F(n+m+1)=F(n+1)F(m+1)+F(n)F(m)
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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.
Proof
References
- S.L. Basin and V.E. Hoggatt, Jr.: A Primer on the Fibonacci Sequence Part I (1963)... (previous)... (next) (uses $p$ instead of $m$)
