Question

Consider the sequence g₀ = 1, g₁ = 1, g₂ = 21, g₃ = 41, g₄ = 461, g₅ = 1281, g₆ = 10501,... whose linear generator is g_n+2 = g_n+1 + 20g_n, that is, 20(!) pairs of baby rabbit offspring.

1. As we did for the Fibonacci numbers, please derive a closed form expression for g_n.
2. Consider the sequence h_n = (–1)ⁿ g_n: 1,–1,21,–41,461,–1281,10501,... Please give a second order homogeneous linear recurrence with constant coefficients for h_n and prove that your recurrence is correct for all n.

Answer 1