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, 3212099862174948821718, 28623565473267451344466, 256312533945178149983147, 2283878397650977479239903, 20420964710002966369773032, 181952098315164452547737813, 1625193628709305194920610168, 14480051230931926406392771755

Offset

1,2

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

Table of n, a(n) for n=1..30.

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.

Formula

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

Crossrefs

Cf. A046994, A046995, A145156, A145157.

Sequence in context: A351610 A169608 A184754 * A020998 A012504 A012689

Adjacent sequences: A160238 A160239 A160240 * A160242 A160243 A160244

Keyword

nonn

Author

Nathaniel Johnston, May 05 2009

Extensions

a(11)-a(30) from Andrew Howroyd, Nov 07 2015

Status

approved