We show that the generating function (in n) for the number of walks on the square lattice with steps (1, 1), (1, -1), (2, 2) and (2, -2) from (0, 0) to (2n, 0) in the region 0 ≤ y ≤ w satisfies a very special fifth order nonlinear recurrence relation in w that implies both its numerator and denominator satisfy a linear recurrence relation.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics