ON QUADRAPELL NUMBERS AND QUADRAPELL POLYNOMIALS

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

1. 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.
2. 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.
3. Horn, R. and Johnson, C. Matrix Analysis (Cambridge University Press, 1985).
4. Kilic, E. and Tasci, D. On families of bipartite graphs associated with sums of Fibonacci and Lucas numbers, Ars Combin. 89, 31–40, 2008.
5. Kilic, E. and Tasci, D. On the second order linear recurrences by tridiagonal matrices, Ars Combin. (to appear).
6. 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.
7. 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.
8. 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.