A347672 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k.

1, 1, 1, 1, 6, 1, 1, 14, 14, 1, 1, 24, 69, 24, 1, 1, 36, 203, 203, 36, 1, 1, 50, 463, 972, 463, 50, 1, 1, 66, 903, 3324, 3324, 903, 66, 1, 1, 84, 1585, 9074, 16355, 9074, 1585, 84, 1, 1, 104, 2579, 21168, 61267, 61267, 21168, 2579, 104, 1, 1, 126, 3963, 44028, 188153, 306352, 188153, 44028, 3963, 126, 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.

George Spahn, Counting Baxter Matrices, arXiv:2110.09688 [math.CO], 2021.

Example

The array begins:
1,1,1,1,1,1,1, ...
1,6,14,24,36,50,66, ...
1,14,69,203,463,903,1585, ...
1,24,203,972,3324,9074,21168, ...
1,36,463,3324,16355,61267,188153, ...
1,50,903,9074,61267,306352,1219598, ...
1,66,1585,21168,188153,1219598,6175181, ...
...
The first few antidiagonals are:
1,
1,1,
1,6,1,
1,14,14,1,
1,24,69,24,1,
1,36,203,203,36,1,
1,50,463,972,463,50,1,
1,66,903,3324,3324,903,66,1,
1,84,1585,9074,16355,9074,1585,84,1,
...

Crossrefs

Row 2 is A028557, row 3 is A347673, main diagonal is A347674.

Cf. A347675, A347676.

Sequence in context: A353963 A230073 A143210 * A205133 A152238 A295985

Adjacent sequences: A347669 A347670 A347671 * A347673 A347674 A347675

Keyword

nonn,tabl

Author

N. J. A. Sloane, Sep 10 2021

Extensions

a(25) corrected by and a(46)-a(66) from Michael S. Branicky, Sep 14 2021

Status

approved