A374307 Number of Greek-key tours on an 8 X n grid.

1, 8, 332, 3750, 68591, 899432, 13506023, 180160012, 2510785227, 33330848454, 448079715759, 5893418278271, 77649390052196, 1011970457365017, 13165754032331389, 170232985496817728, 2195480228590892060, 28203099820000893198, 361391865363036263917, 4617813892310295762334

Offset: 1

Author

Jay Pantone, Jul 23 2024

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• N. 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.
• Index entries for linear recurrences with constant coefficients, order 203.

Crossrefs

Row 8 of A378938.

Cf. A145157, A046994, A046995, A145156, A160240, A160241.

Formula

See Links section for generating function.

Extensions

a(20) onwards from Andrew Howroyd, Dec 21 2024