[seqfan] An interesting series of sequences related to A358094

[Yifan Xie]

Dear SeqFans,


Consider the following series of sequences:
a(n) is the number of ways n can be reached in the following method: we start with 1, then add or multiply alternately, and each operand must be included in the set A.
Let A be {2, 3}, then the generated sequence is A358094.
Let A be {2, 3, 4}=A1, {3, 4, 5}=A2, {4, 5, 6}=A3, etc. These sequences have very distinct graphs: (See attached files)
As for A1, the sequence pattern is generally increasing with a major gap between two clusters. The fitting upper bond is approximately 0.3791*x^1.2667.
As for A2 and A3, the increasing patterns are not so apparent, but it appears that the graphs have periodic patterns.
These are interesting problems, so I want to share them with SeqFans.


Best regards,


Yifan Xie (xieyifan4013 at 163.com)