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

0,5

Comments

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

Links

Table of n, a(n) for n=0..27.

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.

Example

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;
  ...

Crossrefs

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

Sequence in context: A176435 A133722 A204155 * A355673 A160390 A002194

Adjacent sequences: A363229 A363230 A363231 * A363233 A363234 A363235

Keyword

nonn,tabl,more

Author

Geoffrey Critzer, May 22 2023

Status

approved