Insertion Of Terms Satisfying The Recurrence Relations Of Horadam Sequence And Bifurcating Fibonacci Sequences

Authors

  • Khushbu J. Das Veer Narmad South Gujarat University, Surat. Gujarat. INDIA.
  • Devbhadra V. Shah Veer Narmad South Gujarat University, Surat. Gujarat. INDIA.

DOI:

https://doi.org/10.23755/rm.v42i0.639

Keywords:

Generalized Fibonacci sequences, Horadam sequence, Bifurcating sequence, Inserted terms, Missing terms.

Abstract

In this article, we consider the problem of finding general formula for the terms introduced between two given positive integers ‘a’ and ‘b’ in such a way that the terms of newly formed finite sequence satisfy the recurrence relations of Horadam sequence and some bifurcating Fibonacci sequences.

Author Biographies

  • Khushbu J. Das, Veer Narmad South Gujarat University, Surat. Gujarat. INDIA.

    Departmennt of Mathematics

    Research Scholar

  • Devbhadra V. Shah, Veer Narmad South Gujarat University, Surat. Gujarat. INDIA.

    Department of Mathematics,

    Associate Professor

References

Agnes M., Buenaventura N., Labao J. J., Soria C. K., Limbaco K. A., and L. Natividad, Inclusion of inserted terms (Fibonacci mean) in a Fibonacci sequence, Math Investigatory Project, Central Luzon State University, 2010.

Bilgici G., New generalizations of Fibonacci and Lucas Sequences, Applied Mathematical Sciences, Vol. 8, No. 29, 2014, 1429 – 1437.

Diwan D. A, Shah D. V., Extended Binet’s formula for the class of generalized Fibonacci sequences, Proceeding 19th Annual Cum 4th International Conference of Gwalior academy of Mathematical Sciences (GAMS), SVNIT, surat, Oct 3-6, 2014, 109 – 113.

Diwan D. A, Shah D. V., Extended Binet’s formula for the class of generalized Fibonacci sequences, VNSGU Journal of Science and Technology, Vol. 4, No. 1, 2015, 205 – 210.

Diwan D. A, Shah D. V., Explicit and recursive formulae for the class of generalized Fibonacci sequence, International Journal of Advanced Research in Engineering, Science and Management, Vol. 1, Issue 10, July 2015, 1 – 6.

Edson M., Yayenie O., A new generalization of Fibonacci sequence and Extended binet’s formula, Integers, Vol. 9, 2009, 639 – 654.

Horadam A. F., Basic properties of certain generalized sequence of numbers, Fibonacci Quarterly, 3, 1965, 161-176.

Howell P., Nth term of the Fibonacci sequence, from Math Proofs: Interesting mathematical results and elegant solutions to various problems, http://mathproofs.blogspot.com/2005/04/nth-term-offibonacci-sequence.

Verma, Bala A., On Properties of generalized Bi-variate Bi-Periodic Fibonacci polynomials, International journal of Advanced science and Technology,29(3), 2020, 8065–8072.

Yayenie O., A note on generalized Fibonacci sequence, Applied Mathematics and computation, 217, 2011, 5603–5611.

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Published

2022-06-30

Issue

Section

Volume 42-2022