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ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS

Year 2009, Volume: 38 Issue: 3, 265 - 275, 01.03.2009

Abstract

References

  • Harary, F. Determinants, permanents and bipartite graphs, Math. Mag. 42, 146–148, 1969. [2] Harne, S. and Parihar, C. L. Some generalized Fibonacci polynomials, J. Indian Acad. Math. 18(2), 251–253, 1996.
  • Harne, S. and Singh, B. Some properties of fourth-order recurrence relations, Vikram Math. J. 20, 79–84, 2000. [4] Horadam, A. F. and Shannon, A. G. Irrational sequence-generated factors of integers, Fi- bonacci Quart. 19 (3), 240–250, 1981.
  • Horn, R. and Johnson, C. Matrix Analysis (Cambridge University Press, 1985).
  • Kilic, E. and Tasci, D. On families of bipartite graphs associated with sums of Fibonacci and Lucas numbers, Ars Combin. 89, 31–40, 2008.
  • Kilic, E. and Tasci, D. On the second order linear recurrences by tridiagonal matrices, Ars Combin. (to appear).
  • Koshy, T. Fibonacci and Lucas Numbers with Applications (John Wiley & Sons Inc., 2001). [9] Lee, G. -Y. k-Lucas numbers and associated Bipartite graphs, Linear Algebra and its Appl. 320, 51–61, 2000. [10] Minc, H. Permanents of (0,1)-circulants, Canad. Math. Bull. 7 (2), 253–263, 1964.
  • Sato, S. On matrix representations of generalized Fibonacci numbers and their applications, in Applications of Fibonacci Numbers, Vol. 5 (St. Andrews, 1992) (Kluwer Acad. Publ., Dordrecht, 1993), 487–496.
  • Tasci, D. and Kirkland, S. Sequence of upper bounds for the Perron root of nonnegative matrix, Linear Algebra and Its Appl. 273, 23–28, 1998.

ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS

Year 2009, Volume: 38 Issue: 3, 265 - 275, 01.03.2009

Abstract

In this paper we define and deal with the quadrapell numbers, D(n), in terms of a linear recurrence relation of order 4, and define the quadrapell polynomials in x. Further we give the generating function, a Binet-like formula and formulae for sums of these numbers.

References

  • Harary, F. Determinants, permanents and bipartite graphs, Math. Mag. 42, 146–148, 1969. [2] Harne, S. and Parihar, C. L. Some generalized Fibonacci polynomials, J. Indian Acad. Math. 18(2), 251–253, 1996.
  • Harne, S. and Singh, B. Some properties of fourth-order recurrence relations, Vikram Math. J. 20, 79–84, 2000. [4] Horadam, A. F. and Shannon, A. G. Irrational sequence-generated factors of integers, Fi- bonacci Quart. 19 (3), 240–250, 1981.
  • Horn, R. and Johnson, C. Matrix Analysis (Cambridge University Press, 1985).
  • Kilic, E. and Tasci, D. On families of bipartite graphs associated with sums of Fibonacci and Lucas numbers, Ars Combin. 89, 31–40, 2008.
  • Kilic, E. and Tasci, D. On the second order linear recurrences by tridiagonal matrices, Ars Combin. (to appear).
  • Koshy, T. Fibonacci and Lucas Numbers with Applications (John Wiley & Sons Inc., 2001). [9] Lee, G. -Y. k-Lucas numbers and associated Bipartite graphs, Linear Algebra and its Appl. 320, 51–61, 2000. [10] Minc, H. Permanents of (0,1)-circulants, Canad. Math. Bull. 7 (2), 253–263, 1964.
  • Sato, S. On matrix representations of generalized Fibonacci numbers and their applications, in Applications of Fibonacci Numbers, Vol. 5 (St. Andrews, 1992) (Kluwer Acad. Publ., Dordrecht, 1993), 487–496.
  • Tasci, D. and Kirkland, S. Sequence of upper bounds for the Perron root of nonnegative matrix, Linear Algebra and Its Appl. 273, 23–28, 1998.
There are 8 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Dursun Tasci This is me

Publication Date March 1, 2009
Published in Issue Year 2009 Volume: 38 Issue: 3

Cite

APA Tasci, D. (2009). ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS. Hacettepe Journal of Mathematics and Statistics, 38(3), 265-275.
AMA Tasci D. ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS. Hacettepe Journal of Mathematics and Statistics. March 2009;38(3):265-275.
Chicago Tasci, Dursun. “ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS”. Hacettepe Journal of Mathematics and Statistics 38, no. 3 (March 2009): 265-75.
EndNote Tasci D (March 1, 2009) ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS. Hacettepe Journal of Mathematics and Statistics 38 3 265–275.
IEEE D. Tasci, “ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS”, Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, pp. 265–275, 2009.
ISNAD Tasci, Dursun. “ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS”. Hacettepe Journal of Mathematics and Statistics 38/3 (March 2009), 265-275.
JAMA Tasci D. ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS. Hacettepe Journal of Mathematics and Statistics. 2009;38:265–275.
MLA Tasci, Dursun. “ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS”. Hacettepe Journal of Mathematics and Statistics, vol. 38, no. 3, 2009, pp. 265-7.
Vancouver Tasci D. ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS. Hacettepe Journal of Mathematics and Statistics. 2009;38(3):265-7.