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A097391 The number of hierarchies with at least one subhierarchy composed of exactly 2 levels and no subhierarchy with more than 2 levels. 1
0, 1, 3, 8, 17, 37, 71, 138, 252, 458 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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) = 17 hierarchies where at least one subhierarchy has exactly 2 levels (and no level l > 2 is allowed):

4|1; 1|4; 3|2; 2|3; 2|2:1; 2|1:2; 1|2:2; 2|1:1|1; 1|2:1|1; 2|1:1:1; 1|2:1:1;

1|1:1:1:1; 1|3:1; 3|1:1; 1|1:2:1; 1|1:1|1:1; 1|1:3.

CROSSREFS

Cf. A034691, A097237, A097392, A000041.

Sequence in context: A106691 A140176 A238496 * A202554 A034481 A295061

Adjacent sequences:  A097388 A097389 A097390 * A097392 A097393 A097394

KEYWORD

nonn

AUTHOR

Thomas Wieder, Aug 13 2004

STATUS

approved

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Last modified October 2 23:51 EDT 2022. Contains 357230 sequences. (Running on oeis4.)