A128941 Cardinality of the free modular lattice generated by two elements and a chain of length n.

4, 28, 138, 629, 2784, 12134, 52366, 224404, 956514, 4060036, 17175130, 72454073, 304941384, 1280898302, 5371301502, 22491017756, 94055344242, 392888085098, 1639534704630, 6835739258996, 28477594607346, 118551827347574

Offset: 0

Author

Lyle Ramshaw (lyle.ramshaw(AT)hp.com), Apr 08 2008

Keywords

• nonn

Comments

If you choose to adjoin a top and a bottom element to each resulting lattice, you must add 2 to these cardinalities: see A137400.

Examples

			When n = 0, the lattice consists of the two elements, their meet and their join, so a(0) = 4.
When n = 1, we get the free modular lattice generated by three elements, so a(1) = 28.
		

References

• G. Birkoff, Lattice Theory, American Mathematical Society, third edition (1967), pp. 63-64 [for the case n = 1].

Links

• M. P. Schützenberger, Construction du treillis modulaire engendré par deux éléments et une chaine finie discrète, Comptes Rendus de lAcad. Sci. Paris, vol. 235 (1952), pp. 926-928.
• K. Takeuchi, On free modular lattices II, Tohoku Mathematical Journal (2), vol. 11 (1959), pp. 1-12 [for the case n = 2].

Crossrefs

Cf. A137400.

Extensions

More terms from Vladeta Jovovic, Feb 05 2010