A057149 Triangle T(n,k) of n X n binary matrices with k ones, with no zero rows or columns, up to row and column permutation.

0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 5, 4, 3, 1, 1, 0, 0, 0, 0, 1, 2, 11, 21, 34, 33, 33, 19, 14, 6, 3, 1, 1, 0, 0, 0, 0, 0, 1, 2, 14, 49, 131, 248, 410, 531, 601, 566, 474, 336, 222, 124, 67, 32, 16, 6, 3, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 15, 69, 288, 840, 2144, 4488, 8317, 13160

Offset: 1

Author

Vladeta Jovovic, Aug 14 2000

Keywords

• nonn
• tabf

Comments

Row sums give A054976.

Examples

			[0,1], [0,0,1,1,1], [0,0,0,1,2,5,4,3,1,1],...;
T(4,6)=11, i.e. there are 11 4 X 4 binary matrices with 6 ones, with no zero rows or columns, up to row and column permutation:
[0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1]
[0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 1 0]
[0 0 0 1] [0 0 1 0] [0 0 1 0] [0 0 1 1] [0 1 1 0] [0 0 1 1]
[1 1 1 0] [1 1 0 1] [1 1 1 0] [1 1 0 0] [1 0 1 0] [1 1 0 0]
and
[0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1] [0 0 0 1]
[0 0 1 0] [0 0 1 0] [0 0 1 0] [0 0 1 0] [0 0 1 0]
[0 1 0 0] [0 1 0 1] [0 1 0 1] [0 1 0 1] [1 1 0 0]
[1 0 1 1] [1 0 0 1] [1 0 1 0] [1 1 0 0] [1 1 0 0].
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1029
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A056080, A056037, A056079, A057150-A057152, A049311.