A273988 The number of slim, rectangular lattices of length n>=2.

1, 2, 6, 19, 78, 387, 2327, 16384, 132336, 1203145, 12146959, 134749221, 1628840129, 21308361378, 299940041508, 4520381905248, 72625922986869, 1239160455312246, 22377511072312218, 426411855436193451, 8550614540544797370, 179989316790109543775, 3968315581691624472787, 91451247683519227059456

Offset: 2

Author

Tamas Dekany, Jun 06 2016

Keywords

• nonn

Comments

The initial term is the four element diamond shape lattice.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 2..400
• Gábor Czédli, Tamás Dékány, Gergő Gyenizse, Júlia Kulin, The number of slim rectangular lattices, Algebra Universalis, 2016, Volume 75, Issue 1, pp 33-50

Crossrefs

Cf. A000085, A273596.

Formula

a(n) = 1/2*( A273596(n) + Sum_{k=1..floor(n/2)} binomial(n-k-1,k-1)*A000085(n-2k) ).

a(n) ~ exp(2) * n! / (2*n^2). - Vaclav Kotesovec, Jun 30 2016