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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.

%I A347675 #16 Sep 16 2021 03:35:39
%S A347675 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,
%T A347675 1,42,240,172,172,240,42,1,1,56,490,744,92,744,490,56,1,1,72,896,2364,
%U A347675 956,956,2364,896,72,1,1,90,1512,6174,5328,422,5328,6174,1512,90,1
%N 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.
%H A347675 Michael S. Branicky, <a href="/A347675/b347675.txt">Table of n, a(n) for n = 1..96</a>
%H A347675 Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/baxter-matrices.pdf">Baxter matrices</a>, Preprint, Sep 05 2021.
%F A347675 a(n) <= A347672(n). - _Michael S. Branicky_, Sep 15 2021
%e A347675 The array begins:
%e A347675 1,1,1,1,1,1,1,...
%e A347675 1,2,6,12,20,30,42,...
%e A347675 1,6,6,32,100,240,490,...
%e A347675 1,12,32,22,172,744,2364,...
%e A347675 1,20,100,172,92,956,5328,...
%e A347675 1,30,240,744,956,422,5492,...
%e A347675 1,42,490,2364,5328,5492,2074,...
%e A347675 ...
%e A347675 The first few antidiagonals are:
%e A347675 1,
%e A347675 1,1,
%e A347675 1,2,1,
%e A347675 1,6,6,1,
%e A347675 1,12,6,12,1,
%e A347675 1,20,32,32,20,1,
%e A347675 1,30,100,22,100,30,1,
%e A347675 1,42,240,172,172,240,42,1,
%e A347675 1,56,490,744,92,744,490,56,1,
%e A347675 ...
%Y A347675 Cf. A347672, A347676.
%Y A347675 The main diagonal is A001181.
%K A347675 nonn,tabl
%O A347675 1,5
%A A347675 _N. J. A. Sloane_, Sep 10 2021
%E A347675 a(46)-a(66) from _Michael S. Branicky_, Sep 14 2021