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Numerous geometric patterns identified in nature, art or science can be generated fromrecurrent sequences, such as for example certain fractals or Fermat's spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multi-symmetric patterns can be recovered for selected parameter values. Some applications are also suggested. [ABSTRACT FROM AUTHOR]

We introduce in this paper a straightforward but useful method for computing indefinite rational matrix products. The method is used to prove a certain identity involving definite sums and a definite integral. [ABSTRACT FROM AUTHOR]