A334518 Array read by antidiagonals: T(m,n) (m>=1, n>=1) = number of m X n whirlpool permutations.

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

Table of n, a(n) for n=1..38.

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

Columns: A000142, A261683, A334516; main diagonal = A334517.

See also A334519.

Sequence in context: A269722 A091441 A269565 * A099490 A167878 A351928

Adjacent sequences: A334515 A334516 A334517 * A334519 A334520 A334521

Keyword

nonn,tabl

Author

N. J. A. Sloane, May 06 2020

Status

approved