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ON THE BINOMIAL SUMS OF HORADAM SEQUENCE

Year 2015, Volume: 3 Issue: 1, 115 - 120, 01.04.2015

Abstract

The main purpose of this paper is to establish some new properties of Horadam numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between Horadam and generalized Lucas numbers are revealed to get a more strong result.

References

  • [1] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly 3, (1965), 161-176.
  • [2] E. Kilic, E. Tan, On Binomial Sums for the General Second Order Linear Recurrence, Integers 10 (2010), 801{806.
  • [3] E. Kilic, Y. Turker Ulutas, N. Omur, Sums of Products of the Terms of Generalized Lucas Sequence fVkng ; Hacettepe Journal of Mathematics and Statistics, Volume 40(2), (2011), 147 {161.
  • [4] G. Udrea, A note on sequence of A.F. Horadam, Portugaliae Mathematica 53(24), (1996), 143-144.
  • [5] H.H. Gulec, N. Taskara, On The Properties of Fibonacci Numbers with Binomial Coecients, Int. J. of Contemp. Math. Sci. 4(25), (2009), 1251-1256.
  • [6] MS. El Naschie, The Fibonacci code behind super strings and P-Branes, an answer to M. Kakus fundamental question, Chaos, Solitons & Fractals 31(3), (2007), 537-47.
  • [7] N. Taskara, K. Uslu, H.H. Gulec, On the properties of Lucas numbers with binomial coe- cients, Appl. Math. Lett. 23(1), (2010), 68-72.
  • [8] N. Taskara, K. Uslu, Y. Yazlik, N. Yilmaz, The Construction of Horadam Numbers in Terms of the Determinant of Tridiagonal Matrices, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings 1389, (2011), 367-370.
  • [9] N. Yilmaz, N. Taskara, K. Uslu & Y. Yazlik, On The Binomial Sums of k-Fibonacci and k- Lucas Sequences, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings 1389, (2011), 341-344.
  • [10] S. Falcon, On the k-Lucas Numbers, Int. J. Contemp. Math. Sciences, Vol. 6, no. 21, (2011), 1039-1050.
  • [11] S. Falcon, A. Plaza, On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation 208, (2009), 180-185.
  • [12] S. Falcon, A. Plaza, the k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solitons & Fractals 33, (2007), 38-49.
  • [13] S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Dover Publications New York (2007).
  • [14] T. Horzum, E.G. Kocer, On Some Properties of Horadam Polynomials, Int. Math. Forum, 4, 25, (2009), 1243-1252.
  • [15] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY (2001).
  • [16] T. Mansour, A formula for the generating functions of powers of Horadam's sequence, Aus- tralasian Journal of Combinatorics 30, (2004), 207-212.
Year 2015, Volume: 3 Issue: 1, 115 - 120, 01.04.2015

Abstract

References

  • [1] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly 3, (1965), 161-176.
  • [2] E. Kilic, E. Tan, On Binomial Sums for the General Second Order Linear Recurrence, Integers 10 (2010), 801{806.
  • [3] E. Kilic, Y. Turker Ulutas, N. Omur, Sums of Products of the Terms of Generalized Lucas Sequence fVkng ; Hacettepe Journal of Mathematics and Statistics, Volume 40(2), (2011), 147 {161.
  • [4] G. Udrea, A note on sequence of A.F. Horadam, Portugaliae Mathematica 53(24), (1996), 143-144.
  • [5] H.H. Gulec, N. Taskara, On The Properties of Fibonacci Numbers with Binomial Coecients, Int. J. of Contemp. Math. Sci. 4(25), (2009), 1251-1256.
  • [6] MS. El Naschie, The Fibonacci code behind super strings and P-Branes, an answer to M. Kakus fundamental question, Chaos, Solitons & Fractals 31(3), (2007), 537-47.
  • [7] N. Taskara, K. Uslu, H.H. Gulec, On the properties of Lucas numbers with binomial coe- cients, Appl. Math. Lett. 23(1), (2010), 68-72.
  • [8] N. Taskara, K. Uslu, Y. Yazlik, N. Yilmaz, The Construction of Horadam Numbers in Terms of the Determinant of Tridiagonal Matrices, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings 1389, (2011), 367-370.
  • [9] N. Yilmaz, N. Taskara, K. Uslu & Y. Yazlik, On The Binomial Sums of k-Fibonacci and k- Lucas Sequences, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings 1389, (2011), 341-344.
  • [10] S. Falcon, On the k-Lucas Numbers, Int. J. Contemp. Math. Sciences, Vol. 6, no. 21, (2011), 1039-1050.
  • [11] S. Falcon, A. Plaza, On k-Fibonacci numbers of arithmetic indexes, Applied Mathematics and Computation 208, (2009), 180-185.
  • [12] S. Falcon, A. Plaza, the k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solitons & Fractals 33, (2007), 38-49.
  • [13] S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Dover Publications New York (2007).
  • [14] T. Horzum, E.G. Kocer, On Some Properties of Horadam Polynomials, Int. Math. Forum, 4, 25, (2009), 1243-1252.
  • [15] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons Inc, NY (2001).
  • [16] T. Mansour, A formula for the generating functions of powers of Horadam's sequence, Aus- tralasian Journal of Combinatorics 30, (2004), 207-212.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nazmiye Yılmaz

Necati Taskara

Publication Date April 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 1

Cite

APA Yılmaz, N., & Taskara, N. (2015). ON THE BINOMIAL SUMS OF HORADAM SEQUENCE. Konuralp Journal of Mathematics, 3(1), 115-120.
AMA Yılmaz N, Taskara N. ON THE BINOMIAL SUMS OF HORADAM SEQUENCE. Konuralp J. Math. April 2015;3(1):115-120.
Chicago Yılmaz, Nazmiye, and Necati Taskara. “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”. Konuralp Journal of Mathematics 3, no. 1 (April 2015): 115-20.
EndNote Yılmaz N, Taskara N (April 1, 2015) ON THE BINOMIAL SUMS OF HORADAM SEQUENCE. Konuralp Journal of Mathematics 3 1 115–120.
IEEE N. Yılmaz and N. Taskara, “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”, Konuralp J. Math., vol. 3, no. 1, pp. 115–120, 2015.
ISNAD Yılmaz, Nazmiye - Taskara, Necati. “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”. Konuralp Journal of Mathematics 3/1 (April 2015), 115-120.
JAMA Yılmaz N, Taskara N. ON THE BINOMIAL SUMS OF HORADAM SEQUENCE. Konuralp J. Math. 2015;3:115–120.
MLA Yılmaz, Nazmiye and Necati Taskara. “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”. Konuralp Journal of Mathematics, vol. 3, no. 1, 2015, pp. 115-20.
Vancouver Yılmaz N, Taskara N. ON THE BINOMIAL SUMS OF HORADAM SEQUENCE. Konuralp J. Math. 2015;3(1):115-20.
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