A145157 Number of Greek-key tours on an n X n board; i.e., self-avoiding walks on n X n grid starting in top left corner.

1, 2, 8, 52, 824, 22144, 1510446, 180160012, 54986690944, 29805993260994, 41433610713353366, 103271401574007978038, 660340630211753942588170, 7618229614763015717175450784, 225419381425094248494363948728158

Offset: 1

Author

Nathaniel Johnston, Oct 03 2008

Keywords

• hard
• nonn
• walk

Comments

The sequence may be enumerated using standard methods for counting Hamiltonian cycles on a modified graph with two additional nodes, one joined to a corner vertex and the other joined to all other vertices. - Andrew Howroyd, Nov 08 2015

Links

• Nathaniel Johnston, On Maximal Self-Avoiding Walks
• Ville H. Pettersson, Enumerating Hamiltonian Cycles, The Electronic Journal of Combinatorics, Volume 21, Issue 4, 2014.

Crossrefs

Main diagonal of A378938.

Cf. A046994, A046995, A145156, A160240, A160241.

Cf. A000532, A001184, A120443, A003763, A271507, A007764.

Extensions

a(9)-a(15) from Andrew Howroyd, Nov 08 2015