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%I #15 Jun 15 2018 21:29:28
%S 1,4,14,40,97,206,394,694,1145,1792,2686,3884,5449,7450,9962,13066,
%T 16849,21404,26830,33232,40721,49414,59434,70910,83977,98776,115454,
%U 134164,155065,178322,204106,232594,263969,298420,336142
%N a(n) = 6*binomial(n,4) + 3*binomial(n,3) + 4*binomial(n,2) - n + 2.
%H Harry J. Smith, <a href="/A066375/b066375.txt">Table of n, a(n) for n = 1..1000</a>
%H M. Azaola and F. Santos, <a href="http://personales.unican.es/santosf/Articulos/">The number of triangulations of the cyclic polytope C(n,n-4)</a>, Discrete Comput. Geom., 27 (2002), 29-48.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _Colin Barker_, Apr 20 2012: (Start)
%F a(n) = (8 - 14*n + 13*n^2 - 4*n^3 + n^4)/4.
%F G.f.: x*(1 - x + 4*x^2 + 2*x^4)/(1-x)^5. (End)
%t 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 *)
%o (PARI) { for (n=1, 1000, a=6*binomial(n,4) + 3*binomial(n,3) + 4*binomial(n,2) - n + 2; write("b066375.txt", n, " ", a) ) } \\ _Harry J. Smith_, Feb 11 2010
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jan 04 2002
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