Abstract: 
Linear recurrences with constant coefficients are an
interesting class of recurrence equations that can be solved
explicitly. The most famous example are certainly the Fibonacci
numbers with the equation f(n) =
f(n1) +
f(n  2) and the quite
nonobvious closed form
(φ^{n}

(φ)^{n})
/ √5 where φ is the golden ratio.
In this work, I build on existing tools in
Isabelle – such as formal power series and polynomial
factorisation algorithms – to develop a theory of these
recurrences and derive a fully executable solver for them that can be
exported to programming languages like Haskell. 
BibTeX: 
@article{Linear_RecurrencesAFP,
author = {Manuel Eberl},
title = {Linear Recurrences},
journal = {Archive of Formal Proofs},
month = oct,
year = 2017,
note = {\url{https://isaafp.org/entries/Linear_Recurrences.html},
Formal proof development},
ISSN = {2150914x},
}
