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A282733 Number of triangulations of a convex 4-gon in the plane each of whose sides is subdivided by n points. 1
2, 30, 604, 12168, 238848, 4569624, 85553528, 1573583616, 28524904904, 510897232692, 9058858525800, 159264273415260, 2779746787907304, 48213275987175024, 831677499017068080, 14277768950229574080, 244075525406535998808, 4156705946210758680468 (list; graph; refs; listen; history; text; internal format)
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 * A160694 A278884 A013525

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

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)