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, 36566354210304

Offset: 0

Author

Oliver Wienand, Apr 11 2006

Keywords

• nonn
• hard
• more

Comments

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

Examples

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

Crossrefs

Cf. A046873, A000372, A059119.

Formula

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

Extensions

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

a(7) corrected by Lennart Van Hirtum, Apr 02 2025