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A128941
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Cardinality of the free modular lattice generated by two elements and a chain of length n.
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1
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4, 28, 138, 629, 2784, 12134, 52366, 224404, 956514, 4060036, 17175130, 72454073, 304941384, 1280898302, 5371301502, 22491017756, 94055344242, 392888085098, 1639534704630, 6835739258996, 28477594607346, 118551827347574
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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.
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REFERENCES
| G. Birkoff, Lattice Theory, American Mathematical Society, third edition (1967), pp. 63-64 [for the case n = 1].
M. P. Schutzenberger, Construction du treillis modulaire engendre par deux elements et une chaine finie discrete, 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].
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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.
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CROSSREFS
| Sequence in context: A196514 A131459 A139736 * A051536 A043013 A145544
Adjacent sequences: A128938 A128939 A128940 * A128942 A128943 A128944
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KEYWORD
| nonn
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AUTHOR
| Lyle Ramshaw (lyle.ramshaw(AT)hp.com), Apr 08 2008
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 05 2010
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