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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

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 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

| | |

6 9--10 13 24

| | | | |

7---8 11--12 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

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Last modified November 27 03:04 EST 2022. Contains 358362 sequences. (Running on oeis4.)