How to select special rows from a dataframe and escape others iteratively?

We can try:

df = pd.DataFrame(dict(zip(range(10), range(1, 11))), index=range(10))
s = pd.Series([True, False]).repeat(pd.Series({True : 5, False : 3}))
df[np.tile(s, int(np.ceil(len(df) / len(s))))[:len(df)]]

   0  1  2  3  4  5  6  7  8   9
0  1  2  3  4  5  6  7  8  9  10
1  1  2  3  4  5  6  7  8  9  10
2  1  2  3  4  5  6  7  8  9  10
3  1  2  3  4  5  6  7  8  9  10
4  1  2  3  4  5  6  7  8  9  10
8  1  2  3  4  5  6  7  8  9  10
9  1  2  3  4  5  6  7  8  9  10