A160241 Number of Greek-key tours on a 7 X n grid.

1, 7, 164, 1337, 16262, 144476, 1510446, 13506023, 132712481, 1185979605, 11264671456, 100572103736, 935551716239, 8347069749600, 76604373779441, 683160282998544, 6213169249692192, 55392188422262591, 500676083630457127, 4462726297606450762, 40165465812088131228, 357958181000067374304

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. 31.
• Index entries for linear recurrences with constant coefficients, order 71.

Crossrefs

Row 7 of A378938.

Cf. A046994, A046995, A145156, A145157.

Formula

See Links section for generating function. Jay Pantone, Aug 06 2024

Extensions

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