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

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

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.

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.

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

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

Abstract

-

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.
There are 9 citations in total.

Details

Primary Language Turkish
Journal Section Mathematics
Authors

E. Kılıç This is me

P. Stanica This is me

Publication Date January 1, 2013
Published in Issue Year 2013 Volume: 42 Issue: 1

Cite

APA Kılıç, E., & Stanica, P. (2013). General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics, 42(1), 1-7.
AMA Kılıç E, Stanica P. General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics. January 2013;42(1):1-7.
Chicago Kılıç, E., and P. Stanica. “General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT”. Hacettepe Journal of Mathematics and Statistics 42, no. 1 (January 2013): 1-7.
EndNote Kılıç E, Stanica P (January 1, 2013) General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics 42 1 1–7.
IEEE E. Kılıç and P. Stanica, “General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 1, pp. 1–7, 2013.
ISNAD Kılıç, E. - Stanica, P. “General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT”. Hacettepe Journal of Mathematics and Statistics 42/1 (January 2013), 1-7.
JAMA Kılıç E, Stanica P. General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics. 2013;42:1–7.
MLA Kılıç, E. and P. Stanica. “General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 1, 2013, pp. 1-7.
Vancouver Kılıç E, Stanica P. General Approach in Computing Sums of Products of Binary Sequences ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics. 2013;42(1):1-7.