{Fsubn} n>=o is defined Fsub0=0, Fsub1=1, fsub(n+2) = fsub(n+1) + fsub(n) [fibonacci]. Show for all n>=0:

Sum [(m, k=0) F^2(subk)] = Fsubm * Fsub(m+1).

So I got this far:

Induction shows 0 to work.

Sum + (m+1)^2 = Fsubm + Dsub(m+1) + (m+2)^2 = Fsub(m+1) * Fsub(m+2)

Fsub(m+1) * Fsub(m+2) = Fsub(m+1) * [Fsub(m+1) + Fsubm] = Fsubm * Fsub(m+1) + Fsub(m+1) * Fsub(m+1)

As far as I got.