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

Year 2011, Volume: 40 Issue: 2, 147 - 161, 01.02.2011

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.

References

  • Carlitz, L. Generating function for powers of a certain sequences of numbers, Duke Math. J. 29, 521–537, 1962.
  • Dujella, A. A bijective proof of Riordan’s theorem on powers of Fibonacci numbers, Discrete Math. 199, 217–220, 1999.
  • Golomb, S. W. Problem 4720, Amer. Math. Monthly 64, 49, 1957.
  • Hoggatt Jr., V. E. Fibonacci numbers and generalized binomial coefficients, The Fibonacci Quarterly 5, 383–400, 1967.
  • Horadam, A. F. Generating functions for powers of a certain generalized sequence of num- bers, Duke Math. J. 32, 437–446, 1965.
  • 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.
  • 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).
  • Riordan, J. Inverse relations and combinatorial identities, Amer. Math. Monthly 71 (5), –498, 1964.
  • Seibert, J. and Trojovsky, P. On sums of certain products of Lucas numbers, The Fibonacci Quarterly 44, 172–180, 2006.
  • Seibert, J and Trojovsky, P. On multiple sums of products of Lucas numbers, J. Integer Seq. , 1–17, 2007.
  • Shannon, A. G. A Method of Carlitz applied to the kth power generating function for Fi- bonacci numbers, The Fibonacci Quarterly 12, 293–299, 1974.
  • Stanica, P. Generating function, weighted and non-weighted sums for powers of second-order recurrence sequences, The Fibonacci Quarterly 41 (4), 321–333, 2003.
  • Vajda, S. Fibonacci and Lucas numbers and the Golden Section (Halsted Press, Brisbane, ).

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

Year 2011, Volume: 40 Issue: 2, 147 - 161, 01.02.2011

Abstract

References

  • Carlitz, L. Generating function for powers of a certain sequences of numbers, Duke Math. J. 29, 521–537, 1962.
  • Dujella, A. A bijective proof of Riordan’s theorem on powers of Fibonacci numbers, Discrete Math. 199, 217–220, 1999.
  • Golomb, S. W. Problem 4720, Amer. Math. Monthly 64, 49, 1957.
  • Hoggatt Jr., V. E. Fibonacci numbers and generalized binomial coefficients, The Fibonacci Quarterly 5, 383–400, 1967.
  • Horadam, A. F. Generating functions for powers of a certain generalized sequence of num- bers, Duke Math. J. 32, 437–446, 1965.
  • 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.
  • 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).
  • Riordan, J. Inverse relations and combinatorial identities, Amer. Math. Monthly 71 (5), –498, 1964.
  • Seibert, J. and Trojovsky, P. On sums of certain products of Lucas numbers, The Fibonacci Quarterly 44, 172–180, 2006.
  • Seibert, J and Trojovsky, P. On multiple sums of products of Lucas numbers, J. Integer Seq. , 1–17, 2007.
  • Shannon, A. G. A Method of Carlitz applied to the kth power generating function for Fi- bonacci numbers, The Fibonacci Quarterly 12, 293–299, 1974.
  • Stanica, P. Generating function, weighted and non-weighted sums for powers of second-order recurrence sequences, The Fibonacci Quarterly 41 (4), 321–333, 2003.
  • Vajda, S. Fibonacci and Lucas numbers and the Golden Section (Halsted Press, Brisbane, ).
There are 13 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
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
Published in Issue Year 2011 Volume: 40 Issue: 2

Cite

APA Kılıç, E., Ulutaş, Y., Ulutaş, Y. T., Ömür, . (2011). SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics, 40(2), 147-161.
AMA Kılıç E, Ulutaş Y, Ulutaş YT, Ömür . SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics. February 2011;40(2):147-161.
Chicago Kılıç, E., Y.t. Ulutaş, Yücel Türker Ulutaş, and  n. Ömür. “SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}”. Hacettepe Journal of Mathematics and Statistics 40, no. 2 (February 2011): 147-61.
EndNote Kılıç E, Ulutaş Y, Ulutaş YT, Ömür  (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 E. Kılıç, Y. Ulutaş, Y. T. Ulutaş, and  . 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, 2011.
ISNAD Kılıç, E. et al. “SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}”. Hacettepe Journal of Mathematics and Statistics 40/2 (February 2011), 147-161.
JAMA Kılıç E, Ulutaş Y, Ulutaş YT, Ömür . 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, 2011, pp. 147-61.
Vancouver Kılıç E, Ulutaş Y, Ulutaş YT, Ömür . SUMS OF PRODUCTS OF THE TERMS OF THE GENERALIZED LUCAS SEQUENCE {Vkn}. Hacettepe Journal of Mathematics and Statistics. 2011;40(2):147-61.