F(n+m+1)=F(n+1)F(m+1)+F(n)F(m)

Theorem

The following formula holds: $$F(n+m+1)=F(n+1)F(m+1)+F(n)F(m),$$ where $F(n)$ denotes a Fibonacci number.

References

• S.L. Basin and V.E. Hoggatt, Jr.: A Primer on the Fibonacci Sequence Part I (1963)... (previous)... (next) (uses $p$ instead of $m$)