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A332637 The number of n X n replace matrices: binary matrices A where the i-th row contains exactly i zeros and A[i,j] >= A[j,i] for all i < j.

%I A332637 #24 Feb 22 2020 05:45:34
%S A332637 1,2,8,68,1270,53200,5068960,1109820882,562711290616,664773220895406
%N A332637 The number of n X n replace matrices: binary matrices A where the i-th row contains exactly i zeros and A[i,j] >= A[j,i] for all i < j.
%C A332637 Defined in Felsner, Definition 2.
%H A332637 Stefan Felsner, <a href="http://page.math.tu-berlin.de/~felsner/Paper/numarr.pdf">On the number of arrangements of pseudolines</a>, preprint.
%H A332637 Stefan Felsner, <a href="https://doi.org/10.1007/PL00009318">On the number of arrangements of pseudolines</a>, Discrete & Computational Geometry, 18 (1997), 257-267.
%F A332637 According to [Felsner, Theorem 2] the number is at most 2^(0.6974*n^2) for large n.
%e A332637 For n = 3, all nine 0-1-matrices with the correct number of zeros and ones in each row are replace matrices except
%e A332637     [ 1 0 1 ]
%e A332637 A = [ 1 0 0 ]
%e A332637     [ 0 0 0 ]
%K A332637 nonn,more
%O A332637 1,2
%A A332637 _Günter Rote_, Feb 18 2020
%E A332637 a(8)-a(9) from _Giovanni Resta_, Feb 19 2020
%E A332637 a(10) from _Giovanni Resta_, Feb 21 2020