Question

consider language s*,where s={aa,b} how many words does this language of length 4?
i know its answer but it is hard to calculate.is there any formula that give us exact answer rather than we do combination.i know how to get legth 4.by adding 2 to aa and adding 3 to b.but it is calculated by making combinations.
kindly give a general formula which will tell me about how many words of a specific length can be made by a given alphabet.

Answer 1

HERE is the solution

number of words of length 0 = 1 [null]

number of words of length 1 = 1 [b]

number of words of length 2 = 2  [aa,bb]

number of words of length 3 = 3 Add aa to 1 letter word , add b to 2 letter word

[baa,aab,bbb]

Hence we can see a relation here which is

where f(x) denotes number of words of length x

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