Calculate the nth term of the sequence 1,3,8,22,60,164,448,1224…? [duplicate]

Answer 1

You can use the folowing fact. If you consider the matrix

    (0 1)
A = (2 2)

You can use the fact that a_n = A^n-2 * (1, 3)[1] (here (1,3) is a vector) and [1] means second coordinate of the vector. Here you can use binary exponentiation for the matrix. Consider the cases for n<=2 separately.