \\ Andrew Howroyd, Feb 20 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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