A145156 Number of Greek-key tours on a 5 X n board; i.e., self-avoiding walks on 5 X n grid starting in top left corner.

1, 5, 38, 160, 824, 3501, 16262, 68591, 304177, 1276805, 5522791, 23117164, 98562435, 411870513, 1740941765, 7267608829, 30557297042, 127482101761, 534250130959, 2227966210989, 9317736040747, 38847892461656, 162258421050635, 676389635980185, 2822813259030961, 11766012342819549, 49078395756348338, 204555232240144477, 852962192769193199, 3554945699146438849

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

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

Nathaniel Johnston, Self-avoiding walks table of values

Formula

Empirical 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)). - Colin Barker, Nov 09 2015

Crossrefs

Cf. A046994, A046995, A145157.

Sequence in context: A097276 A280437 A222646 * A318102 A163698 A294053

Adjacent sequences: A145153 A145154 A145155 * A145157 A145158 A145159

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

Status

approved