A145157 - OEIS

%I #29 Dec 20 2024 10:44:53

%S 1,2,8,52,824,22144,1510446,180160012,54986690944,29805993260994,

%T 41433610713353366,103271401574007978038,660340630211753942588170,

%U 7618229614763015717175450784,225419381425094248494363948728158

%N Number of Greek-key tours on an n X n board; i.e., self-avoiding walks on n X n grid starting in 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. - _Andrew Howroyd_, Nov 08 2015

%H Nathaniel Johnston, <a href="http://www.njohnston.ca/2009/05/on-maximal-self-avoiding-walks">On Maximal Self-Avoiding Walks</a>

%H Ville H. Pettersson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i4p7">Enumerating Hamiltonian Cycles</a>, The Electronic Journal of Combinatorics, Volume 21, Issue 4, 2014.

%Y Main diagonal of A378938.

%Y Cf. A046994, A046995, A145156, A160240, A160241.

%Y Cf. A000532, A001184, A120443, A003763, A271507, A007764.

%K hard,nonn,walk

%O 1,2

%A _Nathaniel Johnston_, Oct 03 2008

%E a(9)-a(15) from _Andrew Howroyd_, Nov 08 2015