Question: For n 1, let an count the number of binary strings of length n, where there is no run of l's of odd length.

For n ≥ 1, let an count the number of binary strings of length n, where there is no run of l's of odd length. Consequently, when n = 6, for instance, we want to include the strings 110000 (which has a run of two l's and a run of four 0's) and 011110 (which has two runs of one 0 and one run of four l's), but we do not include either 100011 (which starts with a run of one 1) or 110111 (which ends with a run of three l's). Find and solve a recurrence relation for an.

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