General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT

Year 2013, Volume: 42 Issue: 1 , 1 - 7 , 01.01.2013

E. Kılıç P. Stanica

https://izlik.org/JA34RB28DZ

Abstract

In this paper we find a general approach to find closed forms of sumsof products of arbitrary sequences satisfying the same recurrence withdifferent initial conditions. We apply successfully our technique to sumsof products of such sequences with indices in (arbitrary) arithmeticprogressions. It generalizes many results from literature. We proposealso an extension where the sequences satisfy different recurrences.

Keywords

Second order recurrences; Sums; Products

General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT

https://izlik.org/JA34RB28DZ

Abstract

-

Keywords

-

References

• Belbachir H. and Bencherif, F. Sums of products of generalized Fibonacci and Lucas numbers, Arxiv:0708.2347v1, 2009.
• Cerin, Z. Sums of products of generalized Fibonacci and Lucas numbers, Demons. Math., 42 (2), 247–258, 2009.
• Cerin, Z. On Sums of Products of Horadam Numbers, Kyungpook Math. J., 49, 483–492, 200 Cerin, Z. and Gianella G.M. On sums of squares of Pell-Lucas numbers, Integers 6 A15, 16 pp., 2006.
• Cerin, Z. Alternating sums of Fibonacci products, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 53 (2), 331–344, 2005.
• Cerin, Z. Some alternating sums of Lucas numbers, Cent. Eur. J. Math. 3 (1) , 1–13, 2005. Kılı¸ c, E. Sums of the squares of terms of sequence {u n }, Proc. Indian Acad. Sci. 118 (1), 27–41, 2008.
• Koshy, T. Fibonacci and Lucas numbers with applications, Pure and Appl. Math., WileyInterscience, New York, 2001.
• Mead, D.G. Problem B-67, Fibonacci Quart. 3 (4), 326–327, 1965.
• Melham, R.S. On sums of powers of terms in a linear recurrence, Portugal. Math. 56 (4), 501–508, 1999.
• Rao, K.S. Some properties of Fibonacci numbers, The Amer. Math. Monthly, 60, 680–684, 19 Vajda, S. Fibonacci & Lucas numbers, and the golden section, John Wiley & Sons, Inc., New York, 1989.