Consider the following third-order recurrent sequence (T)n>1: Tn+3 = 2T+2 +2T,+1 Tn, for T1 = 20, T2 = 12, T3 = 70. 1.1. Calculate the first 20 terms of this sequence (check the terms in the OEIS). 1.2. Derive the formula of the general term T, of the sequence. 1.3. Find the matrix A for which we have [T+4 Tn+3 Tn+2] = A [Tn+1 Tn Tn1]', for n = 2,3,..., where X' denotes the transpose of the vector/matrix X. 1.4. Compute the limit of the ratio n+3, asn 0o. T