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:
You may also compute the coefficients of the closed form.
Using this formula, you can compute an directly:
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, ...