math.CO/0409509 number 66

### What is the conjecture
See #1468 for the definition of $A_3$. The conjecture:

$$
A_3(1,2,3,n+2)=1+2^{\lfloor\lg n\rfloor}+\sum_{k=1}^n\frac{3^{v_2(n)}+1}{2}.
$$

### Prerequisites needed

Status: open

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [X] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reading issue #1468 for the definition of A_3 and compare this conjecture with the repository's existing formalized statements. Add the displayed A_3(1,2,3,n+2) conjecture to the collection and verify that the Lean project accepts the addition.

Written by the indexing model from the issue text.