ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS

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

Dursun Tasci

Abstract

ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS

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.

Keywords

Quadrapell numbers, Quadrapell polynomials, 2000 AMS Classification: 11 B 39

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.