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

1,6

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.

Links

Table of n, a(n) for n=1..21.

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

Example

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

Crossrefs

Cf. A048194, A055080, A347700.

Sequence in context: A177976 A034781 A110470 * A055080 A034367 A058717

Adjacent sequences: A347696 A347697 A347698 * A347700 A347701 A347702

Keyword

nonn,tabl,more

Author

N. J. A. Sloane, Oct 13 2021

Status

approved