A334518 - OEIS

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

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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:

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.