Use f(0)=3\displaystyle {f{{\left({0}\right)}}}=-{3} and f(1)=1\displaystyle {f{{\left({1}\right)}}}=-{1} to compute f(4)\displaystyle {f{{\left({4}\right)}}}  given:

 f(p+2)=1f(p)+1f(p+1)\displaystyle {f{{\left({p}+{2}\right)}}}=\frac{{1}}{{f{{\left({p}\right)}}}}+\frac{{1}}{{f{{\left({p}+{1}\right)}}}} 

 f(4)=\displaystyle {f{{\left({4}\right)}}}=