CMIS 160

Discrete Mathematics

Erich Prisner

UMUC SG

Spring 2002

##
A Recurrence Equation

We consider the recurrence equation

a_{n} = 4 a_{n-1} - a_{n-2} - 6 a_{n-3}

a_{n} - 4 a_{n-1} + a_{n-2} + 6 a_{n-3} = 0

Fill in the first three entries (a_{1}, a_{2}, a_{3})
and generate the next values

Generate more values by proceeding:
You may also compute the coefficients of the closed form.
Using this formula, you can compute a_{n} directly:
Try to start with the sequence 1,2,4, ....

What about 1,3,9, ... ?

Try the head 100, 200, 399, and compute a_{15} and a_{16}.

What is the 15th term in the sequence 1, 2, 5, 12, ...