Should Pell be extended by one term?

[creigh at o2online.de]

Hi, 

Before submitting slight variations of the following relations as comments, I 
would like to ask: Should Pell be extended by one term?
(not to be seen as some sort of error message)

Define a(n+1) = P(n) = A000129(n), a(0) = 1.

Then (it seems) we have 

2a(n) = A001333(n+2) - A048694(n)  ( = 2P(n-1) for n > 0)

2a(n) = A001333(n+1) + 2*A001333(n) - A048655(n)  ( = 2P(n-1) for n > 0)

2a(n) = a(n+2) - A078343(n)  ( = 2P(n-1) for n > 0)

a(n) = a(n-2) + 2a(n-1), a(0) = 1, a(1) = 0  (same recurrence relation with 
different initial values)

Sincerely, 
Creighton