A282733 - OEIS

%I #17 Nov 23 2017 12:33:53

%S 2,30,604,12168,238848,4569624,85553528,1573583616,28524904904,

%T 510897232692,9058858525800,159264273415260,2779746787907304,

%U 48213275987175024,831677499017068080,14277768950229574080,244075525406535998808,4156705946210758680468

%N Number of triangulations of a convex 4-gon in the plane each of whose sides is subdivided by n points.

%H Lars Blomberg, <a href="/A282733/b282733.txt">Table of n, a(n) for n = 0..99</a>

%H Andrei Asinowski, Christian Krattenthaler, Toufik Mansour, <a href="http://arxiv.org/abs/1604.02870">Counting triangulations of some classes of subdivided convex polygons</a>, arXiv:1604.02870 [math.CO], 2016.

%F From Asinowski and Krattenthaler equation 2.7: a(n) = tr(4,n+1). - _Lars Blomberg_, Mar 04 2017

%t F[n_] := F[n] = Expand[F[n - 2] t + F[n - 1]]; F[1] = 1; F[0] = 1;

%t cee = Function[{n}, Total@MapIndexed[(#1 CatalanNumber[4 n - #2[[1]] - 1] (-1)^(#2[[1]] + 1)) &, CoefficientList[F[n]^4, t]]];

%t Table[cee[n], {n, 20}] (* _Adam P. Goucher_, Nov 23 2017 *)

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Mar 03 2017

%E More terms from _Lars Blomberg_, Mar 04 2017