OFFSET
1,3
LINKS
Vincenzo Librandi, 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 (2,2,-6,0,6,-2,-2,1).
FORMULA
G.f.: x*(1-x-4*x^5+x^6-2*x^2+4*x^3+2*x^4+2*x^7) / ( (1+x)^3*(1-x)^5 ). - R. J. Mathar, Aug 07 2014
From Colin Barker, May 04 2017: (Start)
a(n) = (n^4 - 8*n^3 + 52*n^2 - 112*n + 128) / 64 for n even.
a(n) = (n^4 - 8*n^3 + 54*n^2 - 120*n + 137) / 64 for n odd.
a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n>8.
(End)
MAPLE
A066456 := proc(n) local m; if n mod 2 = 0 then m := n/2; 6*binomial(m, 4)+3*binomial(m, 3)+4*binomial(m, 2)-m+2; else m := (n+1)/2; 6*binomial(m, 4)+5*binomial(m, 2)-4*m+5; fi; end;
MATHEMATICA
CoefficientList[Series[-(1 - x - 4 x^5 + x^6 - 2 x^2 + 4 x^3 + 2 x^4 + 2 x^7)/((1 + x)^3 (x - 1)^5), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 07 2014 *)
PROG
(PARI) Vec(x*(1 - x - 2*x^2 + 4*x^3 + 2*x^4 - 4*x^5 + x^6 + 2*x^7) / ((1 - x)^5*(1 + x)^3) + O(x^60)) \\ Colin Barker, May 04 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 04 2002
STATUS
approved