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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 15 02:21 EDT 2021. Contains 343909 sequences. (Running on oeis4.)