A282733 Number of triangulations of a convex 4-gon in the plane each of whose sides is subdivided by n points.

2, 30, 604, 12168, 238848, 4569624, 85553528, 1573583616, 28524904904, 510897232692, 9058858525800, 159264273415260, 2779746787907304, 48213275987175024, 831677499017068080, 14277768950229574080, 244075525406535998808, 4156705946210758680468

Offset

0,1

Links

Lars Blomberg, Table of n, a(n) for n = 0..99

Andrei Asinowski, Christian Krattenthaler, Toufik Mansour, Counting triangulations of some classes of subdivided convex polygons, arXiv:1604.02870 [math.CO], 2016.

Formula

From Asinowski and Krattenthaler equation 2.7: a(n) = tr(4,n+1). - Lars Blomberg, Mar 04 2017

Mathematica

F[n_] := F[n] = Expand[F[n - 2] t + F[n - 1]]; F[1] = 1; F[0] = 1;
cee = Function[{n}, Total@MapIndexed[(#1 CatalanNumber[4 n - #2[[1]] - 1] (-1)^(#2[[1]] + 1)) &, CoefficientList[F[n]^4, t]]];
Table[cee[n], {n, 20}] (* Adam P. Goucher, Nov 23 2017 *)

Crossrefs

Sequence in context: A208881 A297490 A324957 * A363113 A160694 A278884

Adjacent sequences: A282730 A282731 A282732 * A282734 A282735 A282736

Keyword

nonn

Author

N. J. A. Sloane, Mar 03 2017

Extensions

More terms from Lars Blomberg, Mar 04 2017

Status

approved