

A014628


Number of segments (and sides) created by diagonals of an ngon in general position.


1



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
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OFFSET

3,1


COMMENTS

There is a connection to A014626: number of intersection points of diagonals of ngon, plus number of vertices, b(n) = n*(n+1)*(n^27*n+18)/24 and A006522: number of regions created by sides and diagonals of ngon, c(n) = (n1)*(n2)*(n^23*n+12)/24. These are related by the Eulerformula: b(n) + c(n)  a(n) = 1.  Georg Wengler, Mar 31 2005


LINKS



FORMULA

a(n) = (n^46*n^3+17*n^224*n)/12 + n; or equally n*(n1)*(n^25*n+12)/12.
G.f.: x^3*(37*x+10*x^25*x^3+x^4)/(1x)^5.  Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009


MATHEMATICA

Table[Binomial[n, 2]+2Binomial[n, 4], {n, 3, 50}] (* Harvey P. Dale, Oct 03 2020 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

G.f. proposed by Maksym Voznyy, checked and corrected by R. J. Mathar, Sep 16 2009


STATUS

approved



