1,2

N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, Order 21 (2004), 83-89.

Thomas Wieder, Home Page.

Thomas Wieder, Old Home Page.

egf = exp(-(exp(z)^2-2*exp(z)+1)/(-2+exp(z)))

a(3) = 12. Let : denote the partition of n labeled individuals 1,2,3,4 into

x=2 sets (i.e. "societies"). E.g. in 12:34 one has a single society

with members 1 and 2 and a further single society with members 3 and 4.

Let | denote a higher level (within a single society), e.g. in 1|2 the

individual 2 is one level up with respect to individual 1. The order of

indiviuals on a level is insignificant, eg. 12|34 is equivalent to

21|43. For n = 3 and x = 2 one has

12|3; 23|1; 13|2; 1|23; 2|13; 3|12; 1|2|3; 2|3|1; 3|1|2; 1|3|2; 3|2|1;

2|1|3;

which gives 12 different societies with at least 2 occupied levels.

with(combstruct); SetSeq2SetL:=[T, {T=Set(S), S=Sequence(U, card>=2), U=Set(Z, card >= 1)}, labeled]; #where x is an integer 1, 2, 3, ... # x=2 gives 2 levels per society. seq(count(SetSeq2SetL, size=j), j=1..12);

Cf. A075729, A097236.

Adjacent sequences: A097234 A097235 A097236 this_sequence A097238 A097239 A097240

Sequence in context: A105927 A052887 A052867 this_sequence A055531 A059435 A143923

nonn

Thomas Wieder (wieder.thomas(AT)t-online.de), Aug 02 2004