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

2, 6, 64, 20, 852, 46456, 70, 12170, 2822648, 736983568, 252, 182132, 182881520, 208902766788, 260420548144996, 924, 2801708, 12244184472, 61756221742966, 341816489625522032, 1999206934751133055518, 3432, 43936824, 839660660268, 18792896208387012, 464476385680935656240, 12169409954141988707186052, 332633840844113103751597995920

Offset

1,1

Comments

The limit of T(2,n)^(1/n) is (611+sqrt(73))/36. - Stepan Orevkov, Jan 31 2022

Links

Stepan Orevkov, Table of n, a(n) for n = 1..55 (rows 1 to 10).

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

S. Yu. Orevkov, Counting lattice triangulations: Fredholm equations in combinatorics, arXiv:2201.12827 [math.CO], 2022.

S. Yu. Orevkov, Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5, arXiv:2412.17065 [math.CO], 2024.

Igor Pak, Complexity problems in enumerative combinatorics, arXiv:1803.06636 [math.CO], 2018.

Example

Triangle begins:
    2;
    6,     64;
   20,    852,     46456;
   70,  12170,   2822648,    736983568;
  252, 182132, 182881520, 208902766788, 260420548144996;
  ...

Crossrefs

Row/columns 1..2 are A000984, A296165.

Row/columns 5..9 are A351484, A351485, A351486, A351487, A351488.

Row sums: A151686. - N. J. A. Sloane, Jun 02 2009

Sequence in context: A145756 A392849 A030170 * A139695 A347949 A241590

Adjacent sequences: A082637 A082638 A082639 * A082641 A082642 A082643

Keyword

nonn,tabl

Author

Ralf Stephan, May 15 2003

Status

approved