Use f(0)=6\displaystyle {f{{\left({0}\right)}}}=-{6} and f(1)=2\displaystyle {f{{\left({1}\right)}}}=-{2} to compute f(5)\displaystyle {f{{\left({5}\right)}}}  given:

 f(p+2)=4f(p)3f(p+1)+6\displaystyle {f{{\left({p}+{2}\right)}}}=-{4}{f{{\left({p}\right)}}}-{3}{f{{\left({p}+{1}\right)}}}+{6} 

 f(5)=\displaystyle {f{{\left({5}\right)}}}=