University of Guilan Journal of Mathematical Modeling 2345-394X 10 1 2022 01 01 Factorization of the $t$-extension of the $p$-Fibonacci and the Pascal matrices 161 172 4916 10.22124/jmm.2021.18678.1597 EN Mansoor Hashemi Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. Elahe Mehraban Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran. Journal Article 2021 01 19 In this paper, we consider the 2-generator $p$-groups of nilpotency class 2.  We  find the Fibonacci length and the period of the generalized order $k$--Pell sequences of these groups. Pascal matrix $t$-extension of the $p$-Fibonacci matrix factorization of a matrix https://jmm.guilan.ac.ir/article_4916_14f18658cbb403e3ee8c63d62fe81496.pdf