A006966 -id:A006966 - cp's OEIS frontend

A271078 Number of non-isomorphic atomic lattices on n nodes.

0, 1, 1, 0, 1, 1, 2, 4, 9, 22, 59, 181

Offset: 0

Jori Mäntysalo, Mar 30 2016

for i in range(0, 12):
    n = 0
    for P in Posets(i):
        if P.is_lattice():
            L = LatticePoset(P)
            if L.is_atomic():
                n += 1
    print(n)

A373922 Number of lattices on n unlabeled nodes, up to duality.

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 11, 33, 129, 577, 3113, 19092, 132318, 1011665

Offset: 0

Jukka Kohonen, Jun 30 2024

Number of nonisomorphic lattices on n nodes, when from each pair of dual lattices only one is counted.

			a(5)=4: These are the four lattices. The dual of the last one is not counted.
  o      o        o       o
  |     / \      /|\      |
  o    o   |    o o o     o
  |    |   o     \|/     / \
  o    o   |      o     o   o
  |     \ /              \ /
  o      o                o
  |
  o

Volker Gebhardt and Stephen Tawn, Catalogue of unlabelled lattices on up to 16 elements, Western Sydney University (2018).

a(n) = (A006966(n) + A373894(n)) / 2.

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A271078 Number of non-isomorphic atomic lattices on n nodes.

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A373922 Number of lattices on n unlabeled nodes, up to duality.

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