perplexus.info :: Just Math : Counting words

Counting words (Posted on 2022-04-27)

Given an alphabet of 3 letters i.e. a,b,c evaluate
the number of n-letter words containing even number of “a”s.

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

How to get to a closed form?

| Comment 4 of 7 |

The closed form I found is: f(n) = (3^n + 1)/2

I found it by trial and error.

Is there a mathematical way to go from:

Sigma{even k <=n} C(n,k)*2^(n-k)

to the closed form?

Posted by Larry on 2022-04-27 09:52:13

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