Question

Given the following definition, compute Q(5).

Q(n) = 

0
if n = 0
2
if n = 1
4
if n = 2
Q(n − 1) + Q(n − 2) + Q(n − 3)  
if n > 2

Answer 1

`Q(n)=\begin{cases}0&\text{for }n=0\\2&\text{for }n=1\\4&\text{for }n=2\\Q(n-1)+Q(n-2)+Q(n-3)&\text{for }n>2\end{cases}`


`\implies Q(3)=Q(2)+Q(1)+Q(0)=4+2+0=6`

`\implies Q(4)=Q(3)+Q(2)+Q(1)=6+4+2=12`

`\implies Q(5)=Q(4)+Q(3)+Q(2)=12+6+4=22`