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A096969
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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).
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5
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1, 8, 40, 552, 8648, 458696, 27070560, 6046626568, 1490832682992, 1460089659025264, 1573342970540617696, 6905329711608694708440, 33304011435341069362631160, 663618176813467308855850585056, 14527222735920532980525200234503048
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OFFSET
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1,2
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COMMENTS
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Number of directed Hamiltonian paths in (n X n)-grid graph. - Max Alekseyev, May 03 2009
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LINKS
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FORMULA
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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
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EXAMPLE
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One of the 8648 numberings of a 5 X 5 grid is
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3---2---1 20--21
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4 17--18--19 22
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5 16--15--14 23
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6 9--10 13 24
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7---8 11--12 25
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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