Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.3

A Note on the Enumeration of Diffusion Walks in the First Octant by Their Number of Contacts with the Diagonal


Heinrich Niederhausen
Department of Mathematical Sciences
Florida Atlantic University
Boca Raton, FL 33431
USA

Abstract: Diffusion walks take steps in the four directions N, E, S, and W. We derive a closed form for the number of diffusion walks from the origin to some point (n,n) on the diagonal in k steps inside the first octant, touching the diagonal exactly c times.

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(Concerned with sequence A005558 .)

Received October 29 2004; revised version received September 1 2005; Published in Journal of Integer Sequences September 1 2005.

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