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ON THE BINOMIAL SUMS OF HORADAM SEQUENCE

Yıl 2015, Cilt: 3 Sayı: 1, 115 - 120, 01.04.2015

Öz

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.

Kaynakça

  • [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.
Yıl 2015, Cilt: 3 Sayı: 1, 115 - 120, 01.04.2015

Öz

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Nazmiye Yılmaz

Necati Taskara

Yayımlanma Tarihi 1 Nisan 2015
Gönderilme Tarihi 10 Temmuz 2014
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 1

Kaynak Göster

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. Nisan 2015;3(1):115-120.
Chicago Yılmaz, Nazmiye, ve Necati Taskara. “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”. Konuralp Journal of Mathematics 3, sy. 1 (Nisan 2015): 115-20.
EndNote Yılmaz N, Taskara N (01 Nisan 2015) ON THE BINOMIAL SUMS OF HORADAM SEQUENCE. Konuralp Journal of Mathematics 3 1 115–120.
IEEE N. Yılmaz ve N. Taskara, “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”, Konuralp J. Math., c. 3, sy. 1, ss. 115–120, 2015.
ISNAD Yılmaz, Nazmiye - Taskara, Necati. “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”. Konuralp Journal of Mathematics 3/1 (Nisan 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 ve Necati Taskara. “ON THE BINOMIAL SUMS OF HORADAM SEQUENCE”. Konuralp Journal of Mathematics, c. 3, sy. 1, 2015, ss. 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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