Hey guys! I need some help with this problem
Consider the sequence defined by
an = 8an−1 − 12an−2 + 3n for n ≥ 2 and a0 = 0, a1 = 1
Prove by induction on n that an = 6^n + 2^(n+1) − 3^(n+1) is a solution to this recurrence.
an = 6^n + 2^(n+1) − 3^(n+1) doesn't appear to be a valid solution. Check for n = 2. According to the recurrence: a2 = 8a1 - 12a0 + 3*2 = 8 - 0 + 6 = 14. Substituting n = 2 in the purported solution gives a2 = 6^2 + 2^3 - 3^3 = 36 + 8 - 27 = 17.