A066375 a(n) = 6*binomial(n,4) + 3*binomial(n,3) + 4*binomial(n,2) - n + 2.

1, 4, 14, 40, 97, 206, 394, 694, 1145, 1792, 2686, 3884, 5449, 7450, 9962, 13066, 16849, 21404, 26830, 33232, 40721, 49414, 59434, 70910, 83977, 98776, 115454, 134164, 155065, 178322, 204106, 232594, 263969, 298420, 336142, 377336, 422209, 470974, 523850, 581062

Offset: 1

Author

N. J. A. Sloane, Jan 04 2002

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• M. Azaola and F. Santos, The number of triangulations of the cyclic polytope C(n,n-4), Discrete Comput. Geom., 27 (2002), 29-48.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

Mathematica

Table[6Binomial[n,4]+3Binomial[n,3]+4Binomial[n,2]-n+2,{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,4,14,40,97},40] (* Harvey P. Dale, Feb 05 2017 *)

PARI

a(n) = { 6*binomial(n,4) + 3*binomial(n,3) + 4*binomial(n,2) - n + 2 } \\ Harry J. Smith, Feb 11 2010

Formula

From Colin Barker, Apr 20 2012: (Start)

a(n) = (8 - 14*n + 13*n^2 - 4*n^3 + n^4)/4.

G.f.: x*(1 - x + 4*x^2 + 2*x^4)/(1-x)^5. (End)