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.

Answer 2

you don't need an array at all to achieve this.

int n = 5;
int result = 0;

for (int i=0; i<n; ++i)
{
    int t1_new = (2*(t1+t2)) % MOD;
    int t2_new = t1;

    result = (t1_new + t2_new) % MOD;
    t1 = t1_new;
    t2 = t2_new;
}

int res = result;

that way, you will get the nth term, and not all of them across the way until n.