Problem 1
The tribonacci numbers {Tn} are defined for non-negative integers n as follows.
⎧⎨ T 0 = T 1 = 0 ⎩ T2 = 1
Tn+3 =Tn+2 +Tn+1 +Tn (n≥0). Answer the following questions.
(1) Find the matrix A that satisfies Eq. (1.1) for all non-negative integers n.
⎛T⎞⎛T⎞ n+3 n+2
⎝ Tn+2 ⎠=A⎝ Tn+1 ⎠. Tn+1 Tn
(1.1)