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A014626 Number of intersection points of diagonals of an n-gon in general position, plus number of vertices.

%I A014626 #34 Sep 08 2022 08:44:39
%S A014626 0,1,2,3,5,10,21,42,78,135,220,341,507,728,1015,1380,1836,2397,3078,
%T A014626 3895,4865,6006,7337,8878,10650,12675,14976,17577,20503,23780,27435,
%U A014626 31496,35992,40953,46410,52395,58941,66082,73853,82290,91430,101311
%N A014626 Number of intersection points of diagonals of an n-gon in general position, plus number of vertices.
%C A014626 If Y is a 3-subset of an n-set X then, for n >= 4, a(n-3) is the number of 4-subsets of X which have neither one element nor two elements in common with Y; a(n-3) is then also the number of (n-4)-subsets of X which have neither one element nor two elements in common with Y. - _Milan Janjic_, Dec 28 2007
%H A014626 Vincenzo Librandi, <a href="/A014626/b014626.txt">Table of n, a(n) for n = 0..10000</a>
%H A014626 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A014626 a(n) = (n^4 - 6*n^3 + 11*n^2 + 18*n)/24.
%F A014626 From _Paul Barry_, Sep 23 2004: (Start)
%F A014626 Binomial transform of (0, 1, 0, 0, 1, 0, 0, 0, ...), or g.f. x+x^4.
%F A014626 G.f.: x*(1-3*x+3*x^2)/(1-x)^5;
%F A014626 a(n) = C(n,1) + C(n,4). (End)
%F A014626 E.g.f.: x*(24 + x^3)*exp(x)/24. - _G. C. Greubel_, Nov 08 2018
%t A014626 Table[(n^4 -6*n^3 +11*n^2 +18*n)/24, {n, 0, 50}] (* _G. C. Greubel_, Nov 08 2018 *)
%o A014626 (Magma) [(n^4-6*n^3+11*n^2-6*n)/24 +n: n in [0..50]]; // _Vincenzo Librandi_, Aug 21 2011
%o A014626 (PARI) vector(50, n, n--; (n^4 -6*n^3 +11*n^2 +18*n)/24) \\ _G. C. Greubel_, Nov 08 2018
%K A014626 nonn,easy
%O A014626 0,3
%A A014626 _Mohammad K. Azarian_
%E A014626 Corrected and extended by _Erich Friedman_