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%I #25 Sep 08 2022 08:44:52
%S 4,8,12,17,22,28,34,41,48,56,64,73,82,92,102,113,124,136,148,161,174,
%T 188,202,217,232,248,264,281,298,316,334,353,372,392,412,433,454,476,
%U 498,521,544,568,592,617,642,668,694,721,748,776,804,833
%N Size of maximal triangulation of an n-antiprism with regular polygonal base.
%H Vincenzo Librandi, <a href="/A036573/b036573.txt">Table of n, a(n) for n = 3..1000</a>
%H 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 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) = floor((n^2 + 8n - 16)/4). - _Ralf Stephan_, Oct 13 2003
%F a(n) = (-33+(-1)^n+16*n+2*n^2)/8. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: -x^3*(x^3-4*x^2+4) / ((x-1)^3*(x+1)). - _Colin Barker_, Sep 06 2013
%t CoefficientList[Series[-(x^3 - 4 x^2 + 4)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)
%t LinearRecurrence[{2,0,-2,1},{4,8,12,17},60] (* _Harvey P. Dale_, Nov 28 2014 *)
%o (PARI) Vec(-x^3*(x^3-4*x^2+4)/((x-1)^3*(x+1)) + O(x^100)) \\ _Colin Barker_, Sep 06 2013
%o (Magma) [Floor((n^2+8*n-16)/4): n in [3..60]]; // _Vincenzo Librandi_, Oct 21 2013
%Y Cf. A036572.
%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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