Find the general formula of this sequence

Question

Here is the sequence

1 2 2 4 4 6 6 10 10 14 14 20 20 26 26 36 36 46 46 60 60 ···

I just know the recursion formula:$\displaystyle f\left(n\right)=1+\sum_{i=1}^{\left\lfloor\frac{n}{2}\right\rfloor}{f\left(i\right)}$. But I do not know how to find that, or is there any other recursion formula.

Answer 1

OEIS tells us this is the "Binary partition function: number of partitions of n into powers of 2."