login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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

%I #21 Jul 02 2016 02:26:19

%S 1,2,6,19,78,387,2327,16384,132336,1203145,12146959,134749221,

%T 1628840129,21308361378,299940041508,4520381905248,72625922986869,

%U 1239160455312246,22377511072312218,426411855436193451,8550614540544797370,179989316790109543775,3968315581691624472787,91451247683519227059456

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

%C The initial term is the four element diamond shape lattice.

%H Vaclav Kotesovec, <a href="/A273988/b273988.txt">Table of n, a(n) for n = 2..400</a>

%H Gábor Czédli, Tamás Dékány, Gergő Gyenizse, Júlia Kulin, <a href="http://dx.doi.org/10.1007/s00012-015-0363-y">The number of slim rectangular lattices</a>, Algebra Universalis, 2016, Volume 75, Issue 1, pp 33-50

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

%F a(n) ~ exp(2) * n! / (2*n^2). - _Vaclav Kotesovec_, Jun 30 2016

%Y Cf. A000085, A273596.

%K nonn

%O 2,2

%A _Tamas Dekany_, Jun 06 2016