cp's OEIS Frontend

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

%I A036572 #26 Sep 08 2022 08:44:52
%S A036572 3,6,10,14,19,24,30,36,43,50,58,66,75,84,94,104,115,126,138,150,163,
%T A036572 176,190,204,219,234,250,266,283,300,318,336,355,374,394,414,435,456,
%U A036572 478,500,523,546,570,594,619,644,670,696,723,750,778,806
%N A036572 Number of tetrahedra in largest triangulation of polygonal prism with regular polygonal base.
%H A036572 Vincenzo Librandi, <a href="/A036572/b036572.txt">Table of n, a(n) for n = 3..1000</a>
%H A036572 J. A. De Loera, F. Santos and F. Takeuchi, <a href="https://doi.org/10.1137/S0895480199366238">Extremal properties of optimal dissections of convex polytopes</a>, SIAM Journal Discrete Mathematics, 14, 2001, 143-161.
%H A036572 M. Develin, <a href="http://arXiv.org/abs/math.CO/0309220">Maximal triangulations of a regular prism</a>
%H A036572 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A036572 a(n) = ceiling((n*n + 6*n - 16)/4) = A004116(n) - 3. - _Ralf Stephan_, Oct 13 2003
%F A036572 From _Colin Barker_, Sep 05 2013: (Start)
%F A036572 a(n) = (-31 - (-1)^n + 12*n + 2*n^2)/8.
%F A036572 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A036572 G.f.: x^3*(2*x^2-3) / ((x-1)^3*(x+1)). (End)
%t A036572 CoefficientList[Series[(2 x^2 - 3)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)
%t A036572 LinearRecurrence[{2,0,-2,1},{3,6,10,14},60] (* _Harvey P. Dale_, Jun 05 2017 *)
%o A036572 (PARI) Vec(x^3*(2*x^2-3)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Sep 05 2013
%o A036572 (Magma) [Ceiling((n*n+6*n-16)/4): n in [3..60]]; // _Vincenzo Librandi_, Oct 21 2013
%Y A036572 Cf. A036573.
%K A036572 nonn,easy
%O A036572 3,1
%A A036572 Jesus De Loera (deloera(AT)math.ucdavis.edu)
%E A036572 More terms from _Ralf Stephan_, Oct 13 2003