Geodesic
Continued Classification of 3D Lattice Models in the Positive Octant
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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We continue the investigations of lattice walks in the three-dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that their generating function is D-finite, and we isolate a small set of models whose nature remains unclear and requires further investigation. For these, we give some experimental results about their asymptotic behaviour, based on the inspection of a large number of initial terms. At least for some of them, the guessed asymptotic form seems to tip the balance towards non-D-finiteness. 
@article{DMTCS_2020_special_379_a97,
     author = {Bacher, Axel and Kauers, Manuel and Yatchak, Rika},
     title = {Continued {Classification} of {3D} {Lattice} {Models} in the {Positive} {Octant}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6415},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6415/}
}
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%D 2020
%V DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)
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Bacher, Axel; Kauers, Manuel; Yatchak, Rika. Continued Classification of 3D Lattice Models in the Positive Octant. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6415. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6415/

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