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A097392 The number of hierarchies with at least one subhierarchy composed of exactly 3 levels and no subhierarchy with more than 3 levels. 1
0, 0, 1, 4, 12, 32, 78, 183, 408, 886 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..10.

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

EXAMPLE

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.

CROSSREFS

Cf. A034691, A097237, A097391, A000041.

Sequence in context: A260145 A260778 A118885 * A090634 A260186 A097067

Adjacent sequences:  A097389 A097390 A097391 * A097393 A097394 A097395

KEYWORD

nonn

AUTHOR

Thomas Wieder, Aug 13 2004

STATUS

approved

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Last modified October 6 18:21 EDT 2022. Contains 357270 sequences. (Running on oeis4.)