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A334518
Array read by antidiagonals: T(m,n) (m>=1, n>=1) = number of m X n whirlpool permutations.
4
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, 40320, 147985824, 273315542400, 15584878111040, 15584878111040, 273315542400, 147985824, 40320, 362880, 12338740736
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
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
Columns: A000142, A261683, A334516; main diagonal = A334517.
See also A334519.
Sequence in context: A269722 A091441 A269565 * A099490 A167878 A351928
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, May 06 2020
STATUS
approved