# Is there a closed form or series representation for this linear recurrence?

Define the linear recurrence $a_n=F_na_{n-1}+a_{n-2}$ with $a_0=1$, $a_1=2$, and $F_n$ being the Fibonacci series ($F_0=F_1=1$). Is there a possible closed form for $a_n$, or even a series representation? I've looked at several resources, but many of them just deal with recurrences with constant coefficients.

• Check again your recursive formula. – hamam_Abdallah Dec 27 '16 at 15:10
• Is the second term really $an$, or did you mean $a_n$, or even $a_{n-2}$? – J. M. is a poor mathematician Dec 27 '16 at 15:10
• I have often seen two definitions of Fibonacci series. Either $F_0=0$ and $F_1=1$ or $F_0=F_1=1$. Which definition are you using here? – Noble Mushtak Dec 27 '16 at 15:13
• @J.M.isn'tamathematician Sorry, forgot an underscore – LegionMammal978 Dec 27 '16 at 15:24
• This is A026822 in OEIS. There's not much more information there. – rogerl Dec 27 '16 at 15:32