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Search: id:A014628
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| A014628 |
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Number of segments (and sides) created by diagonals of n-gon. |
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+0
2
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| 3, 8, 20, 45, 91, 168, 288, 465, 715, 1056, 1508, 2093, 2835, 3760, 4896, 6273, 7923, 9880, 12180, 14861, 17963, 21528, 25600, 30225, 35451, 41328, 47908, 55245, 63395, 72416, 82368, 93313, 105315, 118440, 132756, 148333, 165243, 183560
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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There is a connection to A014626: number of intersection points of diagonals of n-gon, plus number of vertices, b(n) = n*(n+1)*(n^2-7*n+18)/24 and A006522: number of regions created by sides and diagonals of n-gon, c(n) = (n-1)*(n-2)*(n^2-3*n+12)/24. These are related by the Euler-formula: b(n) + c(n) - a(n) = 1. - Georg Wengler (georg.wengler(AT)gmx.at), Mar 31 2005
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FORMULA
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a(n) = (n^4-6*n^3+17*n^2-24*n)/12 + n; or equally n*(n-1)*(n^2-5*n+12)/12.
G.f.: x*(3-7*x+10*x^2-5*x^3+x^4)/(1-x)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
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CROSSREFS
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Cf. A014626, A006522.
Sequence in context: A096585 A057765 A134393 this_sequence A034504 A140481 A027928
Adjacent sequences: A014625 A014626 A014627 this_sequence A014629 A014630 A014631
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
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G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
Corrected the first offset. - Mohammad K. Azarian (azarian(AT)evansville.edu), Nov 19 2008
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