Sequence relating to Pell numbers; a new technique

[creigh at o2online.de]

>
>So my point (which I was trying not to make by not sending but am >now forced 
to because of my mistake), is that 1) there are always >intersting identities 
to be found and similarly 2) there are always new >sequences which aren't 
yet in the OEIS. 
>
>Mitch 

I'm glad you mentioned this. I am aware of 2)- for ex., 
it was important (at least for me) to confirm that 
a way had been found to generate infinitely many 
sequences of the form:
http://www.research.att.com/projects/OEIS?Anum=A097947
Of course, I did not begin the long procedure of submitting  
these sequences to OEIS.  

I wrote "has this been seen before?"
>I get: A022095(n) = 2Fib(n) + Fib(n+5) 
but should have simply written: has anyone observed
all the 5's in there?
Refering to:
1. A022095 is the Fibonacci sequence beginning 1 5
2. Fib certainly has a lot to do with the number 5
3.  A term involved is Fib(n+5), etc. 

Just to add... two other areas of interest for me at them moment:

- Why is FAMP spitting out any of these sequences in the first place? 
(FAMP certainly wasn't explicitly constructed to work out recurrence relations, 
among other things). Also, one would think that minutely 
changing a floretion which generates, say, Fib via "ves" would
lead to "Fib at 0 3" or "Fib at 1 7". It usually doesn't (as stated, 
it was only the "new method" which allowed me to see  Fib at 
0 5 for the first time) - instead, it gives some alltogether new sequence 
which is generally related to the first but on a deeper level-
reminding the reader that the Smith College, Fibonacci, and
Lucas sequences were generated by three floretions
which look almost exaclty the same...) 

- How does a minute change to a floretion, such as replacing a minus 
sign with a plus sign, affect the resulting integer sequence? I would really
like to know, for ex., exactly how the symmetry of a given floretion 
must be altered in order to generate its binomial transform. 

Sincerely, 
Creighton