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Consider the sequence g0 = 1, g1 = 1, g2 = 21, g3 = 41, g4...

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

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