|
%I #24 Aug 21 2020 09:11:02
%S 1,5,38,160,824,3501,16262,68591,304177,1276805,5522791,23117164,
%T 98562435,411870513,1740941765,7267608829,30557297042,127482101761,
%U 534250130959,2227966210989,9317736040747,38847892461656,162258421050635,676389635980185,2822813259030961,11766012342819549,49078395756348338,204555232240144477,852962192769193199,3554945699146438849
%N 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.
%C From _Andrew Howroyd_, Nov 07 2015: (Start)
%C Greek Key Tours are self-avoiding walks that touch every vertex of the grid and start at the top-left corner.
%C 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.
%C (End)
%H Nathaniel Johnston, <a href="http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/">Self-avoiding walks table of values</a>
%F 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
%Y Cf. A046994, A046995, A145157.
%K nonn
%O 1,2
%A _Nathaniel Johnston_, Oct 03 2008
%E a(11)-a(15) added by _Nathaniel Johnston_, Oct 12 2008
%E a(16) added by _Ruben Zilibowitz_, Jul 10 2015
%E a(17)-a(30) from _Andrew Howroyd_, Nov 07 2015
|
