Iterative Process in Numbers

The missing number of the given Lucas series that has to come before $47$ is $30$.

$2, 1, 3, 4, 7, 11, 18, 47, 76, 123$

The next number of the given Lucas sequence is $2, 1, 3, 4, 7, 11, 18$ is _____

The numbers as the sum of its two immediately previous terms is called _____ numbers.

Choose the missing number of the given fibonacci series that has to come before $34$.

$0, 1, 1, 2, 3, 5, 8, 13, 34$

The next number of the given fibonacci sequence is $0, 1, 1, 2, 3, 5, 8, 13$ is _____

The next number of the given fibonacci sequence is $0, 1, 1, 2, 3, 5, 8, 13, 21, 34$ is _____

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 $0.$

The value of $b_6$ is