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Back to Generating Functions

Exercise 1

Avg difficulty 2.5

Find the generating function for each of the following sequences by relating them back to a sequence with known generating function.

  1. 4,4,4,4,4,…4,4,4,4,4,\ldots.
  2. 2,4,6,8,10,…2, 4, 6, 8, 10, \ldots.
  3. 0,0,0,2,4,6,8,10,…0,0,0,2,4,6,8,10,\ldots.
  4. 1,5,25,125,…1, 5, 25, 125, \ldots.
  5. 1,−3,9,−27,81,…1, -3, 9, -27, 81, \ldots.
  6. 1,0,5,0,25,0,125,0,…1, 0, 5, 0, 25, 0, 125, 0, \ldots.
  7. 0,1,0,0,2,0,0,3,0,0,4,0,0,5,…0, 1, 0, 0, 2, 0, 0, 3, 0, 0, 4, 0, 0, 5, \ldots.

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §6.1 Generating Functions, Exercise 1

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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.