A128941 - OEIS

%I #8 May 01 2024 13:43:19

%S 4,28,138,629,2784,12134,52366,224404,956514,4060036,17175130,

%T 72454073,304941384,1280898302,5371301502,22491017756,94055344242,

%U 392888085098,1639534704630,6835739258996,28477594607346,118551827347574

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

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

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

%H M. P. Schützenberger, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k31876/f926.item">Construction du treillis modulaire engendré par deux éléments et une chaine finie discrète</a>, Comptes Rendus de lAcad. Sci. Paris, vol. 235 (1952), pp. 926-928.

%H K. Takeuchi, <a href="https://doi.org/10.2748/tmj/1178244623">On free modular lattices II</a>, Tohoku Mathematical Journal (2), vol. 11 (1959), pp. 1-12 [for the case n = 2].

%e When n = 0, the lattice consists of the two elements, their meet and their join, so a(0) = 4.

%e When n = 1, we get the free modular lattice generated by three elements, so a(1) = 28.

%Y Cf. A137400.

%K nonn

%O 0,1

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

%E More terms from _Vladeta Jovovic_, Feb 05 2010