AI Tutor
Back to Generating Functions

Exercise 13

Avg difficulty 2.5

You may assume that 1,1,2,3,5,8,…1, 1, 2, 3, 5, 8,\ldots has generating function 11−x−x2\dfrac{1}{1-x-x^2} (because it does). Use this fact to find the sequence generated by each of the following generating functions.

  1. x21−x−x2\frac{x^2}{1-x-x^2}.
  2. 11−x2−x4\frac{1}{1-x^2-x^4}.
  3. 11−3x−9x2\frac{1}{1-3x-9x^2}.
  4. 1(1−x−x2)(1−x)\frac{1}{(1-x-x^2)(1-x)}.

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §6.1 Generating Functions, Exercise 13

AI Tutor

Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.