CMIS 160
Discrete Mathematics
Erich Prisner
UMUC SG
Spring 2002

A Recurrence Equation

We consider the recurrence equation
an = 4 an-1 - an-2 - 6 an-3

an - 4 an-1 + an-2 + 6 an-3 = 0

Fill in the first three entries (a1, a2, a3) and generate the next values

Generate more values by proceeding:
n: an-2: an-1: an:
You may also compute the coefficients of the closed form.
an = *3n + *2n + *(-1)n
Using this formula, you can compute an directly:
n: an:
Try to start with the sequence 1,2,4, ....
What about 1,3,9, ... ?
Try the head 100, 200, 399, and compute a15 and a16.
What is the 15th term in the sequence 1, 2, 5, 12, ...