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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

Table of n, a(n) for n=1..8.

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

Cf. A048143 (clutters), A030019 (hypertrees), A052888 (tail trees).

Sequence in context: A290879 A054914 A329021 * A291808 A161745 A048566

Adjacent sequences:  A275304 A275305 A275306 * A275308 A275309 A275310

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Jul 22 2016

STATUS

approved

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Last modified July 10 13:04 EDT 2020. Contains 335576 sequences. (Running on oeis4.)