A347675 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k that contain the minimal number of 1's.

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 6, 12, 1, 1, 20, 32, 32, 20, 1, 1, 30, 100, 22, 100, 30, 1, 1, 42, 240, 172, 172, 240, 42, 1, 1, 56, 490, 744, 92, 744, 490, 56, 1, 1, 72, 896, 2364, 956, 956, 2364, 896, 72, 1, 1, 90, 1512, 6174, 5328, 422, 5328, 6174, 1512, 90, 1

Offset

1,5

Links

Michael S. Branicky, Table of n, a(n) for n = 1..96

Don Knuth, Baxter matrices, Preprint, Sep 05 2021.

Formula

a(n) <= A347672(n). - Michael S. Branicky, Sep 15 2021

Example

The array begins:
1,1,1,1,1,1,1,...
1,2,6,12,20,30,42,...
1,6,6,32,100,240,490,...
1,12,32,22,172,744,2364,...
1,20,100,172,92,956,5328,...
1,30,240,744,956,422,5492,...
1,42,490,2364,5328,5492,2074,...
...
The first few antidiagonals are:
1,
1,1,
1,2,1,
1,6,6,1,
1,12,6,12,1,
1,20,32,32,20,1,
1,30,100,22,100,30,1,
1,42,240,172,172,240,42,1,
1,56,490,744,92,744,490,56,1,
...

Crossrefs

Cf. A347672, A347676.

The main diagonal is A001181.

Sequence in context: A168641 A255914 A143185 * A157635 A075798 A155864

Adjacent sequences: A347672 A347673 A347674 * A347676 A347677 A347678

Keyword

nonn,tabl

Author

N. J. A. Sloane, Sep 10 2021

Extensions

a(46)-a(66) from Michael S. Branicky, Sep 14 2021

Status

approved