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

%I A347672 #24 Oct 19 2021 23:44:02
%S A347672 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,
%T A347672 463,50,1,1,66,903,3324,3324,903,66,1,1,84,1585,9074,16355,9074,1585,
%U A347672 84,1,1,104,2579,21168,61267,61267,21168,2579,104,1,1,126,3963,44028,188153,306352,188153,44028,3963,126,1
%N A347672 Array read by antidiagonals: T(n,k) (n>=1, k>=1) = number of Baxter matrices of size n X k.
%H A347672 Michael S. Branicky, <a href="/A347672/b347672.txt">Table of n, a(n) for n = 1..96</a>
%H A347672 Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/baxter-matrices.pdf">Baxter matrices</a>, Preprint, Sep 05 2021.
%H A347672 George Spahn, <a href="https://arxiv.org/abs/2110.09688">Counting Baxter Matrices</a>, arXiv:2110.09688 [math.CO], 2021.
%e A347672 The array begins:
%e A347672 1,1,1,1,1,1,1, ...
%e A347672 1,6,14,24,36,50,66, ...
%e A347672 1,14,69,203,463,903,1585, ...
%e A347672 1,24,203,972,3324,9074,21168, ...
%e A347672 1,36,463,3324,16355,61267,188153, ...
%e A347672 1,50,903,9074,61267,306352,1219598, ...
%e A347672 1,66,1585,21168,188153,1219598,6175181, ...
%e A347672 ...
%e A347672 The first few antidiagonals are:
%e A347672 1,
%e A347672 1,1,
%e A347672 1,6,1,
%e A347672 1,14,14,1,
%e A347672 1,24,69,24,1,
%e A347672 1,36,203,203,36,1,
%e A347672 1,50,463,972,463,50,1,
%e A347672 1,66,903,3324,3324,903,66,1,
%e A347672 1,84,1585,9074,16355,9074,1585,84,1,
%e A347672 ...
%Y A347672 Row 2 is A028557, row 3 is A347673, main diagonal is A347674.
%Y A347672 Cf. A347675, A347676.
%K A347672 nonn,tabl
%O A347672 1,5
%A A347672 _N. J. A. Sloane_, Sep 10 2021
%E A347672 a(25) corrected by and a(46)-a(66) from _Michael S. Branicky_, Sep 14 2021