Here is the *Maple* code (not
recommended; this takes really forever ...), and here is
the *Mathematica* code (this is,
surprisingly, much faster), for generating
the matrices **A_{00}**, **A_{01}**, **A_{12}**, and
**A_{20}**
of the proof of Theorem 4.6, and for testing the recurrence (4.8).

Here is the *Maple* code (not
recommended; this takes really forever ...), and here is
the *Mathematica* code (this is,
surprisingly, much faster), for generating
the matrices **A_{00}**, **A_{01}**, **A_{12}**,
**A_{23}**, **A_{34}**, and **A_{40}**
of the proof of Theorem 4.8, and for testing the recurrence (4.22).

Here is the proof of the above mentioned fact in the Remark on page 33, together with the computer data on which it is based.