A296165 a(n) is the number of unimodular triangulations of [0,2]x[0,n].

6, 64, 852, 12170, 182132, 2801708, 43936824

Offset

1,1

Comments

As stated by Kaibel and Ziegler, the number of unimodular triangulations of [0,1]x[0,n] is (2n)!/(n!*n!). This gives a(1)=6.

No formula for a(n) is known. Aichholzer computed a(n) for n<=15.

Kaibel and Ziegler computed a(n) for n<=375. Aichholzer also computed the number of unimodular triangulations of [0,m]x[0,n] for m=3,4,5 and various n, and Kaibel-Ziegler extended these calculations to m=6.

References

V. Kaibel and G. Ziegler, "Counting lattice triangulations," London Math. Soc. Lecture Notes Series, Vol. 307, pp. 277-307, 2003.

Links

Table of n, a(n) for n=1..7.

O. Aichholzer, Counting Triangulations - Olympics, 2006.

V. Kaibel and G. M. Ziegler, Counting Lattice Triangulations, arXiv:math/0211268 [math.CO], 2002.

Crossrefs

Second column of array A082640.

Sequence in context: A156887 A239847 A264634 * A173500 A141008 A336114

Adjacent sequences: A296162 A296163 A296164 * A296166 A296167 A296168

Keyword

nonn,more

Author

John Kieffer, Dec 06 2017

Status

approved