recurrence relation

Question

 

 

 

solve by recurrence relation

Comments

HI there, you don't have a typo in your expression do you?

If the recurrence relatioon is: a_n = 6.a_(n-1) + 11.a_(n-2) - 6.a(n-3),

then my computer algebra package tells me that there is no solution. (At least not one you would want to look at !)

However, if the recurrence relatioon is: a_n = 6.a_(n-1) - 11.a_(n-2) + 6.a(n-3), (swap the + and - signs)

then there is a solution.

Could you check your text/signs ?

Answer 1

We identify a type of recurrence that can be solved by special methods.

DEF: A recurrence relation

an = f (a0,...,an-1

has degree k if the function f depends on the term an-k and if it depends on no terms of lower index. It is linear of degree k if it has the form

am = c1an-1 + c2an-2+...+ ckan-k + g (n)

where each ck is a real function and ck = 0. It is homo genous if g (n) = 0

aExample 6.2.1: The recurrence system with intial condition

a0=0

and recurrence relation

an = an-1 + 2n - 1

is linear of degree one and non-homo geneous.