cp's OEIS Frontend

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.

%I A145156 #40 Dec 21 2024 14:18:58
%S A145156 1,5,38,160,824,3501,16262,68591,304177,1276805,5522791,23117164,
%T A145156 98562435,411870513,1740941765,7267608829,30557297042,127482101761,
%U A145156 534250130959,2227966210989,9317736040747,38847892461656,162258421050635,676389635980185,2822813259030961,11766012342819549
%N 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.
%C A145156 From _Andrew Howroyd_, Nov 07 2015: (Start)
%C A145156 Greek Key Tours are self-avoiding walks that touch every vertex of the grid and start at the top-left corner.
%C A145156 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 A145156 (End)
%H A145156 Andrew Howroyd, <a href="/A145156/b145156.txt">Table of n, a(n) for n = 1..500</a>
%H A145156 Nathaniel Johnston, <a href="http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks/">Self-avoiding walks table of values</a>
%H A145156 Jay Pantone, Alexander R. Klotz, and Everett Sullivan, <a href="https://arxiv.org/abs/2407.18205">Exactly-solvable self-trapping lattice walks. II. Lattices of arbitrary height</a>, arXiv:2407.18205 [math.CO], 2024. See p. 30.
%H A145156 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (4,14,-54,-33,117,2,-84,-6,9,0,-14,0,-2).
%F A145156 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]
%Y A145156 Row 5 of A378938.
%Y A145156 Cf. A046994, A046995, A145157.
%K A145156 nonn
%O A145156 1,2
%A A145156 _Nathaniel Johnston_, Oct 03 2008
%E A145156 a(11)-a(15) added by _Nathaniel Johnston_, Oct 12 2008
%E A145156 a(16) added by _Ruben Zilibowitz_, Jul 10 2015
%E A145156 a(17) onwards from _Andrew Howroyd_, Nov 07 2015