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Discrete Dynamics in Nature and Society
Volume 2009, Article ID 453750, 10 pages
http://dx.doi.org/10.1155/2009/453750
Research Article

K-nacci Sequences in Finite Triangle Groups

Department of Mathematics, Faculty of Sicence, Atatürk University, 25240 Erzurum, Turkey

Received 10 March 2009; Revised 16 July 2009; Accepted 14 September 2009

Academic Editor: Leonid Shaikhet

Copyright © 2009 Erdal Karaduman and Ömür Deveci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. M. Campbell, H. Doostie, and E. F. Robertson, “Fibonacci length of generating pairs in groups,” in Applications of Fibonacci Numbers, G. E. Bergum, Ed., vol. 3, pp. 27–35, Kluwer Academic Publisher, Dordrecht, The Netherlands, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. D. D. Wall, “Fibonacci series module m,” The American Mathematical Monthly, vol. 67, pp. 525–532, 1969. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. C. M. Campbell and P. P. Campbell, “On the Fibonacci length of powers of dihedral groups,” in Applications of Fibonacci Numbers, F. T. Howard, Ed., vol. 9, pp. 69–85, Kluwer Academic Publisher, Dordrecht, The Netherlands, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. H. Doostie and C. M. Campbell, “Fibonacci length of automorphism groups involving Tribonacci numbers,” Vietnam Journal of Mathematics, vol. 28, no. 1, pp. 57–65, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Aydın and R. Dikici, “General Fibonacci sequences in finite groups,” The Fibonacci Quarterly, vol. 36, no. 3, pp. 216–221, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Aydın and G. C. Smith, “Finite p-quotients of some cyclically presented groups,” Journal of the London Mathematical Society, vol. 49, no. 1, pp. 83–92, 1994. View at Google Scholar · View at MathSciNet
  7. E. Karaduman and H. Aydın, “On the relationship between the recurrences in nilpotent groups and the binomial formula,” Indian Journal of Pure and Applied Mathematics, vol. 35, no. 9, pp. 1093–1103, 2004. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. M. Campbell and P. P. Campbell, “The Fibonacci length of certain centro-polyhedral groups,” Journal of Applied Mathematics & Computing, vol. 19, no. 1-2, pp. 231–240, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Doostie and M. Maghasedi, “Fibonacci length of direct products of groups,” Vietnam Journal of Mathematics, vol. 33, no. 2, pp. 189–197, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Doostie and M. Hashemi, “Fibonacci lengths involving the Wall number k(n),” Journal of Applied Mathematics & Computing, vol. 20, no. 1-2, pp. 171–180, 2006. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. Özkan, “On truncated Fibonacci sequences,” Indian Journal of Pure and Applied Mathematics, vol. 38, no. 4, pp. 241–251, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. J. Wilcox, “Fibonacci sequences of period n in groups,” The Fibonacci Quarterly, vol. 24, no. 4, pp. 356–361, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Steven W. Knox, “Fibonacci sequences in finite groups,” The Fibonacci Quarterly, vol. 30, no. 2, pp. 116–120, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. M. Campbell and P. P. Campbell, “The Fibonacci lengths of binary polyhedral groups and related groups,” Congressus Numerantium, vol. 194, pp. 95–102, 2009. View at Google Scholar
  15. J. H. Conway, H. S. M. Coxeter, and G. C. Shephard, “The centre of a finitely generated group,” Tensor. New Series, vol. 25, pp. 405–418, 1972. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, Springer, Berlin, Germany, 3rd edition, 1972. View at Zentralblatt MATH · View at MathSciNet
  17. M. D. E. Conder, “Group actions on graphs, maps and surfaces with maximum symmetry,” in Groups St. Andrews 2001 in Oxford, C. M. Campbell, E. F. Robertson, and G. C. Smith, Eds., vol. 1, pp. 63–91, Cambridge University Press, Cambridge, UK, 2003. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. M. A. Albar and W. M. Al-Hamdan, “The triangle groups,” Rendiconti del Seminario Matematico della Universita di Padova, vol. 89, pp. 103–111, 1993. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet