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Horadam sequences: a survey update and extension. (English) Zbl 1419.11030

Summary: We give an update on work relating to Horadam sequences that are generated by a general linear recurrence formula of order two.
This article extends a first ever survey published in early 2013 in this Bulletin [the author et al., Bull. Inst. Comb. Appl. 67, 49–72 (2013; Zbl 1281.11012)], and includes coverage of a new research area opened up in recent times. 65 References.
Cited items not covered by zbMATH:
O. Bagdasar, P. J. Larcombe and A. Anjum, Particular orbits of periodic Horadam sequences, Oct. Math. Mag. 21, 87–98 (2013).
G. Cerda, Matrix methods in Horadam sequences, Bol. Mat. 19, 97–106 (2012).
P. J. Larcombe, A short monograph on exposition and the emotive nature of research and publishing, Math. Today 52, 86–90 (2016).
N. Taskara, K. Uslu, Y. Yazlik and N. Yilmaz, The construction of Horadam numbers in terms of the determinant of tridiagonal matrices, Proc. 9th Int. Conf. Num. Anal. Appl. Math. (A.I.P. Conf. Proc. No. 1389), Halkidiki, Greece, 367–370 (2011).
Y. Yazlik and N. Taskara, On the negatively and positively subscripted generalized \(k\)-Horadam sequences and their matrix presentations, World Appl. Sci. J., 27, 1561–1565 (2013).

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11-02 Research exposition (monographs, survey articles) pertaining to number theory

Citations:

Zbl 1281.11012
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