Bounds on Number of Odd Terms in Pascal's Triangle

Theorem
Let $P_n$ be the number of odd elements in the first $n$ rows of Pascal's triangle.

Then:
 * $0 \cdotp 812 \ldots < \dfrac {P_n} {n^{\lg 3} } < 1$

where $\lg 3$ denotes logarithm base $2$ of $3$.

The lower bound $0 \cdotp 812 \ldots$ is known as the Stolarsky-Harborth constant.

Also see

 * Definition:Stolarsky-Harborth Constant