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We consider a variation of Dyck paths, where additionally to steps $(1,1)$and $(1,-1)$ down-steps $(1,-j)$, for $j\ge2$ are allowed.  We give credits to Emeric Deutsch for that.  The enumeration of such objects living in a strip is performed. Methods arethe kernel method and techniques from linear algebra.

Lattice paths with infinitely many down steps -- the negative boundary model