OFFSET
1,3
COMMENTS
A clutter is a set of sets comprising a connected antichain in the Boolean algebra B_n. A blob is defined as a clutter that cannot be capped by a tree.
LINKS
Louis J. Billera, On the Composition and Decomposition of Clutters, J. Combinatorial Theory 11, 234-245 (1971).
Gus Wiseman, Every Clutter is a Tree of Blobs (preprint)
FORMULA
Every clutter is a tree of blobs, so we have A048143(n) = Sum_p n^(k-1) Prod_i a(|p_i|+1), where the sum is over all set partitions U(p_1,...,p_k) = {1,...,n-1}.
EXAMPLE
The a(3)=2 blobs are: {{1,2,3}}, {{1,2},{1,3},{2,3}}.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 22 2016
STATUS
approved