Paired Fibonacci recurrence
= Paired Fibonacci recurrence
{title2=$(F_{n+1},F_{n+2})=(F_{n+1},F_n+F_{n+1})$}
Compute adjacent <Fibonacci numbers> together, starting at $(0,1)$ and applying $(a,b)\mapsto(b,a+b)$. The shared pair avoids repeating the same recursive subproblem and gives $n$ additions for $F_n$. This counts arithmetic operations; exact <integers> grow with $n$.