New asymmetric generalizations of the Filbert and Lilbert matrices (Q2317461)

After a concise review of related literature, two matrices $\mathcal{W}$ and $\mathcal{Z}$ are defined whose entries consist of products of Fibonacci and Lucas numbers with indices depending on four integer parameters allowing asymmetric growth and decrease of indices. Explicite formulae for the LU decomposition of $\mathcal{Z}$ and $\mathcal{W}$ and their inverses are given. The authors state that these formulae were obtained by computer algebra experiments. Verification of the guessed formulae is routine but tedious and is provided explicitely in the paper for $\mathcal{W}$.