A118077 Number of edges in the representation of all linear extensions of the inclusion ordering on P({1,...,n}) as distributive lattice contained in P(P({1,...,n})).

1, 2, 6, 32, 454, 35512, 66584412, 2414682040997

Offset

0,2

Comments

The numbers of vertices are the Dedekind numbers (A000372) and A046873 is the total number of linear extensions.

Links

Table of n, a(n) for n=0..7.

Formula

a(n) = Sum_{m=1..C(n,floor(n/2))} A059119(n,m)*m. - Geoffrey Critzer, Aug 11 2020

Example

a(2) = 6 as the lattice is { {}, { {} }, { {}, {1} }, { {}, {2} }, { {}, {1}, {2}}, { {}, {1}, {2}, {1, 2} } }.

Prog

(Python) # using an inference method for computing the set of linear extensions of arbitrary posets.

Crossrefs

Cf. A046873, A000372, A059119.

Sequence in context: A067735 A326901 A332537 * A013976 A213435 A083666

Adjacent sequences: A118074 A118075 A118076 * A118078 A118079 A118080

Keyword

nonn,hard,more

Author

Oliver Wienand, Apr 11 2006

Extensions

a(7) added by Geoffrey Critzer, Aug 11 2020 from A059119

Status

approved