Yıl: 2011 Cilt: 40 Sayı: 2 Sayfa Aralığı: 147 - 161 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}

Öz:
In this study we consider the generalized Lucas sequence {$V _{kn}$} with indices in arithmetic progression. We also compute the sums of products of the terms of the Lucas sequence {$V _{kn}$} for positive odd integers k.
Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [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] Kılıç, 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] Kılıç, E. and Stanica, P. Factorizations and representations of binary polynomial recurrences by matrix methods, Rocky Mount. J. Math., in press.
  • [8] Riordan, J. Generating functions for powers of Fibonacci numbers, Duke Math. J. 29, 5–12, 1962.
  • [9] Riordan, J. Combinatorial Identities (J. Wiley, New York, 1968).
  • [10] Riordan, J. Inverse relations and combinatorial identities, Amer. Math. Monthly 71 (5), 485–498, 1964.
  • [11] Seibert, J. and Trojovsky, P. On sums of certain products of Lucas numbers, The Fibonacci Quarterly 44, 172–180, 2006.
  • [12] Seibert, J and Trojovsky, P. On multiple sums of products of Lucas numbers, J. Integer Seq. 10, 1–17, 2007.
  • [13] 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.
  • [14] Stanica, P. Generating function, weighted and non-weighted sums for powers of second-order recurrence sequences, The Fibonacci Quarterly 41 (4), 321–333, 2003.
  • [15] Vajda, S. Fibonacci and Lucas numbers and the Golden Section (Halsted Press, Brisbane, 1989).
APA Kılıç E, ULUTAŞ Y, ÖMÜR N (2011). Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. , 147 - 161.
Chicago Kılıç Emrah,ULUTAŞ Yücel Türker,ÖMÜR Neşe Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. (2011): 147 - 161.
MLA Kılıç Emrah,ULUTAŞ Yücel Türker,ÖMÜR Neşe Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. , 2011, ss.147 - 161.
AMA Kılıç E,ULUTAŞ Y,ÖMÜR N Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. . 2011; 147 - 161.
Vancouver Kılıç E,ULUTAŞ Y,ÖMÜR N Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. . 2011; 147 - 161.
IEEE Kılıç E,ULUTAŞ Y,ÖMÜR N "Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}." , ss.147 - 161, 2011.
ISNAD Kılıç, Emrah vd. "Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}". (2011), 147-161.
APA Kılıç E, ULUTAŞ Y, ÖMÜR N (2011). Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. Hacettepe Journal of Mathematics and Statistics, 40(2), 147 - 161.
Chicago Kılıç Emrah,ULUTAŞ Yücel Türker,ÖMÜR Neşe Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. Hacettepe Journal of Mathematics and Statistics 40, no.2 (2011): 147 - 161.
MLA Kılıç Emrah,ULUTAŞ Yücel Türker,ÖMÜR Neşe Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. Hacettepe Journal of Mathematics and Statistics, vol.40, no.2, 2011, ss.147 - 161.
AMA Kılıç E,ULUTAŞ Y,ÖMÜR N Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. Hacettepe Journal of Mathematics and Statistics. 2011; 40(2): 147 - 161.
Vancouver Kılıç E,ULUTAŞ Y,ÖMÜR N Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}. Hacettepe Journal of Mathematics and Statistics. 2011; 40(2): 147 - 161.
IEEE Kılıç E,ULUTAŞ Y,ÖMÜR N "Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}." Hacettepe Journal of Mathematics and Statistics, 40, ss.147 - 161, 2011.
ISNAD Kılıç, Emrah vd. "Sums of products of the terms of the generalized Lucas sequence {$V _{kn}$}". Hacettepe Journal of Mathematics and Statistics 40/2 (2011), 147-161.