Solve the recurrence relation with initial conditions x0 2

Solve the recurrence relation with initial conditions x_0 = 2, x_1 = 6, x_2 = 15, and x_3 = 36.

Solution

Put n=4,

x₄=6x₃-13x₂+12x₁-4x₀

Now Put all the values in it.

x₄=6(36)-13(15)+12(6)-4(2)

    = 216-195+72-8

   = 85