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Exercise 12

Avg difficulty 2.5

Starting with the generating function for 1,2,3,4,…1,2,3,4, \ldots, find a generating function for each of the following sequences.

  1. 1,0,2,0,3,0,4,…1, 0, 2, 0, 3, 0, 4,\ldots.
  2. 1,−2,3,−4,5,−6,…1, -2, 3, -4, 5, -6, \ldots.
  3. 0,3,6,9,12,15,18,…0, 3, 6, 9, 12, 15, 18, \ldots.
  4. 0,3,9,18,30,45,63,…0, 3, 9, 18, 30, 45, 63,\ldots. (Hint: relate this sequence to the previous one.)

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §6.1 Generating Functions, Exercise 12

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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.