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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). 5
1, 8, 40, 552, 8648, 458696, 27070560, 6046626568, 1490832682992, 1460089659025264, 1573342970540617696, 6905329711608694708440, 33304011435341069362631160, 663618176813467308855850585056, 14527222735920532980525200234503048 (list; graph; refs; listen; history; text; internal format)
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

Stéphane Duguay, 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

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

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

Sequence in context: A117083 A007987 A343868 * 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

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Last modified December 2 10:47 EST 2021. Contains 349440 sequences. (Running on oeis4.)