Vol. 37, No. 1, 1971

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Weighted lattice paths

Robert Dutton Fray and David Paul Roselle

Vol. 37 (1971), No. 1, 85–96

A lattice path in the plane from (0,0) to (m,n) with weighted horizontal, vertical, and diagonal steps will be called a weighted lattice path. We determine the number of unrestricted weighted lattice paths, the number of paths below a line, and the number of paths which must remain between two parallel lines wilh unil slope. We also obtain generating functions for the number of paths which remain below the line y = x; these extend results obtained by Carlitz and Riordan for the ballot numbers.

Mathematical Subject Classification 2000
Primary: 05A15
Received: 23 July 1970
Published: 1 April 1971
Robert Dutton Fray
David Paul Roselle