A332307 Array read by antidiagonals: T(m,n) is the number of (undirected) Hamiltonian paths in the m X n grid graph.

1, 1, 1, 1, 4, 1, 1, 8, 8, 1, 1, 14, 20, 14, 1, 1, 22, 62, 62, 22, 1, 1, 32, 132, 276, 132, 32, 1, 1, 44, 336, 1006, 1006, 336, 44, 1, 1, 58, 688, 3610, 4324, 3610, 688, 58, 1, 1, 74, 1578, 12010, 26996, 26996, 12010, 1578, 74, 1, 1, 92, 3190, 38984, 109722, 229348, 109722, 38984, 3190, 92, 1

Offset: 1

Author

Andrew Howroyd, Feb 09 2020

Keywords

• nonn
• tabl

Examples

			Array begins:
================================================
m\n | 1  2   3     4      5       6        7
----+-------------------------------------------
  1 | 1  1   1     1      1       1        1 ...
  2 | 1  4   8    14     22      32       44 ...
  3 | 1  8  20    62    132     336      688 ...
  4 | 1 14  62   276   1006    3610    12010 ...
  5 | 1 22 132  1006   4324   26996   109722 ...
  6 | 1 32 336  3610  26996  229348  1620034 ...
  7 | 1 44 688 12010 109722 1620034 13535280 ...
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..435
• J. L. Jacobsen, Exact enumeration of Hamiltonian circuits, walks and chains in two and three dimensions, J. Phys. A: Math. Theor. 40 (2007) 14667-14678.
• J.-M. Mayer, C. Guez and J. Dayantis, Exact computer enumeration of the number of Hamiltonian paths in small square plane lattices, Physical Review B, Vol. 42 Number 1, 1990.
• Eric Weisstein's World of Mathematics, Grid Graph
• Eric Weisstein's World of Mathematics, Hamiltonian Path

Crossrefs

Rows n=1..9 are A000012, A003682, A003685, A003695, A003778, A145402, A358794, A358795, A358796.

Main diagonal is A120443.

Cf. A064298, A231829, A271465, A271592, A288518, A321172.

Formula

T(n,m) = T(m,n).