A363232 Triangular array read by rows. T(n,k) is the number of idempotent Boolean relation matrices with rank k, n >= 0, 0 <= k <= n.

1, 1, 1, 1, 7, 3, 1, 37, 66, 19, 1, 175, 975, 990, 219, 1, 781, 12090, 32575, 23345, 4231, 1, 3367, 135903, 866550, 1514610, 814903, 130023

Offset: 0

Author

Geoffrey Critzer, May 22 2023

Keywords

• nonn
• tabl
• more

Comments

Explicit formulas for columns k=0,1,2,3,4 are given in the Butler-Markowsky link.

Examples

			Triangle begins:
  1;
  1,    1;
  1,    7,      3;
  1,   37,     66,     19;
  1,  175,    975,    990,    219;
  1,  781,  12090,  32575,   23345,   4231;
  1, 3367, 135903, 866550, 1514610, 814903, 130023;
  ...
		

Links

• K. K.-H. Butler and G. Markowsky, The Number of Maximal Subgroups of the Semigroup of Binary Relations, Kyungpook Math. J. Vol 12, June 1972.

Crossrefs

Cf. A121337 (row sums), A001035 (main diagonal), A005061 (column k=1).