Previous |  Up |  Next

Article

Keywords:
Convolution; generating function; linear recurrence sequences; Fibonacci sequence.
Summary:
We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.
References:
[1] Szakács, T.: Convolution of second order linear recursive sequences I. Annales Mathematicae et Informaticae, 46, 2016, 205-216, MR 3607013 | Zbl 1374.11026
[2] Griffiths, M., Bramham, A.: The Jacobsthal numbers: Two results and two questions. The Fibonacci Quarterly, 53, 2, 2015, 147-151, MR 3353492
[3] Inc., OEIS Foundation: The On-Line Encyclopedia of Integer Sequences. 2011, http://oeis.org
[4] Zhang, Z., He, P.: The Multiple Sum on the Generalized Lucas Sequences. The Fibonacci Quarterly, 40, 2, 2002, 124-127, MR 1902748 | Zbl 1039.11003
[5] Zhang, W.: Some Identities Involving the Fibonacci Numbers. The Fibonacci Quarterly, 35, 3, 1997, 225-229, MR 1465835 | Zbl 0880.11018
[6] Vajda, S.: Fibonacci & Lucas numbers, and the golden section. Ellis Horwood Books In Mathematics And Its Application, 1989, MR 1015938 | Zbl 0695.10001
[7] Jones, J.P., Kiss, P.: Linear recursive sequences and power series. Publ. Math. Debrecen, 41, 1992, 295-306, MR 1189111 | Zbl 0769.11007
Partner of
EuDML logo