A117662 n*(n-1)*(n-2)*(n+3)/12.

0, 0, 0, 3, 14, 40, 90, 175, 308, 504, 780, 1155, 1650, 2288, 3094, 4095, 5320, 6800, 8568, 10659, 13110, 15960, 19250, 23023, 27324, 32200, 37700, 43875, 50778, 58464, 66990, 76415, 86800, 98208, 110704, 124355, 139230, 155400, 172938, 191919

Offset

0,4

Comments

Essentially the same as A050297 and A005701.

Also, the number of external intersections of the diagonals of a general n-gon = (A176145) - (A000332). - Michel Lagneau, Apr 21 2010

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

G.f.: x^3*(3-x)/(1-x)^5. [Colin Barker, Jan 31 2012]

Maple

seq(n*(n-1)*(n-2)*(n+3)/12, n=0..40); # Wesley Ivan Hurt, Oct 10 2013

Mathematica

Table[n(n-1)(n-2)(n+3)/12, {n, 0, 100}] (* Wesley Ivan Hurt, Sep 26 2013 *)
CoefficientList[Series[x^3 (3 - x)/(1 - x)^5, {x, 0, 80}], x] (* Vincenzo Librandi, Oct 10 2013 *)

Prog

(Magma) [n*(n-1)*(n-2)*(n+3)/12: n in [0..50]]; // Vincenzo Librandi, Oct 10 2013

Crossrefs

Sequence in context: A034130 A005701 A050297 * A196236 A213482 A296267

Adjacent sequences: A117659 A117660 A117661 * A117663 A117664 A117665

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 11 2006

Extensions

Edited by N. J. A. Sloane, Apr 23 2006

Status

approved