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 A036572 Number of tetrahedra in largest triangulation of polygonal prism with regular polygonal base. 2

%I

%S 3,6,10,14,19,24,30,36,43,50,58,66,75,84,94,104,115,126,138,150,163,

%T 176,190,204,219,234,250,266,283,300,318,336,355,374,394,414,435,456,

%U 478,500,523,546,570,594,619,644,670,696,723,750,778,806

%N Number of tetrahedra in largest triangulation of polygonal prism with regular polygonal base.

%D J. A. De Loera, F. Santos and F. Takeuchi, ``Extremal properties of optimal dissections of convex polytopes'', SIAM Journal Discrete Mathematics, 14, 2001, 143-161.

%H Vincenzo Librandi, <a href="/A036572/b036572.txt">Table of n, a(n) for n = 3..1000</a>

%H M. Develin, <a href="http://arXiv.org/abs/math.CO/0309220">Maximal triangulations of a regular prism</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F a(n) = ceil((n*n+6*n-16)/4) = A004116(n) - 3. - _Ralf Stephan_, Oct 13 2003

%F a(n) = (-31-(-1)^n+12*n+2*n^2)/8. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: x^3*(2*x^2-3) / ((x-1)^3*(x+1)). - _Colin Barker_, Sep 05 2013

%t CoefficientList[Series[(2 x^2 - 3)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)

%t LinearRecurrence[{2,0,-2,1},{3,6,10,14},60] (* _Harvey P. Dale_, Jun 05 2017 *)

%o (PARI) Vec(x^3*(2*x^2-3)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Sep 05 2013

%o (MAGMA) [Ceiling((n*n+6*n-16)/4): n in [3..60]]; // _Vincenzo Librandi_, Oct 21 2013

%Y Cf. A036573.

%K nonn,easy

%O 3,1

%A Jesus De Loera (deloera(AT)math.ucdavis.edu)

%E More terms from _Ralf Stephan_, Oct 13 2003

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Last modified March 21 07:23 EDT 2019. Contains 321367 sequences. (Running on oeis4.)