Let-a-n-denote-the-number-of-all-n-digit-positive-integers-formed-by-the-digits-0-1-or-both-such-that-no-consecutive-digits-in-them-are-0-Let-b-n-the-number-of-such-n-digit-integers-ending-with-

Question Number 21913 by Tinkutara last updated on 06/Oct/17

Let a_{n} denote the number of all n - digit

positive integers formed by the digits

0, 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 .

1 . Which of the following is correct ?

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

(2) c_{17} \neq c_{16} + c_{15}

(3) b_{17} \neq b_{16} + c_{16}

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

2 . The value of b_{6} is