Bednarz, Urszula; Włoch, Andrzej; Wołowiec-Musiał, Małgorzata Distance Fibonacci numbers, their interpretations and matrix generators. (English) Zbl 1361.11008 Commentat. Math. 53, No. 1, 35-46 (2013). Summary: In this paper we define a distance Fibonacci numbers, also for negative integers, which generalize the classical Fibonacci numbers and Padovan numbers, simultaneously. We give different interpretations of these numbers with respect to special partitions and compositions, also in graphs. We show a construction of the sequence of distance Fibonacci numbers using the Pascal’s triangle. Moreover, we give matrix generators of these numbers, for negative integers, too. Cited in 6 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11C20 Matrices, determinants in number theory 15B36 Matrices of integers 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:distance Fibonacci numbers; Padovan numbers; partitions; compositions; matching; covering; matrix representations; generalized Fibonacci numbers PDFBibTeX XMLCite \textit{U. Bednarz} et al., Commentat. Math. 53, No. 1, 35--46 (2013; Zbl 1361.11008)