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I've searched on web some exercises about closed form formula of recursive sequence, but I have not found more difficult ones. For example the majority of them ask me to find close form formula for $a_n$, so I'm wondering if there are other ones that ask me for $a_{2n}$ or something similar. Furthermore the types of exercises that I'm looking for concerns linear sequence like these:

  1. $a_n = 3a_{n-1} +2$
  2. $a_n = 2a_{n-1} + 2a_{n-2}$

Someone of you know where I can find exercises like these? Thanks.

user515933
  • 563
  • You could always try examples in Rosen's Discrete Mathematics. –  Jan 22 '18 at 12:24
  • Google for 1) generating functions 2) homogeneous recurrence sequences and 3) characteristic polynomials – rtybase Jan 22 '18 at 12:25
  • Or look at some other example like https://math.stackexchange.com/questions/2547762/recursion-y-n-ky-n-1ry-n-2-y-0-2-y-1-k-and-fermat-theorem/ or https://math.stackexchange.com/questions/2559687/show-that-the-sequence-a-1-1-a-2-2-a-n2-a-n1a-n-2-converges-b/ – rtybase Jan 22 '18 at 12:29

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