0
votes
2answers
109 views

fill-in-the-blank induction proof

I'm stuck at homework task I'm working on. I would really appreciate some help. Here is the task: Let $f$ be a function on binary numbers defined recursively as follows. $f(0) = 1$ and ...
0
votes
0answers
67 views

recursion for paths in binary tree

I have a binary tree, with {a,b,c} nodes and {p,q} edges. When $ p + q = 1 $. the first tree a - p - b - q - c this generate the expresion $ bq + cq $ ...
1
vote
0answers
131 views

1s surpassing 0s in binary strings of odd length

Let $A(k)$ be the number of distinct binary strings of length $2k+1,$ for which the number of $1$s surpasses the number of $0$s for the first time at digit number $2k +1$, i.e., in the final digit in ...