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, 11437008315770485918, 65791536638478271291, 377999748832914166324, 2169320756101096085597, 12436728915873118081588, 71232070407411735554025

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. 30.

Formula

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

Crossrefs

Cf. A046994, A046995, A145156, A145157.

Sequence in context: A167498 A250388 A231248 * A069669 A145359 A087600

Adjacent sequences: A160237 A160238 A160239 * A160241 A160242 A160243

Keyword

nonn

Author

Nathaniel Johnston, May 05 2009

Extensions

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

Status

approved