Investigation of Dual-Complex Fibonacci, Dual-Complex Lucas Numbers and Their Properties
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DOI: 10.1007/s00006-017-0813-z
Abstract: In this study, we define the dual complex Fibonacci and Lucas numbers. We give the generating functions and Binet formulas for these numbers. Moreover, the well-known properties e.g. Cassini and Catalan identities have been obtained… read more here.
Keywords: lucas numbers; complex fibonacci; investigation dual; dual complex ... See more keywords
Generalized Lucas Numbers Which are Concatenations of Two Repdigits
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DOI: 10.1007/s00025-021-01456-9
Abstract: A generalization of the well–known Lucas sequence is the k–Lucas sequence with some fixed integer $$k\ge 2$$ . The first k terms of this sequence are $$0,\ldots ,0,2,1$$ , and each term afterwards is the… read more here.
Keywords: generalized lucas; concatenations two; lucas numbers; two repdigits ... See more keywords
Symmetric functions of the k-Fibonacci and k-Lucas numbers
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DOI: 10.1142/s1793557121500315
Abstract: In this paper, we introduce a new operator in order to derive some new symmetric properties of k-Fibonacci and k-Lucas numbers and Fibonacci polynomials. By making use of the new operator defined i... read more here.
Keywords: fibonacci lucas; lucas numbers; functions fibonacci; symmetric functions ... See more keywords
Pythagorean triples containing generalized Lucas numbers
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DOI: 10.3906/mat-1702-102
Abstract: Let $P$ and $Q$ be nonzero integers. Generalized Fibonacci and Lucas sequences are defined as follows: $U_{0}(P,Q)=0,U_{1}(P,Q)=1,$ and $ U_{n+1}(P,Q)=PU_{n}(P,Q)+QU_{n-1}(P,Q)$ for $n\geq 1$ and $ V_{0}(P,Q)=2,V_{1}(P,Q)=P,$ and $V_{n+1}(P,Q)=PV_{n}(P,Q)+QV_{n-1}(P,Q)$ for $n\geq 1,$ respectively. In this paper,… read more here.
Keywords: triples containing; pythagorean triples; generalized lucas; lucas numbers ... See more keywords
Repdigits as sums of two generalized Lucas numbers
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DOI: 10.3906/mat-2011-59
Abstract: A generalization of the well–known Lucas sequence is the k -Lucas sequence with some fixed integer k ≥ 2 . The first k terms of this sequence are 0, . . . , 0, 2,… read more here.
Keywords: generalized lucas; sums two; lucas; repdigits sums ... See more keywords