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A282734 Number of triangulations of a convex 5-gon in the plane each of whose sides is subdivided by n points. 1
5, 250, 13740, 699310, 33138675, 1484701075, 63681535780, 2639190848280, 106403568809545, 4194330516135610, 162275686298727710, 6180361117463387590, 232249233257266145145, 8627435520542763854065, 317285140062014506979360, 11566298576075812803892160 (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(5,n+1). - 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[5, n+1];

Table[a[n], {n, 0, 15}] (* Jean-Fran├žois Alcover, Oct 10 2018 *)

CROSSREFS

Sequence in context: A068727 A135095 A219872 * A115739 A142202 A042219

Adjacent sequences:  A282731 A282732 A282733 * A282735 A282736 A282737

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 July 5 01:22 EDT 2020. Contains 335457 sequences. (Running on oeis4.)