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Triangle T(m,n) read by rows: unimodular triangulations of the grid P(m,n), m,n > 0, n <= m.
12

%I #46 Feb 09 2022 09:03:55

%S 2,6,64,20,852,46456,70,12170,2822648,736983568,252,182132,182881520,

%T 208902766788,260420548144996,924,2801708,12244184472,61756221742966,

%U 341816489625522032,1999206934751133055518

%N Triangle T(m,n) read by rows: unimodular triangulations of the grid P(m,n), m,n > 0, n <= m.

%C The limit of T(2,n)^(1/n) is (611+sqrt(73))/36. - _Stepan Orevkov_, Jan 31 2022

%H Stepan Orevkov, <a href="/A082640/b082640.txt">Table of n, a(n) for n = 1..45</a> (rows 1..9)

%H V. Kaibel and G. M. Ziegler, <a href="https://arxiv.org/abs/math/0211268">Counting Lattice Triangulations</a>, arXiv:math/0211268 [math.CO], 2002.

%H S. Yu. Orevkov, <a href="https://arxiv.org/abs/2201.12827">Counting lattice triangulations: Fredholm equations in combinatorics</a>, arXiv:2201.12827 [math.CO], 2022.

%H Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.

%e Triangle begins:

%e 2;

%e 6, 64;

%e 20, 852, 46456;

%e 70, 12170, 2822648, 736983568;

%e ...

%Y First column is T(m, 1) = A000984(m).

%Y Second column is T(m,2) = A296165(m).

%Y Row sums: A151686. - _N. J. A. Sloane_, Jun 02 2009

%K nonn,tabl

%O 1,1

%A _Ralf Stephan_, May 15 2003