We give an explicit evaluation, in terms of products of Jacobsthal numbers, of the Hankel determinants of order a power of two for the period-doubling sequence. We also explicitly give the eigenvalues and eigenvectors of the corresponding Hankel matrices. Similar considerations give the Hankel determinants for other orders.
['Robbert Fokkink', 'Cor Kraaikamp', 'Jeffrey Shallit']
Hankel Matrices for the Period-Doubling Sequence