

A145156


Number of Greekkey tours on a 5 X n board; i.e., selfavoiding walks on 5 X n grid starting in top left corner.


3



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
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OFFSET

1,2


COMMENTS

From Andrew Howroyd, Nov 07 2015: (Start)
Greek Key Tours are selfavoiding walks that touch every vertex of the grid and start at the topleft 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, Selfavoiding 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



