A160240 Number of Greek-key tours on a 6 X n grid.

1, 6, 78, 469, 3501, 22144, 144476, 899432, 5585508, 34092855, 206571444, 1241016042, 7407467656, 43975776229, 259779839242, 1528563721468, 8960651209082, 52368047294410, 305173796833144, 1774059940879290, 10289839706255591, 59564855651625602, 344177608427972004, 1985502681113986836

Offset: 1

Author

Nathaniel Johnston, May 05 2009

Keywords

• nonn

Comments

Greek-key tours are self-avoiding walks that touch every vertex of the grid and start at the bottom-left corner.

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 07 2015

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Nathaniel Johnston, On Maximal Self-Avoiding Walks.
• Jay Pantone, Generating function.
• Jay Pantone, Alexander R. Klotz, and Everett Sullivan, Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height, arXiv:2407.18205 [math.CO], 2024. See p. 30.
• Index entries for linear recurrences with constant coefficients, order 37.

Crossrefs

Row 6 of A378938.

Cf. A046994, A046995, A145156, A145157.

Formula

See Links section for generating function. - Jay Pantone, Aug 01 2024

Extensions

a(11) onwards from Andrew Howroyd, Nov 07 2015