대한수학회지 (Journal of the Korean Mathematical Society)

  • 제42권1호
  • /
  • Pages.135-151
  • /
  • 2005
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS

  • OZGUR NIHAL YILMAZ (Balikesir University Faculty of Art and Sciences Department of Mathematics)
  • 발행 : 2005.01.01
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초록

In this paper, we obtain some properties of the sequences $U^{q}_n\;and\;V^{q}_n$ introduced in [6]. We find polynomial representations and formulas of them. For q = 5, $U^{5}_n$ is the Fibonacci sequence $F_n\;and\;V^{5}_n$ is the Lucas sequence $L_n$.

키워드

참고문헌

  1. R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Press, 1997
  2. M. Gardner, Mathematical Circus: More Puzzles, Games, Paradoxes and Other Mathematical Entertainments from Scientific American., New York: Knopf, 1979
  3. E. Hecke, Uber die bestimmung Dirichletscher reihen durch ihre funktionalgle- ichungen, Math. Ann. 112 (1936), 664-699 https://doi.org/10.1007/BF01565437
  4. V. E. Hogatt, The Fibonacci and Lucas Numbers, Boston MA: Houghton Mifflin, 1969
  5. S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Halsted Press, 1989
  6. N. Yilmaz Ozgur, Generalizations of Fibonacci and Lucas sequences, Note. Mat. 21 (1) (2002), 113-125
  7. N. Yilmaz Ozgur, Principal congruence subgroups of Hecke groups H$(\sqrt{q})$, Submitted.

피인용 문헌

  1. Principal Congruence Subgroups of Hecke Groups $$ H{\left( {{\sqrt q }} \right)} $$ vol.22, pp.2, 2006, https://doi.org/10.1007/s10114-005-0609-2
  2. The Generalized Order-kLucas Sequences in Finite Groups vol.2012, 2012, https://doi.org/10.1155/2012/464580
  3. Some properties of the generalized Fibonacci and Lucas sequences related to the extended Hecke groups vol.2013, pp.1, 2013, https://doi.org/10.1186/1029-242X-2013-398