Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

The Log-Behavior of the Partial Sum for the Tribonacci Numbers


Affiliations
  • Shanghai University, Department of Mathematics, China
     

   Subscribe/Renew Journal


Let {Tn}n ≥ 0 and {Tn[1]}n ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {Tn}n ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of Tn[1]}n ≥ 1 and the log-balancedness of some sequences involving Tn[1]. In addition, we discuss the monotonicity of some sequences related to Tn[1].

Keywords

Fibonacci Sequence, Tribonacci Sequence, Log-Convexity, Log-Concavity, Log-Balancedness, Monotonicity.
Subscription Login to verify subscription
User
Notifications
Font Size


  • N. N. Cao and F. Z. Zhao, Some properties of hyper bonacci and hyperlucas numbers, Journal of Integer Sequences, 13 (2010), Article 10.8.8.
  • W. Y. C. Chen, J. J. F. Guo and L. X. W. Wang, In nitely logarithmically monotonic combinatorial sequences, Advances in Applied Mathematics, 52 (2014), 99{120.
  • H. Davenport, G. Polya, On the product of two power series, Canadian Journal of Mathematics, 1 (1949), 1{5.
  • A. Dil and I. Mezo, A symmetric algorithm for hyperharmonic and Fibonacci numbers, Applied Mathematics and Computation, 206 (2008), 942{951.
  • T. Doslic, Log-balanced combinatorial sequences, International Journal of Mathematics and Mathematical Sciences, 4 (2005), 507{522.
  • R. A. Dunlap, The golden ratio and Fibonacci numbers, revised ed., World Scienti c, Singapore, 1997, p.61.
  • B. Hacene and B. Amine, Combinatorial expressions involving Fibonacci, hyper bonacci, and incomplete Fibonacci numbers, Journal of Integer Sequences, 17 (2014), Article 14.4.3.
  • Q. H. Hou, Z. W. Sun and H. M. Wen, On monotonicity of some combinatorial sequences, Publicationes Mathematicae Debrecen, 85 (2014), 285{295.
  • J. Li, Z. L. Jiang and F. L. Lu, Determinants, norms, and the spread of circulant matrices with tribonacci and generalized Lucas numbers, Abstract and Applied Analysis 2014, Article ID 381829.
  • R. Liu and F. Z. Zhao, On the sums of reciprocal hyper bonacci numbers and hyperlucas numbers, Journal of Integer Sequences, 15 (2012), Article 12.4.5.
  • F. Luca and P. Stanica, On some conjectures on the monotonicity of some arithmetical sequences, Journal of Combinatorics and Number Theory, 4 (2012), 115{123.
  • Z. W. Sun, Conjectures involving arithmetical sequences, Proceedings of the 6th China-Japan Seminar, S. Kanemitsu, H. Li and J. Liu eds., World Scienti c, Singapore, 2013, 244{258.
  • Y. Wang and Y-N Yeh, Log-concavity and LC-positivity, Journal of Combinatorial Theory. Series A, 114 (2007), 195{210.
  • Y. Wang and B. X. Zhu, Proofs of some conjectures on monotonicity of number-theoretic and combinatorial sequences, Science China Mathematics, 57 (2014), 2429{2435.
  • F. Z. Zhao, The log-behavior of the Catalan-Larcombe-French sequence, International Journal of Number Theory, 10 (2014), 177{182.
  • L. N. Zheng, R. Liu and F. Z. Zhao, On the log-concavity of hyper bonacci Numbers and hyperlucas Numbers, Journal of Integer Sequences, 17 (2014), Article 14.1.4.

Abstract Views: 441

PDF Views: 0




  • The Log-Behavior of the Partial Sum for the Tribonacci Numbers

Abstract Views: 441  |  PDF Views: 0

Authors

Feng-Zhen Zhao
, China

Abstract


Let {Tn}n ≥ 0 and {Tn[1]}n ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {Tn}n ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of Tn[1]}n ≥ 1 and the log-balancedness of some sequences involving Tn[1]. In addition, we discuss the monotonicity of some sequences related to Tn[1].

Keywords


Fibonacci Sequence, Tribonacci Sequence, Log-Convexity, Log-Concavity, Log-Balancedness, Monotonicity.

References