On Distance<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Fibonacci Numbers and Their Combinatorial and Graph Interpretations

Bród, Dorota

doi:10.1155/2015/879510

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Binet-like Form Of General Linear Recurrence1

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Cited by 2 publications

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“…Many mathematicians, working primarily in the field of combinatorics and discrete mathematics, began to deal with the other sequences which are a similar generalization of the Fibonacci sequence (see [34,[37][38][39][40][41][42][43][44][45]). In [34], the authors noted that from recurrence relation (13) of the sequence (F 2 (q, n)) n≥0 immediately follows that:…”

Section: Binet-like Form Of General Linear Recurrencementioning

confidence: 99%

On Coding by (2,q)-Distance Fibonacci Numbers

Matoušová

Trojovský

2020

Mathematics

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In 2006, A. Stakhov introduced a new coding/decoding process based on generating matrices of the Fibonacci p-numbers, which he called the Fibonacci coding/decoding method. Stakhov’s papers have motivated many other scientists to seek certain generalizations by introducing new additional coefficients into recurrence of Fibonacci p-numbers. In 2013, I. Włoch et al. studied (2,q)-distance Fibonacci numbers F2(q,n) and found some of their combinatorial properties. In this paper, we state a new coding theory based on the sequence (Tq(n))n=−∞∞, which is an extension of Włoch’s sequence (F2(q,n))n=0∞.

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