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

0,1

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.

References

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

Links

Table of n, a(n) for n=0..21.

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].

Example

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.

Crossrefs

Cf. A137400.

Sequence in context: A139736 A259987 A241778 * A272017 A270218 A273574

Adjacent sequences: A128938 A128939 A128940 * A128942 A128943 A128944

Keyword

nonn

Author

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

Extensions

More terms from Vladeta Jovovic, Feb 05 2010

Status

approved