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.

1, 2, 8, 68, 1270, 53200, 5068960, 1109820882, 562711290616, 664773220895406

Offset: 1

Author

Günter Rote, Feb 18 2020

Keywords

• nonn
• more

Comments

Defined in Felsner, Definition 2.

Examples

			For n = 3, all nine 0-1-matrices with the correct number of zeros and ones in each row are replace matrices except
    [ 1 0 1 ]
A = [ 1 0 0 ]
    [ 0 0 0 ]
		

Links

• Stefan Felsner, On the number of arrangements of pseudolines, preprint.
• Stefan Felsner, On the number of arrangements of pseudolines, Discrete & Computational Geometry, 18 (1997), 257-267.

Formula

According to [Felsner, Theorem 2] the number is at most 2^(0.6974*n^2) for large n.

Extensions

a(8)-a(9) from Giovanni Resta, Feb 19 2020

a(10) from Giovanni Resta, Feb 21 2020