# Solve a reccurence relation

• Dec 15th 2009, 09:45 AM
HaitiBoy
Solve a reccurence relation
I am having hard times figuring out this problem:

Solve the recurrence relation using generating functions:
$
a_{n}=3a_{n-1}-4n
$

$
n\ge 1 , a_{0}=2
$

Thanks, John
• Dec 16th 2009, 12:59 AM
Shanks
Substitute the recursive relation in the generating function to get a function equation of the generating function.
solve the equation to get generating function, and expand it to get a_n.