A322067 Size of the free distributive lattice on the meet semilattice of partitions.

2, 3, 10, 328

Offset

1,1

Links

Table of n, a(n) for n=1..4.

Example

n=1: There is one partition of {1}, and the free distributive lattice on this (the unique) one-element meet-semilattice has a(1)=2 elements.
n=2: There are two partitions of {1,2}, and the free distributive lattice on this (the unique) two-element meet-semilattice has a(2)=3 elements.
n=3: There are five partitions of {1,2,3}, and the free distributive lattice on the meet semilattice {123, 12, 23, 13, top) has a(3)=10 elements.
n=4: There are 15 partitions of {1,2,3,4}, and the free distributive lattice on this meet-semilattice has
     328 = 1            +
           C(6,0) * 2^7 +
           C(6,1) * 2^4 +
           C(6,2) * 2^2 +
           C(6,3)       +
           C(6,4)       +
           C(6,5)       +
           C(6,6)       +
           1
elements, where the C(n,k) are binomial coefficients.

Crossrefs

Cf. A000110, A000372.

Sequence in context: A364140 A358391 A132536 * A302250 A290638 A330294

Adjacent sequences: A322064 A322065 A322066 * A322068 A322069 A322070

Keyword

nonn,more

Author

David Spivak, Nov 25 2018

Status

approved