Saruman`s Level Up

Saruman's army of orcs and other dark minions continuously mine and harvest lumber out of the land surrounding his mighty tower for $n$ continuous days. On day number $i$, Saruman either chooses to spend resources on mining coal and harvesting more lumber, or on raising the level (i.e., height) of his tower. He levels up his tower by one unit only on days where the binary representation of $i$ contains a total number of $1$'s that is an exact multiple of $3$. Assume that the initial level of his tower on day $0$ is zero.

For example, Saruman will level up his tower on day $7$ (binary $111$), next on day $11$ (binary $1011$) and then day $13$, day $14$, day $19$, and so on.

Saruman would like to forecast the level of his tower after $n$ days. Can you write a program to help?