

A096969


Number of ways to number the cells of an n X n square grid with 1,2,3,...,n^2 so that successive integers are in adjacent cells (horizontally or vertically).


5



1, 8, 40, 552, 8648, 458696, 27070560, 6046626568, 1490832682992, 1460089659025264, 1573342970540617696, 6905329711608694708440, 33304011435341069362631160, 663618176813467308855850585056, 14527222735920532980525200234503048
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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 presented by A..D 1..4 coordination system. [552]
Stéphane Duguay, Steven Pigeon, Comparison of Pixel Correlation Induced by SpaceFilling 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, 294297.
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
Index entries for sequences related to graphs, Hamiltonian


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
.
321 2021
  
4 171819 22
  
5 161514 23
  
6 910 13 24
    
78 1112 25


CROSSREFS

Cf. A120443, A096970, A143246, A137891, A158651.
Sequence in context: A007987 A343868 A350125 * A209829 A209848 A093104
Adjacent sequences: A096966 A096967 A096968 * A096970 A096971 A096972


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



