Question

Consider the sequence {a_n} defined recursively as: a₀ = a₁ = a₂ = 1, an = a_n−1+a_n−2+a_n−3 for any integer n ≥ 3.

(a) Find the values of a₃, a₄, a₅, a₆.

(b) Use strong induction to prove a_n ≤ 3ⁿ⁻² for any integer n ≥ 3. Clearly indicate what is the base step and inductive step, and indicate what is the inductive hypothesis in your proof.

Answer 1

a) 3 3-13-23-3 4-1, 4-2, 나-3 @g.+ аг + a;