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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
OFFSET
0,1
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 03 2017
EXTENSIONS
More terms from Lars Blomberg, Mar 04 2017
STATUS
approved