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A275307 Number of labeled spanning blobs on n vertices. 38
1, 1, 2, 44, 4983, 7565342, 2414249587694, 56130437054842366160898 (list; graph; refs; listen; history; text; internal format)
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).
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
Cf. A048143 (clutters), A030019 (hypertrees), A052888 (tail trees).
Sequence in context: A290879 A054914 A329021 * A356484 A291808 A161745
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Jul 22 2016
STATUS
approved

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Last modified April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)