Guichard-Combinatorics-Graph-Theory · Problem 3.4.4

Generating Functions

Mathematics — Probability · recurrence-relations-generating-functions

Problem

Find the generating function for the solutions to

h_n = 4h_{n-2}

h_0 = 0

h_1 = 1

, and use it to find a formula for

h_n

. (It is easy to discover this formula directly; the point here is to see that the generating function approach gives the correct answer.)