I am having hard times figuring out this problem:

Solve the recurrence relation using generating functions:

$\displaystyle

a_{n}=3a_{n-1}-4n

$

$\displaystyle

n\ge 1 , a_{0}=2

$

Thanks, John

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- Dec 15th 2009, 08:45 AMHaitiBoySolve a reccurence relation
I am having hard times figuring out this problem:

Solve the recurrence relation using generating functions:

$\displaystyle

a_{n}=3a_{n-1}-4n

$

$\displaystyle

n\ge 1 , a_{0}=2

$

Thanks, John - Dec 15th 2009, 11:59 PMShanks
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.