OFFSET
1,2
COMMENTS
From Andrew Howroyd, Nov 07 2015: (Start)
Greek Key Tours are self-avoiding walks that touch every vertex of the grid and start at the top-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.
(End)
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Nathaniel Johnston, Self-avoiding walks table of values
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, signature (4,14,-54,-33,117,2,-84,-6,9,0,-14,0,-2).
FORMULA
G.f.: -x*(3*x^13 -3*x^12 +17*x^11 -11*x^10 +11*x^9 -21*x^8 +67*x^7 -29*x^6 -65*x^5 +45*x^4 +8*x^3 -4*x^2 -x -1) / ((x +1)*(x^6 -x^5 +8*x^4 -8*x^3 -2*x^2 +5*x -1)*(2*x^6 +11*x^2 -1)). [conjectured by Colin Barker, Nov 09 2015; proved by Jay Pantone, Klotz, and Sullivan, Aug 01 2024]
CROSSREFS
KEYWORD
nonn
AUTHOR
Nathaniel Johnston, Oct 03 2008
EXTENSIONS
a(11)-a(15) added by Nathaniel Johnston, Oct 12 2008
a(16) added by Ruben Zilibowitz, Jul 10 2015
a(17) onwards from Andrew Howroyd, Nov 07 2015
STATUS
approved