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The \(k\)-Fibonacci sequence and the Pascal 2-triangle. (English) Zbl 1152.11308

Summary: The general \(k\)-Fibonacci sequence \(\{F_{k,n}\}^{\infty}_{n=0}\) were found by studying the recursive application of two geometrical transformations used in the well-known 4-triangle longest-edge (4TLE) partition. This sequence generalizes, between others, both the classical Fibonacci sequence and the Pell sequence. In this paper many properties of these numbers are deduced and related with the so-called Pascal 2-triangle.

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
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