Sequence relating to Pell numbers; a new technique

[creigh at o2online.de]

Thank you for that comment! 

Using the new technique described in the last posting on another ex.,
I get:  A022095(n) = 2Fib(n) + Fib(n+5)
Name A022095:  Fibonacci sequence beginning 1 5.

Surely this relation is already known...?

Sincerely, 
Creighton 

>Remember that P(n) can be computed with the help of the general >formula for 
computing the convergents. Thus, 
>
>P(n+2) = 2 P(n+1) + P(n) 
>
>and the formula above can be written: 
>a(n) = 1/2 * ( P(n+2) + 3 P(n+1) - 1) 
>
>or (by substituting again): 
>a(n) = 1/2 * ( 5 P(n+1) + P(n) - 1) 
>
>Regards, 
>
-- 
>Thomas Baruchel