Journal of Integer Sequences, Vol. 28 (2025), Article 25.1.1

Two New Integer Sequences Related to Crossroads and Catalan Numbers


Julien Rouyer and Alain Ninet
Laboratoire de Mathématiques de Reims (LMR) - CNRS UMR 9008
Université de Reims Champagne-Ardenne
U.F.R. Sciences Exactes et Naturelles
Moulin de la Housse - BP 1039
51687 Reims cedex 2
France

Abstract:

The marriageable singles sequence represents the number of noncrossing partitions of the finite set {1, ..., n} in which some pair of singleton blocks can be joined while remaining noncrossing. The lonely singles sequence represents the number of all the other noncrossing partitions of the finite set {1, ..., n} and is the difference between the Catalan numbers sequence and the marriageable singles sequence. The first 16 terms of these sequences are given, as well as some of their properties. These sequences appear when one wants to count the number of ways to cross certain road intersections simultaneously.


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(Concerned with sequences A000108 A363448 A363449.)


Received November 11 2023; revised versions received November 12 2023; November 13 2023; February 12 2024; October 1 2024. Published in Journal of Integer Sequences, January 3 2025.


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