Journal of Integer Sequences, Vol. 1 (1998), Article 98.1.7

Schröder Triangles, Paths, and Parallelogram Polyominoes

Elisa Pergola
Dipart. di Sistemi e Informatica
Universitá di Firenze, Firenze, Italy
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Robert A. Sulanke
Boise State University, Boise, ID, U.S.A
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Abstract: This paper considers combinatorial interpretations for two triangular recurrence arrays containing the Schröder numbers sn = 1, 1, 3, 11, 45, 197, ... and rn = 1, 2, 6, 22, 90, 394, ... , for n = 0, 1, 2, .... These interpretations involve the enumeration of constrained lattice paths and bicolored parallelogram polyominoes, called zebras. In addition to two recent inductive constructions of zebras and their associated generating trees, we present two new ones and a bijection between zebras and constrained lattice paths. We use the constructions with generating function methods to count sets of zebras with respect to natural parameters.


Received Apr. 21 1998 and in revised form May 23 1998. Published in Journal of Integer Sequences May 29, 1998.

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