

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



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



KEYWORD

nonn,walk


AUTHOR



EXTENSIONS



STATUS

approved



