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

Year 2013, Volume: 42 Issue: 4, 431 - 435, 01.04.2013

Abstract

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.

References

  • 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

Year 2013, Volume: 42 Issue: 4, 431 - 435, 01.04.2013

Abstract

References

  • 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.
There are 14 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Zeynep Akyuz This is me

Serpil Halici This is me

Publication Date April 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 4

Cite

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. April 2013;42(4):431-435.
Chicago Akyuz, Zeynep, and Serpil Halici. “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics 42, no. 4 (April 2013): 431-35.
EndNote Akyuz Z, Halici S (April 1, 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 and S. Halici, “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, pp. 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 (April 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 and Serpil Halici. “ON SOME COMBINATORIAL IDENTITIES INVOLVING THE TERMS OF GENERALIZED FIBONACCI AND LUCAS SEQUENCES”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 4, 2013, pp. 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.