A282735 Number of triangulations of a convex n-gon in the plane each of whose sides is subdivided by 2 points.

2, 29, 604, 13740, 332842, 8419334, 219829560, 5880376980, 160327187560, 4439180561629, 124485616405516, 3528306241927428, 100914357176842188, 2908920668838209340, 84423279647430363248, 2464811859798957024196, 72343319478816485276760, 2133323371103124457168580

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,3). - 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, 3];
Table[a[n], {n, 2, 19}] (* Jean-François Alcover, Oct 10 2018 *)

Crossrefs

Sequence in context: A187362 A176938 A006988 * A245252 A090251 A087281

Adjacent sequences: A282732 A282733 A282734 * A282736 A282737 A282738

Keyword

nonn

Author

N. J. A. Sloane, Mar 03 2017

Extensions

More terms from Lars Blomberg, Mar 04 2017

Status

approved