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A014626 Number of intersection points of diagonals of an n-gon in general position, plus number of vertices. 4
0, 1, 2, 3, 5, 10, 21, 42, 78, 135, 220, 341, 507, 728, 1015, 1380, 1836, 2397, 3078, 3895, 4865, 6006, 7337, 8878, 10650, 12675, 14976, 17577, 20503, 23780, 27435, 31496, 35992, 40953, 46410, 52395, 58941, 66082, 73853, 82290, 91430, 101311 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = (n^4 - 6*n^3 + 11*n^2 + 18*n)/24.

From Paul Barry, Sep 23 2004: (Start)

Binomial transform of (0, 1, 0, 0, 1, 0, 0, 0, ...), or g.f. x+x^4.

G.f.: x*(1-3*x+3*x^2)/(1-x)^5;

a(n) = C(n,1) + C(n,4). (End)

E.g.f.: x*(24 + x^3)*exp(x)/24. - G. C. Greubel, Nov 08 2018

MATHEMATICA

Table[(n^4 -6*n^3 +11*n^2 +18*n)/24, {n, 0, 50}] (* G. C. Greubel, Nov 08 2018 *)

PROG

(MAGMA) [(n^4-6*n^3+11*n^2-6*n)/24 +n: n in [0..50]]; // Vincenzo Librandi, Aug 21 2011

(PARI) vector(50, n, n--; (n^4 -6*n^3 +11*n^2 +18*n)/24) \\ G. C. Greubel, Nov 08 2018

CROSSREFS

Sequence in context: A023170 A125312 A300550 * A132418 A024494 A131708

Adjacent sequences:  A014623 A014624 A014625 * A014627 A014628 A014629

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

Corrected and extended by Erich Friedman

STATUS

approved

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Last modified August 6 15:44 EDT 2020. Contains 336254 sequences. (Running on oeis4.)