Question

Find a generating function for the recurrence relation an + an-1 - 6 an-2 = 0 for n>,2

Answer 1

Answer:

An infinite sequence (or just a sequence for short) is an ordered array

a0, a1, a2, . . . , an, . . .

of countably many real or complex numbers, and is usually abbreviated as

(an; n ≥ 0) or just (an). A sequence (an) can be viewed as a function f from

the set of nonnegative integers to the set of real or complex numbers, i.e.,

f : Z≥0 → C, f(n) = an, n = 0, 1, 2, . . .

We call a sequence (an) an arithmetic sequence if it is of the form

a0, a0 + q, a0 + 2q, . . . , a0 + nq, . . .

The general term of such sequences satisfies the recurrence relation

an = an−1 + q, n ≥ 1.

A sequence (an) is called a geometric sequence if it is of the form

a0, a0q, a0q

2

, . . . , a0q

n

, . . .

The general term of such sequences satisfies the recurrence relation

an = qan−1, n ≥ 1.

Answer 2

Step-by-step explanation:

Find a generating function for the recurrence relation an + an-1 6 an-2 = 0 for n>, 2