OFFSET
1,5
COMMENTS
Also number of unlabeled split graphs on n vertices and with a k-element clique (cf. A048194).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
R. J. Clarke, Covering a set by subsets, Discrete Math., 81 (1990), 147-152.
Vladeta Jovovic, Binary matrices up to row and column permutations
G. F. Royle, Counting Set Covers and Split Graphs, J. Integer Seqs., 3 (2000), #00.2.6.
Eric Weisstein's World of Mathematics, Minimal covers
FORMULA
EXAMPLE
Triangle begins:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 6, 9, 4, 1;
1, 9, 23, 17, 5, 1;
1, 12, 51, 65, 28, 6, 1;
1, 16, 103, 230, 156, 43, 7, 1;
1, 20, 196, 736, 863, 336, 62, 8, 1;
...
There are four minimal covers of an unlabeled 3-set: one 1-cover {{1,2,3}}, two 2-covers {{1,2},{3}}, {{1,2},{1,3}} and one 3-cover {{1},{2},{3}}.
PROG
(PARI) \\ Needs A(n, m) from A028657.
T(n, k) = A(n-k, k) - if(k<n, A(n-1-k, k))
{ for(n=1, 10, for(k=1, n, print1(T(n, k), ", ")); print) } \\ Andrew Howroyd, Feb 28 2023
KEYWORD
nonn,tabl
AUTHOR
Vladeta Jovovic, Jun 13 2000
STATUS
approved