Find the equation of a term in function of the second

Question

I want to write A(n) in terms of B(n) but nothing seems to work I can find the appropriate pattern.

 
n    A(n)    B(n)
1     1       0
1     1       1
2     3       1
3     5       2
4     9       3
5     15      5
6     25      8
7     41      13
8     67      21

Answer 1

Hint If $A(8)$ is $67$ and not 61, as in your table, compare $$A(n+1)-A(n) \mbox{ with } 2B(n)$$

Hint 2 $\sum_{k=1}^n A(k+1)-A(k)$ is telecopic. Use $$\sum_{k=1}^n A(k+1)-A(k)=2 \sum_{k=1}^n B(k)$$