Question

) Cars are parked in line as they come off the assembly lines. There are three models: red cars which take up 2 spaces, blue cars which also take up 2 spaces, and green cars which take up only 1 space. Let an be the number of ways of filling the first n parking spaces with red, blue and green cars.

Answer 1

Answer:

Hello your question has some missing information below is the complete question

answer :

$a_{n} = a_{n-2} + a_{n-2} + a_{n-1}$

Step-by-step explanation:

Red car and Blue car take up 2 spaces each

Green cars take up 1 space

lets determine the number of ways of filling up the parking spaces

i) First lets assume the last space is filled by Green car then there will be $n^{th}$ space occupied hence there will be ( n - 1 ) spaces left to be filled in $a_{n-1}$ ways

ii) lets assume the last space is filled by either a Red car or a Blue car then there will be $n^{th} + ( n -1 )^{st}$  parking space occupied hence there will be

( n - 2 ) spaces left to be filled in $a_{n-2}$ ways

Hence A closed formula for $a_{n}$

$a_{n} = a_{n-2} + a_{n-2} + a_{n-1}$

where : a1 = 1 way ,  a2 = 3 ways