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**hastings** The sequence {a_n} = 1,11,41,131,401,... satisfies the relation

a_(n+2) = 4*a_(n+1) - 3*a_n for n>=0. Find a const. coefficient, linear, homogeneous recurrence relation(of smallest order) which is satisfied by the sequence

(1)^2,,(11)^2,(41)^2,(131)^2,... = 1,121,1681,17161,... .

The characteristic equation for the given relation is x^2 - 4*x + 3 = 0. The roots for this equation are 3 and 1. Imposing the values of a_0 and a_1, we find that a_n = 5*(3^n) - 4. Here is the point i don't know what to do next.