Journal of Integer Sequences, Vol. 23 (2020), Article 20.4.3

Enumerating Lattice Walks with Prescribed Steps

Nestor Iwanojko, Steven Klee, Bryn Lasher, and Elena Volpi
Department of Mathematics
Seattle University
901 12th Avenue
Seattle, WA 98122


Given a finite set of integer vectors, S, we consider the set of all lattice walks whose allowable step directions come from S. We partition the set of all such walks according to their length (the number of steps used) and terminal point. In several cases, we are able to give explicit combinatorial formulas that count the number of such paths. We conclude with a Frobenius-type problem for lattice walks with prescribed steps.

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(Concerned with sequences A000027 A000290 A006000 A008865 A330601.)

Received January 16 2020; revised version received March 4 2020. Published in Journal of Integer Sequences, March 18 2020.

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