In terms of Fibonacci sequence
Source: Iranian National Olympiad (3rd Round) 2008
September 12, 2008
functioncombinatorics proposedcombinatorics
Problem Statement
Let be a sequence that:
\left\{
\begin{array}{cc}
S_0\equal{}0\hfill\\
S_1\equal{}1\hfill\\
S_n\equal{}S_{n\minus{}1}\plus{}S_{n\minus{}2}\plus{}F_n& (n>1)
\end{array}
\right.
such that is Fibonacci sequence such that F_1\equal{}F_2\equal{}1. Find in terms of Fibonacci numbers.