A347699 Triangle read by rows: For n >= 1, 0 <= k <= n-1, T(n,k) = 0 if k=0, otherwise the number of inequivalent k X (n-k) 0,1 matrices having at least one 1 in each column.

1, 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 6, 9, 4, 1, 1, 9, 23, 17, 5

Offset: 1

Author

N. J. A. Sloane, Oct 13 2021

Keywords

• nonn
• tabl
• more

Comments

It appears that this is essentially the same as the triangle in A055080, except that the 1's at the ends of the rows in A055080 have been moved to the start of the rows. (This is at present only a conjecture.)

Even if the conjecture turns out to be true, this triangle deserves its own entry because the arrays look so different.

The conjecture would imply the row sums are given by A048194.

Examples

			Triangle begins:
  1;
  1,  1;
  1,  1,  2;
  1,  1,  4,  3;
  1,  1,  6,  9,  4;
  1,  1,  9, 23, 17,  5;
...
		

Links

• H. Sharp, Jr., Enumeration of vacuously transitive relations, Discrete Math. 4 (1973), 185-196.

Crossrefs

Cf. A048194, A055080, A347700.