[Math4u] Help me plz1. - Math doubt

Dear all,

 

  I am studying open university. So I didn't have a proper teacher who can teach me, perticularly math, because of that i studing my self. While i go through the math i have some doubts. Please and kindly give your ideas and notes to clear those my doubts.

 

Math Name : Discrete Mathematics.

Topic : Recurrence Relations

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Problem 1:-

Set up a recurrence relation for the number of n digit sequence on integers (0,1,2,3) having an even number of  0's

 

Solution:-

  Let An denote the number of n-digit sequence containing an even number of 0's. Then there are An-1(n-1) - digit sequence that have an even number of 0's and 4^(n-1)-An-1(n-1) - digit sequence that have an odd number of 0's. To each of the An-1 sequences that have an even number of 0's, the digit 1,2 or 3 can be appended to yield sequence of length n that contain an even number of 0's. To each of the 4^(n-1)-An-1 sequences that have an odd number of 0's, the digit 0 must be appended to yield sequences of length n that contain an even number of 0's.Therefore,for n>=2, An = 3An-1 + 4^(n-1) - An-1 = 2An-1+4^(n-1), with a1=3

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Can anyone help me to understand solution based on the problem. If you mention the with example it would be the great.

 

My Adv. Thank you,

 

Regards

H.Ashok

 

 

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