Starting with u(0) = 0, u(1) = 0, u(2) = 1. we define the sequence of tri-Fibonacci integers u(k) by adding the previous three to get the next one. For instance. u(3) = u(0) + u(l) + u(2) = 1.
(a) Write out the next four tri-Fibonacci integers.
(b) Find a third order iterative equation for the Ath tri-Fibonacci integer.
(c) Find an explicit formula for the solution, using a computer to approximate the eigenvalues.