A TILING APPROACH TO FIBONACCI p-NUMBERS

Öz

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

Anahtar Kelimeler

• Fibonacci p-Numbers
• Generalized Fibonacci Numbers
• Sum Formulas
• Tilings

Kaynakça

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