A128941 - OEIS

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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

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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