Find a closed form for the recurrence relations S0 2 S13 Sn

Find a closed form for the recurrence relations S₀ = 2, S₁=3, S_n+2 = 3S_n - 2S_n+1 for (n grearter than or equal to 0)

Solution

S0 =2

S1 =3

So

S2 = 3S0-2S1 = 6-6 =0

S3 = 3S1-2S2 = 9

S4 = 3S2-2S3 =-18

S5 = -54+56 =2

....

Hence it will be of the form

2, 3, 0, 9, -18, 2, -58, ...