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ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES

Yıl 2013, Cilt: 42 Sayı: 4, 431 - 435, 01.04.2013

Öz

In this paper, we consider the Horadam sequence and some summationformulas involving the terms of the Horadam sequence. We derivecombinatorial identities by using the trace, the determinant, and thenth power of a special matrix.

Kaynakça

  • A. F. Horadam, Basic properties of a certain generalized sequence of numbers, The Fibonaci Quaterly, 3(2) (1965), 161-176.
  • A. F. Horadam, Tschebyscheff and other functions associated with the sequence W n (a, b; p, q), The Fibonaci Quaterly, 7(1)(1969), 14-22.
  • A. Nalli , P. Haukkanen, On generalized Fibonacci and Lucas Polynomials, Chaos, Solutions and Fractals, 42(2009), 3179-3186.
  • D. Jarden, Recurring sequences, Jerusalem; Rivion Lematematika, 1966.
  • E. Kilic, E. Tan, On binomial sums for the general second order linear recurrence, Integers 10(2010), 801-806.
  • E. Lucas, Theorie des fonctions numeriques simplement periodiques, American Journal of Math.(1978), 189-240.
  • G. E. Bergum, V. E. Hoggatt Jr., Sums and products for recurring sequences, The Fibonaci Quaterly, 13(2) (1975), 115-120.
  • H. Belbachir, Linear recurrent sequences and Powers of a square matrix , Integers: Electronic J. of Combinatorial Number Theory, 2006, 1-17.
  • J. Mc. Laughlin, Combinatorial identities deriving from the nth power of a 2 × 2 matrix, Integers: Electronic J. of Combinatorial Number Theory 4(2004), 1-15.
  • K. S. Williams, The nth power of a 2 × 2 matrix (in notes), Math. Magazine, 65(5), 336. M. E. Waddill, L. Sacks, Another generalized Fibonacci sequence, The Fibonaci Quaterly, 5(3)(1967), 209-222.
  • M. S. El Naschie, Notes on super string and the infinite sums of Fibonacci and Lucas numbers, Chaos, Solitions and Fractals 10(8)(1999), 1303-1307.
  • N. Robbins, A new formula for Lucas numbers, The Fibonaci Quaterly, 29.4(1991), 362-363. T. Mansour, A formula for the generating functionsof powers of Horadam’s sequence, Australasian J. of Combinatorics 30(2004), 207-212.
  • T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publications, (2001).
  • R. S. Melham and A. G. Shannon, Some summation identities using generalized Q − matrices, The Fibonaci Quaterly, 33(1)(1995), 64-73.

ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES

Yıl 2013, Cilt: 42 Sayı: 4, 431 - 435, 01.04.2013

Öz

Kaynakça

  • A. F. Horadam, Basic properties of a certain generalized sequence of numbers, The Fibonaci Quaterly, 3(2) (1965), 161-176.
  • A. F. Horadam, Tschebyscheff and other functions associated with the sequence W n (a, b; p, q), The Fibonaci Quaterly, 7(1)(1969), 14-22.
  • A. Nalli , P. Haukkanen, On generalized Fibonacci and Lucas Polynomials, Chaos, Solutions and Fractals, 42(2009), 3179-3186.
  • D. Jarden, Recurring sequences, Jerusalem; Rivion Lematematika, 1966.
  • E. Kilic, E. Tan, On binomial sums for the general second order linear recurrence, Integers 10(2010), 801-806.
  • E. Lucas, Theorie des fonctions numeriques simplement periodiques, American Journal of Math.(1978), 189-240.
  • G. E. Bergum, V. E. Hoggatt Jr., Sums and products for recurring sequences, The Fibonaci Quaterly, 13(2) (1975), 115-120.
  • H. Belbachir, Linear recurrent sequences and Powers of a square matrix , Integers: Electronic J. of Combinatorial Number Theory, 2006, 1-17.
  • J. Mc. Laughlin, Combinatorial identities deriving from the nth power of a 2 × 2 matrix, Integers: Electronic J. of Combinatorial Number Theory 4(2004), 1-15.
  • K. S. Williams, The nth power of a 2 × 2 matrix (in notes), Math. Magazine, 65(5), 336. M. E. Waddill, L. Sacks, Another generalized Fibonacci sequence, The Fibonaci Quaterly, 5(3)(1967), 209-222.
  • M. S. El Naschie, Notes on super string and the infinite sums of Fibonacci and Lucas numbers, Chaos, Solitions and Fractals 10(8)(1999), 1303-1307.
  • N. Robbins, A new formula for Lucas numbers, The Fibonaci Quaterly, 29.4(1991), 362-363. T. Mansour, A formula for the generating functionsof powers of Horadam’s sequence, Australasian J. of Combinatorics 30(2004), 207-212.
  • T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience Publications, (2001).
  • R. S. Melham and A. G. Shannon, Some summation identities using generalized Q − matrices, The Fibonaci Quaterly, 33(1)(1995), 64-73.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Matematik
Yazarlar

Zeynep Akyuz Bu kişi benim

Serpil Halici Bu kişi benim

Yayımlanma Tarihi 1 Nisan 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 42 Sayı: 4

Kaynak Göster

APA Akyuz, Z., & Halici, S. (2013). ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics, 42(4), 431-435.
AMA Akyuz Z, Halici S. ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics. Nisan 2013;42(4):431-435.
Chicago Akyuz, Zeynep, ve Serpil Halici. “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics 42, sy. 4 (Nisan 2013): 431-35.
EndNote Akyuz Z, Halici S (01 Nisan 2013) ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics 42 4 431–435.
IEEE Z. Akyuz ve S. Halici, “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”, Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 4, ss. 431–435, 2013.
ISNAD Akyuz, Zeynep - Halici, Serpil. “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics 42/4 (Nisan 2013), 431-435.
JAMA Akyuz Z, Halici S. ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics. 2013;42:431–435.
MLA Akyuz, Zeynep ve Serpil Halici. “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics, c. 42, sy. 4, 2013, ss. 431-5.
Vancouver Akyuz Z, Halici S. ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES. Hacettepe Journal of Mathematics and Statistics. 2013;42(4):431-5.