A282736 Number of triangulations of a convex n-gon in the plane each of whose sides is subdivided by 3 points.

6, 229, 12168, 699310, 42660740, 2711857491, 177709370440, 11920293880380, 814482988508400, 56490879943263975, 3966899457382283620, 281477669727740682534, 20150660162264704871708, 1453641461401891280903545, 105565083172095676962621280

Offset

2,1

Links

Lars Blomberg, Table of n, a(n) for n = 2..101

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(n,4). - Lars Blomberg, Mar 04 2017

Mathematica

tr[k_, r_] := Sum[(-1)^j 2^l Binomial[k, j] Binomial[k-2+l, l] Binomial[(r-1)k-l-3, r k - (r+1)j - l - 2], {j, 0, k}, {l, 0, r k - (r+1)j - 2}];
a[n_] := tr[n, 4];
Table[a[n], {n, 2, 16}] (* Jean-François Alcover, Oct 10 2018 *)

Crossrefs

Sequence in context: A366252 A338297 A084070 * A277293 A177043 A309009

Adjacent sequences: A282733 A282734 A282735 * A282737 A282738 A282739

Keyword

nonn

Author

N. J. A. Sloane, Mar 03 2017

Extensions

More terms from Lars Blomberg, Mar 04 2017

Status

approved