growing binary trees

[Christian G. Bower]

 From Simon's diagrams, I can see this is analogous to Fibonacci's
rabbits. Basically, the behavior of the node is given by its age.
A node at age 0 or 1 grows and one at age 2 or 3 produces a new node.

 From this its easy to get a g.f. of

(1+x+x^2)/(1-x-x^3+x^5)

1 2 3 4 6 8 10 13 17 21 26 33 41 50 62 77 94 115 142 174 212 260 319 389
475 582 711 867 1060 1296 1581 1930 2359 2880 3514 4292 5242 6397 7809
9537

Also, the number of nodes has g.f.

1/(1-x-x^3+x^5)
1 1 1 2 3 3 4 6 7 8 11 14 16 20 26 31 37 47 58 69 85 106 128 155 192 235
284 348 428 520 633 777 949 1154 1411 1727 2104 2566 3139 3832

which isn't in the EIS either.

------ Original Message ------
From: "Simon Strandgaard" <neoneye at gmail.com>
To: njas at research.att.comCc: seqfan at ext.jussieu.fr
Subject: Re: growing binary trees

...

> visually it works like this:
> 
> step#0
>   1
> 
> 
> step#1
>   2
> 
> 
> step#2
>   3
> 
> 
> step#3
>   3
>  /
> 1
> 
> 
> step#4
>   3
>  / \
> 2   1
> 
> 
> step#5
>   3
>  / \
> 3   2
> 
> 
> step#6
>     3
>    / \
>   3   3
>  /
> 1
> 
> 
> step#7
>       3
>     /   \
>   3       3
>  / \     /
> 2   1   1
> 
> 
> step#8
>       3
>     /   \
>   3       3
>  / \     / \
> 3   2   2   1
> 
> 
> 
> --
> Simon Strandgaard
>