Restricted partitions and \(q\)-Pell numbers
The authors provide new interpretations for the Pell numbers \(p_n\) in terms of finite set partitions. In particular the identify six classes of partitions of size \(n\), each avoiding a set of three classical patterns of length four, all of which have cardinality given by \(p_n\). They also obtained a new polynomial generalization of \(p_n\) as well as the variant of \(q\)-Pell numbers studied by \textit{J. P. O. Santos} and \textit{A. V. Sills} [Discrete Math. 257, No.\,1, 125--142 (2002; Zbl 1007.05017)].
scientific article; zbMATH DE number 5900626
scientific article