OFFSET
1,2
COMMENTS
Number of directed Hamiltonian paths in (n X n)-grid graph. - Max Alekseyev, May 03 2009
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..17
Nicolas Bělohoubek, All possible paths in 4th term (552) presented by A..D 1..4 coordination system.
Nicolas Bělohoubek, All possible paths in 5th term (8648) presented by A..E 1..5 coordination system.
Nicolas Bělohoubek, All possible paths in 5th term (8648) in image, blue to red.
Stéphane Duguay and Steven Pigeon, Comparison of Pixel Correlation Induced by Space-Filling Curves on 2D Image Data, The 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (Metz, France, 2019) Vol. 1, 294-297.
Mary Grace Hanson and David A. Nash, Minimal and maximal Numbrix puzzles, arXiv:1706.09389 [math.CO], 2017.
Eric Weisstein's World of Mathematics, Grid Graph
Eric Weisstein's World of Mathematics, Hamiltonian Path
FORMULA
Conjecture: Limit_{n->oo} log_(n+1)!(a(n+1)) - log_n!(a(n)) = c, where 0.09 < c < 0.11. - Nicolas Bělohoubek, Jun 12 2022
EXAMPLE
One of the 8648 numberings of a 5 X 5 grid is
.
3---2---1 20--21
| | |
4 17--18--19 22
| | |
5 16--15--14 23
| | |
6 9--10 13 24
| | | | |
7---8 11--12 25
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
John W. Layman, Jul 16 2004, at the suggestion of Leroy Quet, Jul 05 2004
EXTENSIONS
a(7) from Giovanni Resta, May 12 2006
a(8)-a(15) added by Andrew Howroyd, Dec 20 2015
STATUS
approved