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We provide exact and asymptotic counting formulas for five singular lattice path models in the quarter plane. Furthermore, we prove that these models have a non D-finite generating function. Nous présentons des résultats énumératifs pour les cinq modèles de marche dans le quart de plan dites "singulière''. Nous prouvons que ces modèles sont non-holonomes.

Singularity analysis via the iterated kernel method