A305005 Number of labeled clutters (connected antichains) spanning some subset of {1,...,n} without singleton edges.

1, 1, 2, 9, 111, 6829, 7783192, 2414627236071, 56130437209370100252463

Offset

0,3

Links

Table of n, a(n) for n=0..8.

Gus Wiseman, Sequences enumerating clutters, antichains, hypertrees, and hyperforests, organized by labeling, spanning, and allowance of singletons.

Formula

Binomial transform of A048143 if we assume A048143(1) = 0.

a(n) = A198085(n) - n + 1. - Gus Wiseman, Jun 11 2018

Example

The a(3) = 9 clutters:
  {}
  {{1,2}}
  {{1,3}}
  {{2,3}}
  {{1,2,3}}
  {{1,2},{1,3}}
  {{1,2},{2,3}}
  {{1,3},{2,3}}
  {{1,2},{1,3},{2,3}}

Crossrefs

Cf. A048143, A198085, A261006, A304912, A304981, A304982, A304983, A304984, A304985, A304986.

Sequence in context: A290714 A062498 A339015 * A326267 A337043 A008269

Adjacent sequences: A305002 A305003 A305004 * A305006 A305007 A305008

Keyword

nonn

Author

Gus Wiseman, May 23 2018

Status

approved