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A082640 Triangle T(m,n) read by rows: unimodular triangulations of the grid P(m,n), m,n > 0, n <= m.

%I A082640 #65 Feb 22 2025 15:48:05
%S A082640 2,6,64,20,852,46456,70,12170,2822648,736983568,252,182132,182881520,
%T A082640 208902766788,260420548144996,924,2801708,12244184472,61756221742966,
%U A082640 341816489625522032,1999206934751133055518,3432,43936824,839660660268,18792896208387012,464476385680935656240,12169409954141988707186052,332633840844113103751597995920
%N A082640 Triangle T(m,n) read by rows: unimodular triangulations of the grid P(m,n), m,n > 0, n <= m.
%C A082640 The limit of T(2,n)^(1/n) is (611+sqrt(73))/36. - _Stepan Orevkov_, Jan 31 2022
%H A082640 Stepan Orevkov, <a href="/A082640/b082640.txt">Table of n, a(n) for n = 1..55</a> (rows 1 to 10).
%H A082640 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 A082640 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 A082640 S. Yu. Orevkov, <a href="https://arxiv.org/abs/2412.17065">Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5</a>, arXiv:2412.17065 [math.CO], 2024.
%H A082640 Igor Pak, <a href="https://arxiv.org/abs/1803.06636">Complexity problems in enumerative combinatorics</a>, arXiv:1803.06636 [math.CO], 2018.
%e A082640 Triangle begins:
%e A082640     2;
%e A082640     6,     64;
%e A082640    20,    852,     46456;
%e A082640    70,  12170,   2822648,    736983568;
%e A082640   252, 182132, 182881520, 208902766788, 260420548144996;
%e A082640   ...
%Y A082640 Row/columns 1..2 are A000984, A296165.
%Y A082640 Row/columns 5..9 are A351484, A351485, A351486, A351487, A351488.
%Y A082640 Row sums: A151686. - _N. J. A. Sloane_, Jun 02 2009
%K A082640 nonn,tabl
%O A082640 1,1
%A A082640 _Ralf Stephan_, May 15 2003