There are six accompanying Maple sessions, one for each model that is solved in the paper: Kreweras model, reverse Kreweras model, double Kreweras model, a D-algebraic model, simple walks, diagonal walks.
Some accompanying Maple sessions: two for standard king walks (part 1 and part 2), two others when one allows steps between (0,-1) and (-1,0) (part 1 and part 2). In each case, one first establishes a system of four polynomial equations (first case, second case) and then derives four individual polynomials equations (first case; for the second case, this is done in the Maple session "Part2" given above). In the first case the four equations are in fact guessed from their first 2000 coefficients, given in these files: series R0, series R1, series B1, series B2.
Here are some accompanying Maple sessions. First, a program that determines whether the orbit of a 2D model is finite (Section 3.2). Then, some files and sessions related to Section 8: the list of the 12883 non-Hadamard models, determination of the corresponding excursion exponent, and finally the asymptotic calculations of Section 9.
The main accompanying Maple session is this one. It points to four other sessions, for the calculation of invariants, of decoupling functions, for proving that no such function exists, and solving the algebraic models.
The accompanying Maple session.
Supplementary material available on Manuel Kauers' webpage.
Another (much bigger) multi-directed animal, generated by Axel Bacher following the algorithm described in his paper Directed and multi-directed animals on the king's lattice.