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

1,5

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

Formula

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

Example

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 ...
  ...

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.

Sequence in context: A132789 A319251 A100754 * A296405 A174035 A303888

Adjacent sequences: A332304 A332305 A332306 * A332308 A332309 A332310

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 09 2020

Status

approved