You are parking your car, and the meter takes only 1 and 2 dollar coins/notes. For 1 hour, there is only one way to insert the coins= 1of $1. For 2 hours, there are 2=$1+ $1 and$2. For 3 hours, there are three ways= $1 +$1+ $1,$1+$2, and$2+$1. Show the formula proving that the number of ways to insert coins for hours forms a fibonacci sequence. 2. Originally Posted by ljonz You are parking your car, and the meter takes only 1 and 2 dollar coins/notes. For 1 hour, there is only one way to insert the coins= 1of$1. For 2 hours, there are 2= $1+$1 and $2. For 3 hours, there are three ways=$1 +$1+$1, $1+$2, and $2+$1. Show the formula proving that the number of ways to insert coins for hours forms a fibonacci sequence.
Let $\displaystyle N(n)$ denote the number of ways of inserting coints for $\displaystyle n$ hours, then
$\displaystyle N(n)=N(n-1)+N(n-2)$
That is coins for parking $\displaystyle n$ hours use a method of inserting coins for $\displaystyle n-1$ hours plus a $\displaystyle \$1$coin, or a method of inserting the coins for$\displaystyle n-2$hours floowed by a$\displaystyle \$2$ coin. The rest follows from your initial conditions.