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 A089243 Number of partitions into strokes of the edges of a star graph with n edges. 2

%I

%S 0,1,3,4,9,22,55

%N Number of partitions into strokes of the edges of a star graph with n edges.

%C Two arrangements are considered the same if one is a rotation or reflection of the other.

%C A "stroke" is defined as follows. If the following conditions are satisfied then the partition to directed paths on a directed graph is called "a partition to strokes on a directed graph". And all directed paths in the partition are called "strokes". C.1. Two different directed paths in a partition do not have the same edges. C.2. A union of two different paths in a partition does not become a directed path. In other word, a "stroke" is a locally maximal path on a directed graph.

%C This sequence has its origin in the strokes made when writing Japanese Kanji.

%e n=3: this the Y graph. Call the center node "0" and the terminal nodes "1", "2", "3". Four partitions exist as follows:

%e {1->0->2, 0->3}

%e {1->0->2, 3->0}

%e {1->0, 2->0, 3->0}

%e {0->1, 0->2, 0->3}

%e So a(3)=4.

%K nonn

%O 1,3

%A _Yasutoshi Kohmoto_

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Last modified May 23 07:08 EDT 2019. Contains 323508 sequences. (Running on oeis4.)