A278691 Number of graded lattices on n nodes.

1, 1, 1, 2, 4, 9, 22, 60, 176, 565, 1980, 7528, 30843, 135248, 630004, 3097780, 15991395, 86267557, 484446620, 2822677523, 17017165987

Offset: 1

Author

Jukka Kohonen, Nov 26 2016

Keywords

• nonn
• more

Comments

A finite lattice is graded if, for any element, all paths from the bottom to that element have the same length.

Links

• J. Heitzig and J. Reinhold, Counting finite lattices, Algebra Universalis, 48 (2002), 43-53.
• J. Kohonen, Generating modular lattices up to 30 elements, arXiv:1708.03750 [math.CO] preprint (2017).
• M. Malandro, The unlabeled lattices on <=15 nodes, (listing of lattices; graded lattices are a subset of these).

Crossrefs

Cf. A006966 (lattices), A229202 (semimodular lattices).

Extensions

a(16)-a(21) from Kohonen (2017), by Jukka Kohonen, Aug 15 2017