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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.
0
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
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
KEYWORD
nonn,tabl,more
AUTHOR
Geoffrey Critzer, May 22 2023
STATUS
approved