Question

Given the following definition, compute Q(5).
Q(n) = {0 if n = 0
Q(n) = {2 if n = 1
Q(n) = {4 if n = 2
Q(n) = {Q(n − 1) + Q(n − 2) + Q(n − 3) if n > 2
Q(5) =?

Answer 1

looks you need the values of Q(3) and Q(4), first

Answer 2

that is not provided or asked in the question

Answer 3

Q(n) = {Q(n − 1) + Q(n − 2) + Q(n − 3)
if n = 5, it means
Q(5) = Q(4) + Q(3) + Q(2)
the value of Q(3) is given, nah how about Q(4) and Q(3) ?

Answer 4

not given, but I just figured it out...the answer is Q(5) = 22

Answer 5

yeah, i got Q(5) = 22

Answer 6

thanks for making me think about it differently

Answer 7

Q(5) = Q(4) + Q(3) + Q(2),

to get the values of Q(3) and Q(4), respectively :
if n = 3, then
Q(3) = Q(2) + Q(1) + Q(0) = 4 + 2 + 0 = 6 and
n = 4, then
Q(4) = Q(3) + Q(2) + Q(1) = 6 + 4 + 2 = 12

therefore,
Q(5) = Q(4) + Q(3) + Q(2),
Q(5) = 12 + 6 + 4 = 22
hope that make sense :)