A097392 The number of hierarchies of n labeled elements with at least one subhierarchy composed of exactly 3 levels and no subhierarchy with more than 3 levels.

0, 0, 1, 4, 12, 32, 78, 183, 408, 886

Offset: 1

Author

Thomas Wieder, Aug 13 2004

Keywords

• nonn
• more

Examples

			Let : denote the separation between two subhierarchies, e.g. 2:3 are two subhierarchies where subhierarchy s=1 contains two elements and subhierarchy s=2 contains three elements. Let | denote the separation between two levels, e.g. 2|2|1 is a hierarchy composed of three levels with two elements on levels l=1 and l=2 and one element on level l=3. For n=5 one has a(5) = 12 hierarchies where at least one subhierarchy has exactly 3 levels (and no level l > 3 is allowed):
3|1|1; 1|3|1; 1|1|3; 2|2|1; 2|1|2; 1|2|2; 1|1|1:2; 1|1|1:1:1; 1|1|1:1|1; 2|1|1:1; 1|2|1:1; 1|1|2:1.
		

Links

• N. J. A. Sloane and Thomas Wieder, The Number of Hierarchical Orderings, arXiv:math/0307064 [math.CO], 2003; Order 21 (2004), 83-89.

Crossrefs

Cf. A034691, A097237, A097391, A000041.