Polynomial Generalizations and Combinatorial Interpretations for Sequences Including the Fibonacci and Pell Numbers

Cecília Pereira de Andrade,
José Plínio de Oliveira Santos,
Elen Viviani Pereira da Silva,
Kênia Cristina Pereira Silva

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References

[1] J. P. O. Santos and M. Ivkovic, “Polynomial Generalizations of the Pell Sequence and the Fibonacci Sequence,” The Fibonacci Quarterly, Vol. 43, No. 4, 2005, pp. 328-338.

[2] J. P. O. Santos and M. Ivkovic, “Fibonacci Numbers and Partitions,” The Fibonacci Quarterly, Vol. 41, No. 3, 2003, pp. 263-278.

[3] J. P. O. Santos, “On the Combinatorics of Polynomial Generalizations of Rogers-Ramanujan-Type Identities,” Discrete Mathematics, Vol. 254, No. 1-3, 2002, pp. 497-511. doi:10.1016/S0012-365X(01)00378-8

[4] G. E. Andrews, “Combinatorics and Ramanujan’s ‘Lost’ Notebook,” In: London Mathematical Society Lecture Note Series, No. 103, Cambridge University Press, London, 1985, pp. 1-23.

[5] J. P. O. Santos, “Computer Algebra and Identities of the Rogers-Ramanujan Type,” Ph.D. Thesis, Pennsylvania State University, University Park, 1991.

[6] L. J. Slater, “Further Identities of the Rogers-Ramanujan Type,” Proceedings London Mathematical Society, Vol. s2-54, No. 1, 1952, pp. 147-167.
doi:10.1112/plms/s2-54.2.147

[7] L. J. Slater, “A New Proof of Roger’s Transformations of Infinite Series,” Proceedings London Mathematical Society, Vol. s2-53, No. 1, 1951, pp. 460-475.
doi:10.1112/plms/s2-53.6.460

[8] A. V. Sills. “RRtools—A Maple Package for Aiding the Discovery and Proof of Finite Rogers-Ramanujan Type Identities,” Journal of Symbolic Computation, Vol. 37, No. 4, 2004, pp. 415-448.
http://math.georgiasouthern.edu/asills/maple/RRtools1