[seqfan] A328074 Coordination sequence depends on the generation number

[Lars Blomberg]

Hello Seqfans,

 

Trying to extend this sequence I found that the coordination sequence (cs)
varies according to which generation is used to compute it.

Generation      Coordination sequence

0                           1

1                           1, 12

2                           1, 12, 16

3                           1, 12, 16, 16

4                           1, 12, 16, 16, 16

5                           1, 12, 16, 16, 40, 52, 96

6                           1, 12, 16, 16, 16, 40, 52, 96

7                           1, 12, 16, 16, 40, 52, 96, 84, 72, 92, 128, 104

8                           1, 12, 16, 16, 16, 40, 52, 96, 84, 72, 92, 128,
104

9                           1, 12, 16, 16, 40, 52, 96, 84, 72, 92, 128, 104,
68, 104, 112, 148, 168

10                        1, 12, 16, 16, 16, 40, 52, 96, 84, 72, 92, 128,
104, 68, 104, 112, 148, 168

It looks from this like there are two variants of cs, but further
computations show there to be more than that.

In the center there is a square of size 3^k/5^k which is unique among all
the squares (k is not generation number).

For each generation one can make a sorted list of all square sizes and note
the position of the center square.

>From this it seems that one can determine which cs variant belongs to that
generation.

 

What is the best way to handle this?

 

/Lars