The first six rows of Pascal's triangle are shown below, beginning with row 0.

How many of the first 100 rows contain at least one even entry and no odd entries other than $1$? (Rows 2 and 4 have this property, for example.)

\begin{tabular}{ccccccccccc}
&&&&&1&&&&&\\
&&&&1&&1&&&&\\
&&&1&&2&&1&&&\\
&&1&&3&&3&&1&&\\
&1&&4&&6&&4&&1&\\
1&&5&&10&&10&&5&&1\\
\end{tabular}
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The first six rows of Pascal's triangle are shown below, beginning with row 0.

How many of the first 100 rows contain at least one even entry and no odd entries other than $1$? (Rows 2 and 4 have this property, for example.)

\begin{tabular}{ccccccccccc}
&&&&&1&&&&&\\
&&&&1&&1&&&&\\
&&&1&&2&&1&&&\\
&&1&&3&&3&&1&&\\
&1&&4&&6&&4&&1&\\
1&&5&&10&&10&&5&&1\\
\end{tabular}
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
The first six rows of Pascal's triangle are shown below, beginning with row 0.

How many of the first 100 rows contain at least one even entry and no odd entries other than $1$? (Rows 2 and 4 have this property, for example.)

\begin{tabular}{ccccccccccc}
&&&&&1&&&&&\\
&&&&1&&1&&&&\\
&&&1&&2&&1&&&\\
&&1&&3&&3&&1&&\\
&1&&4&&6&&4&&1&\\
1&&5&&10&&10&&5&&1\\
\end{tabular}
train