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Let \( \mathrm{a}_{\mathrm{n}} \) denote the number of all n-digit positive integers formed by the digits 0,1 or both such that no
P consecutive digits in them are 0 . Let \( b_{n}= \) the number of

W such \( \mathrm{n} \)-digit integers ending with digit 1 and \( \mathrm{c}_{\mathrm{n}}= \) the number of such \( \mathrm{n} \)-digit integers ending with digit 0 .
Which of the following is correct? [IIT JEE 2012]
(A) \( \mathrm{a}_{17}=\mathrm{a}_{16}+\mathrm{a}_{15} \)
(B) \( \mathrm{c}_{17} \neq \mathrm{c}_{16}+\mathrm{c}_{15} \)
(C) \( b_{17} \neq b_{16}+c_{16} \)
(D) \( a_{17}=c_{17}+b_{16} \)
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