  An infinite $\pm 1$-sequence is called {\it Apwenian} if its Hankel
determinant of order $n$ divided by $2^{n-1}$ is an odd number for every
positive integer $n$. In 1998, Allouche, Peyri\`ere, Wen and Wen discovered and
proved that the Thue--Morse sequence is an Apwenian sequence by direct
determinant manipulations. Recently, Bugeaud and Han re-proved the latter
result by means of an appropriate combinatorial method. By significantly
improving the combinatorial method, we prove that several other Apwenian
sequences related to the Hankel determinants with Computer Assistance.
