In general, in the midst of History Mathematics textbooks, we are faced with a discussion due to curiosity about emblematic Fibonacci Sequence, whose popularization occurred proposition reproduction model immortal rabbits. On other hand, comparison multiple approaches and discussions certain subjects Elementary Mathematics, present work, highlight combinatorial interpretations that, support cha...

In this paper, we introduce tiling representations of Fibonacci p-numbers, which are generalizations the well-known and Narayana numbers, generalized in distance sense. We obtain p-numbers count number distinct ways to tile a 1 × n board using various r, r-ominoes from r = up p + 1. Moreover, product identities sum formulas these numbers with special subscripts given by interpretations that all...

Abstract: In this paper, we investigated relationships between the Fibonacci, Lucas, Padovan numbers and 1-factors of some bipartite graphs with upper Hessenberg adjacency matrix. We calculated permanent of these upper Hessenberg matrices by contraction method and show that their permanents are equal to elements of the Fibonacci, Lucas and Padovan numbers. At the end of the paper, we give some ...