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.
This is a source for sequences A001003, A006318, and A010683.
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