## recurrence relation with initial conditions

consider the recurrence relation a_n = a_(n-2). Show that a_n = i^n and a_n=(-i)^n are solutions, where i= sqrt of -1. For any initial conditions a_0=b and a_1=c, find constants k_1 and k_2 so that a_n=k_1(i^n) +k_2(-i)^n satisfies these initial conditions.