This is a question from my discrete math exam of last semester. And I don't really know how to tackle this question.
$$ a_i $$ is the number of different sequences of i symbols (i >= 0) chosen from {0,1,2}, where no 2 1's appear next to each other (so xxx11xx would be impossible), nor two 2's appearing next to eachother. For example 1200 is a valid sequence for 4 symbols. We assume that $$ a_0 = 1 $$ (the empty row for i = 0)
Question: (a) What do $$ a_1, a_2, a_3 $$ equal to?
(b) Make the recurrent equation (with initial values) for the sequence $$ {a_i} $$ For i from 0 to infinity. Explain your answer (c) Calculate the normal generating function of $$ {a_i} $$ i from 0 to infinity
Please help ^^