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Recently, a new generalization of Pascal's triangle, the so-called hyperbolicPascal triangles were introduced. The mathematical background goes back to theregular mosaics in the hyperbolic plane. In this article, we investigate thepaths in the hyperbolic Pascal triangle corresponding to the regular mosaic$\{4,5\}$, in which the binary recursive sequences $f_{n}=\alpha f_{n-1}\pmf_{n-2}$ are represented ($\alpha\in\mathbb{N}^+$).

Recurrence sequences in the hyperbolic Pascal triangle corresponding to the regular mosaic $\{4,5\}