A347676 -id:A347676 - cp's OEIS frontend

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

N. J. A. Sloane, Sep 10 2021

			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,
...

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.

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

Cf. A347675, A347676.

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

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.

Original entry on oeis.org

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

N. J. A. Sloane, Sep 10 2021

			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,
...

Michael S. Branicky, Table of n, a(n) for n = 1..96
Don Knuth, Baxter matrices, Preprint, Sep 05 2021.

Cf. A347672, A347676.

The main diagonal is A001181.

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

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

A347677 Number of Baxter matrices of size 3 X n that contain n+2 1's.

Original entry on oeis.org

1, 8, 26, 55, 96, 149, 214, 291, 380, 481, 594, 719, 856, 1005, 1166, 1339, 1524, 1721, 1930, 2151, 2384, 2629, 2886, 3155, 3436, 3729, 4034, 4351, 4680, 5021, 5374, 5739, 6116, 6505, 6906, 7319, 7744, 8181, 8630, 9091, 9564, 10049, 10546, 11055, 11576, 12109

Offset: 1

N. J. A. Sloane, Sep 10 2021

Row 3 of array A347676.

Michael S. Branicky, Table of n, a(n) for n = 1..65
George Spahn, Counting Baxter Matrices, arXiv:2110.09688 [math.CO], 2021.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1)

Cf. A347676, A347673.

a(n) = 6*n^2 - 13*n + 11 for n >= 3. - George Spahn, Oct 20 2021

g.f.: x+8*x^2 -x^3 *(26-23*x+9*x^2)/(x-1)^3 . - R. J. Mathar, Aug 20 2022

a(8)-a(46) from Michael S. Branicky, Sep 13 2021

cp's OEIS Frontend

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

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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.

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Author

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A347677 Number of Baxter matrices of size 3 X n that contain n+2 1's.

Views

Author

Keywords

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Links

Crossrefs

Formula

Extensions