OFFSET
1,2
COMMENTS
An m X n whirlpool permutation is an m X n matrix containing the numbers 1..m*n with the property that for every 2 X 2 submatrix the entries (starting anywhere, and read either clockwise or counterclockwise) are in increasing order.
LINKS
D. E. Knuth, Whirlpool Permutations, May 05 2020.
EXAMPLE
There are T(2,2) = 8 2X2 whirlpool permutations, namely [12/43], [14/23], [21/43], [23/14], [32/41], [34/21], [41/32], [43/12].
Array begins:
1,2,6,24,120,...
2,8,84,1632,51040,...
6,84,5904,1064304,402671760,...
24,1632,1064304,2456909824,15584878111040,...
120,51040,402671760,15584878111040,2179875344187129600,...
720,2340480,273315542400,217353588326290944,823110394280028294344640,...
...
The initial antidiagonals are:
1,
2,2,
6,8,6,
24,84,84,24,
120,1632,5904,1632,120,
720,51040,1064304,1064304,51040,720,
5040,2340480,402671760,2456909824,402671760,2340480,5040,
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 06 2020
STATUS
approved