1,3

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

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.

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

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

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

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

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

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

So a(3)=4.

Sequence in context: A116868 A049976 A032789 this_sequence A034921 A038222 A038629

Adjacent sequences: A089240 A089241 A089242 this_sequence A089244 A089245 A089246

nonn

Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)