Journal of Integer Sequences, Vol. 24 (2021), Article 21.3.6

Enumeration of S-omino Towers and Row-Convex k-omino Towers

Alexander M. Haupt
Institute of Mathematics
Hamburg University of Technology
Am Schwarzenberg-Campus 3
21073 Hamburg


We first enumerate a generalization of domino towers that was proposed by Brown, which we call S-omino towers. We establish equations that the generating function must satisfy, and then apply the Lagrange inversion formula to find a closed formula for the number of towers. We also show a connection to generalized Dyck paths and describe an explicit bijection. Finally, we consider the set of row-convex k-omino towers, introduced by Brown, and calculate an exact generating function.

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(Concerned with sequences A000108 A000212 A001523 A338531.)

Received November 1 2020; revised versions received November 9 2020; February 10 2021; February 15 2021. Published in Journal of Integer Sequences, February 16 2021.

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