growing binary trees

[Ralf Stephan]

Simon, sorry for the cryptic reply.

In other words:

Let n>=0, and your sequence a(n) = 1, 2, 3, 4, 6, 8, 10, 13, 17, 21, 
26, 33, 41, 50, 62, 77, 94, 115, 142, 174, 212, 260, 319, ...

then 

A079398(n) = a(n-2) - a(n-1) 
A122511(n) = a(n+1) - a(n)      
A017817(n) = A122511(n+3) - A122511(n+2)

All of these sequences satisfy the recurrence
a(n) = a(n-2) + a(n-3) + c

and are thus related to the Padovan sequence A000931.
With your sequence, c appears to be 3 but this has
to be proved, and all of the above is only a conjecture,
based on solid evidence, though.


ralf