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

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

Offset: 0

Author

Jukka Kohonen, Jun 30 2024

Keywords

• nonn
• hard
• more

Comments

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

Examples

			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
		

Links

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

Formula

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