|
|
A269565
|
|
Array read by antidiagonals: T(n,m) is the number of (directed) Hamiltonian paths in K_n X K_m.
|
|
7
|
|
|
1, 2, 2, 6, 8, 6, 24, 60, 60, 24, 120, 816, 1512, 816, 120, 720, 17520, 83520, 83520, 17520, 720, 5040, 550080, 8869680, 22394880, 8869680, 550080, 5040, 40320, 23839200, 1621680480, 13346910720, 13346910720, 1621680480, 23839200, 40320
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Equivalently, the number of directed Hamiltonian paths on the n X m rook graph.
The above conjecture is true since a path defines an ordering on the rows and columns by the order in which they are first visited by the path. Every permutation of rows and columns therefore gives a different path. - Andrew Howroyd, Feb 08 2021
|
|
LINKS
|
|
|
FORMULA
|
T(n,m) = T(m,n).
T(n,1) = n!. (End)
|
|
EXAMPLE
|
Array begins:
===========================================================
n\m| 1 2 3 4 5
---+-------------------------------------------------------
1 | 1, 2, 6, 24, 120, ...
2 | 2, 8, 60, 816, 17520, ...
3 | 6, 60, 1512, 83520, 8869680, ...
4 | 24, 816, 83520, 22394880, 13346910720, ...
5 | 120, 17520, 8869680, 13346910720, 50657369241600, ...
...
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|