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
Offset: 1
Examples
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
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
Extensions
a(7) from Giovanni Resta, May 12 2006
a(8)-a(15) added by Andrew Howroyd, Dec 20 2015
Comments