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Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k that contain the maximal number of 1's.
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%I #24 Oct 19 2021 23:44:47

%S 1,1,1,1,4,1,1,8,8,1,1,12,26,12,1,1,16,55,55,16,1,1,20,96,156,96,20,1,

%T 1,24,149,354,354,149,24,1,1,28,214,688,1037,688,214,28,1,1,32,291,

%U 1198,2533,2533,1198,291,32,1,1,36,380,1924,5383,7632,5383,1924,380,36,1

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

%H Michael S. Branicky, <a href="/A347676/b347676.txt">Table of n, a(n) for n = 1..96</a>

%H Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/baxter-matrices.pdf">Baxter matrices</a>, Preprint, Sep 05 2021.

%H George Spahn, <a href="https://arxiv.org/abs/2110.09688">Counting Baxter Matrices</a>, arXiv:2110.09688 [math.CO], 2021.

%F a(n) <= A347672(n). - _Michael S. Branicky_, Sep 15 2021

%e The array begins:

%e 1,1,1,1,1,1,1, ...

%e 1,4,8,12,16,20,24, ...

%e 1,8,26,55,96,149,214, ...

%e 1,12,55,156,354,688,1198, ...

%e 1,16,96,354,1037,2533,5383, ...

%e 1,20,149,688,2533,7632,19522, ...

%e 1,24,214,1198,5383,19522,59020, ...

%e ...

%e The first few antidiagonals are:

%e 1,

%e 1,1,

%e 1,4,1,

%e 1,8,8,1,

%e 1,12,26,12,1,

%e 1,16,55,55,16,1,

%e 1,20,96,156,96,20,1,

%e 1,24,149,354,354,149,24,1,

%e 1,28,214,688,1037,688,214,28,1,

%e ...

%Y Cf. A347672, A347675.

%Y Row 3 is A347677.

%K nonn,tabl

%O 1,5

%A _N. J. A. Sloane_, Sep 10 2021

%E a(45)-a(66) from _Michael S. Branicky_, Sep 14 2021