Generalized Fibonacci Lucas sequence its Properties

  • Abstract
  • Keywords
  • References
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  • Abstract

    Sequences have been fascinating topic for mathematicians for centuries. The Fibonacci sequences are a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci number, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula and , where are an nth number of sequences. The Lucas Sequence is defined by the recurrence formula and , where an nth number of sequences are. In this paper, we present generalized Fibonacci-Lucas sequence that is defined by the recurrence relation , with B0= 2s, B1 = s . We present some standard identities and determinant identities of generalized Fibonacci-Lucas sequences by Binets formula and other simple methods.

    Keywords: Fibonacci sequence, Lucas Sequence, Generalized Fibonacci sequence, Binets Formula.

  • References

      1. A.F. Horadam, the Generalized Fibonacci Sequences, the American Math Monthly, 68, No 5 (1961), 455-4592.
      2. A.T. Benjamin and j. j. Quinn. Recounting Fibonacci and Lucas identities collage Math, J., No.5 (1999), 359-366.
      3. Fuller E. Leonard, Generating function for recurrence relations, The Fibonacci Quarterly 19 (1981) 107-110.
      4. J. Z. Lee and Some Properties of Generalization of the Fibonacci sequence, The Fibonacci Quarterly, 1987, No.2, 110-117.
      5. Koshy, T. Fibonacci and Lucas number with application, Wiley, 2001.
      6. L. Carlitz, A note on Fibonacci number, The Fibonacci Quarterly, 2(1964), 15-28.
      7. L. Carlitz, Some Fibonacci and Lucas identities, The Fibonacci Quarterly, 8(1970), 61-73.
      8. Singh, B. and Sikhwal, O. Generalized Fibonacci sequence and Analytical Properties, Vikram Mathematical Journal, 26 (2006), 131-144.
      9. Singh, B. and Sikhwal O. and Bhatnagar, S., Fibonacci-like Sequence & its Properties, Int. Contemp Math. Science, Vol. 5, (2010) No. 18, 857-868.
      10. Singh, B., Sikhwal, O. Jain, S Coupled Fibonacci Sequences of Fifth Order and Some Properties Int. J. of Math Analysis, 4, (2010) 1247-1254
      11. Singh, B., Sikhwal, O. Fibonacci-Triple sequences and Some Fundamental Properties, Tamkang. J. of Mathematics. Sciences, 41, (2010) 325-333.
      12. Sikhwal, O., Generalization of Fibonacci sequence: An Intriguing Sequence, Lap Lambert Academic Publishing GmbH & Co. KG, Germany (2012).
      13. Vajda, S. Fibonacci and Lucas numbers and the golden section, Ellis Horwood Limited, Chi Chester, England, 1989.
      14. Vorobyou, N.N., The Fibonacci number, D.C. health company, Boston, 1963.




Article ID: 2793
DOI: 10.14419/gjma.v2i3.2793

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