Research Article

SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}

Volume: 40 Number: 2 February 1, 2011
  • E. Kılıç
  • Y.t. Ulutaş
  • Yücel Türker Ulutaş
  •  n. Ömür
EN TR

SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}

Abstract

In this study we consider the generalized Lucas sequence {Vn} with indices in arithmetic progression. We also compute the sums of products of the terms of the Lucas sequence {Vkn} for positive odd integers k.

Keywords

References

  1. Carlitz, L. Generating function for powers of a certain sequences of numbers, Duke Math. J. 29, 521–537, 1962.
  2. Dujella, A. A bijective proof of Riordan’s theorem on powers of Fibonacci numbers, Discrete Math. 199, 217–220, 1999.
  3. Golomb, S. W. Problem 4720, Amer. Math. Monthly 64, 49, 1957.
  4. Hoggatt Jr., V. E. Fibonacci numbers and generalized binomial coefficients, The Fibonacci Quarterly 5, 383–400, 1967.
  5. Horadam, A. F. Generating functions for powers of a certain generalized sequence of num- bers, Duke Math. J. 32, 437–446, 1965.
  6. Kılı¸c, E. and Stanica, P. Factorizations and representations of second linear recurrences with indices in arithmetic progressions, Bol. Mex. Math. Soc. 15 (1), 23–36, 2009.
  7. Kılı¸c, E. and Stanica, P. Factorizations and representations of binary polynomial recurrences by matrix methods, Rocky Mount. J. Math., in press. Riordan, J. Generating functions for powers of Fibonacci numbers, Duke Math. J. 29, 5–12, Riordan, J. Combinatorial Identities (J. Wiley, New York, 1968).
  8. Riordan, J. Inverse relations and combinatorial identities, Amer. Math. Monthly 71 (5), –498, 1964.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

E. Kılıç This is me

Y.t. Ulutaş This is me

Yücel Türker Ulutaş This is me

 n. Ömür This is me

Publication Date

February 1, 2011

Submission Date

May 12, 2014

Acceptance Date

-

Published in Issue

Year 2011 Volume: 40 Number: 2

APA
Kılıç, E., Ulutaş, Y., Ulutaş, Y. T., & Ömür, n. (2011). SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics, 40(2), 147-161. https://izlik.org/JA55ZG78SE
AMA
1.Kılıç E, Ulutaş Y, Ulutaş YT, Ömür n. SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics. 2011;40(2):147-161. https://izlik.org/JA55ZG78SE
Chicago
Kılıç, E., Y.t. Ulutaş, Yücel Türker Ulutaş, and  n. Ömür. 2011. “SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}”. Hacettepe Journal of Mathematics and Statistics 40 (2): 147-61. https://izlik.org/JA55ZG78SE.
EndNote
Kılıç E, Ulutaş Y, Ulutaş YT, Ömür n. (February 1, 2011) SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics 40 2 147–161.
IEEE
[1]E. Kılıç, Y. Ulutaş, Y. T. Ulutaş, and  n.Ömür, “SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}”, Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, pp. 147–161, Feb. 2011, [Online]. Available: https://izlik.org/JA55ZG78SE
ISNAD
Kılıç, E. - Ulutaş, Y.t. - Ulutaş, Yücel Türker - Ömür, n. “SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}”. Hacettepe Journal of Mathematics and Statistics 40/2 (February 1, 2011): 147-161. https://izlik.org/JA55ZG78SE.
JAMA
1.Kılıç E, Ulutaş Y, Ulutaş YT, Ömür n. SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics. 2011;40:147–161.
MLA
Kılıç, E., et al. “SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}”. Hacettepe Journal of Mathematics and Statistics, vol. 40, no. 2, Feb. 2011, pp. 147-61, https://izlik.org/JA55ZG78SE.
Vancouver
1.E. Kılıç, Y.t. Ulutaş, Yücel Türker Ulutaş,  n. Ömür. SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics [Internet]. 2011 Feb. 1;40(2):147-61. Available from: https://izlik.org/JA55ZG78SE