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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).

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 (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

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

3---2---1 20--21

| | |

4 17--18--19 22

| | |

5 16--15--14 23

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6 9--10 13 24

| | | | |

7---8 11--12 25

CROSSREFS

Cf. A120443, A096970, A143246, A137891, A158651.

Sequence in context: A007987 A343868 A350125 * A376186 A209829 A209848

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

URL: https://oeis.org/A096969

⇱ A096969 - OEIS