‘0’ and ‘1’ only but no two consecutive Zero

Let  a_{n} denote the number of all n-digit positive integers formed bt the digit ‘0’ and ‘1’ or both such that no consecutive digits in them are 0. Let  b_{n} = the number of such n-digit integers ending with digit 1 and  c_{n} = the number of such n-digit integers ending with digit 0

Which of the following is correct ?

(A) a_{17}=a_{16}+a_{15}

(B)  c_{17}=|c_{16}+c_{15}

(C) b_{17}=|b_{16}+c_{16}

(D) a_{17}=c_{17}+b_{16}

What is the value of b_{6}

(A) 7

(B) 8

(C) 9

(D) 11

 

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