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A347676 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.

%I A347676 #24 Oct 19 2021 23:44:47
%S A347676 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 A347676 1,24,149,354,354,149,24,1,1,28,214,688,1037,688,214,28,1,1,32,291,
%U A347676 1198,2533,2533,1198,291,32,1,1,36,380,1924,5383,7632,5383,1924,380,36,1
%N A347676 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 A347676 Michael S. Branicky, <a href="/A347676/b347676.txt">Table of n, a(n) for n = 1..96</a>
%H A347676 Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/baxter-matrices.pdf">Baxter matrices</a>, Preprint, Sep 05 2021.
%H A347676 George Spahn, <a href="https://arxiv.org/abs/2110.09688">Counting Baxter Matrices</a>, arXiv:2110.09688 [math.CO], 2021.
%F A347676 a(n) <= A347672(n). - _Michael S. Branicky_, Sep 15 2021
%e A347676 The array begins:
%e A347676 1,1,1,1,1,1,1, ...
%e A347676 1,4,8,12,16,20,24, ...
%e A347676 1,8,26,55,96,149,214, ...
%e A347676 1,12,55,156,354,688,1198, ...
%e A347676 1,16,96,354,1037,2533,5383, ...
%e A347676 1,20,149,688,2533,7632,19522, ...
%e A347676 1,24,214,1198,5383,19522,59020, ...
%e A347676 ...
%e A347676 The first few antidiagonals are:
%e A347676 1,
%e A347676 1,1,
%e A347676 1,4,1,
%e A347676 1,8,8,1,
%e A347676 1,12,26,12,1,
%e A347676 1,16,55,55,16,1,
%e A347676 1,20,96,156,96,20,1,
%e A347676 1,24,149,354,354,149,24,1,
%e A347676 1,28,214,688,1037,688,214,28,1,
%e A347676 ...
%Y A347676 Cf. A347672, A347675.
%Y A347676 Row 3 is A347677.
%K A347676 nonn,tabl
%O A347676 1,5
%A A347676 _N. J. A. Sloane_, Sep 10 2021
%E A347676 a(45)-a(66) from _Michael S. Branicky_, Sep 14 2021