%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_
