Recently, some combinatorial properties for the the Catalan-Larcombe-French numbers have been proved by Sun and Wu, and Zhao. Recently, Z. W. Sun conjectured that the root of the Catalan-Larcombe-French numbers is log-concave. In this paper, we confirm Sun's conjecture by establishing the lower and upper bound for the ratios of the Catalan-Larcombe-French numbers.
Published in | American Journal of Mathematical and Computer Modelling (Volume 2, Issue 4) |
DOI | 10.11648/j.ajmcm.20170204.11 |
Page(s) | 95-98 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2017. Published by Science Publishing Group |
The Catalan-Larcombe-French Number, Log-Concavity, Recurrence Relation
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APA Style
Yang Wen. (2017). On the Log-Concavity of the Root of the Catalan-Larcombe-French Numbers. American Journal of Mathematical and Computer Modelling, 2(4), 95-98. https://doi.org/10.11648/j.ajmcm.20170204.11
ACS Style
Yang Wen. On the Log-Concavity of the Root of the Catalan-Larcombe-French Numbers. Am. J. Math. Comput. Model. 2017, 2(4), 95-98. doi: 10.11648/j.ajmcm.20170204.11
@article{10.11648/j.ajmcm.20170204.11, author = {Yang Wen}, title = {On the Log-Concavity of the Root of the Catalan-Larcombe-French Numbers}, journal = {American Journal of Mathematical and Computer Modelling}, volume = {2}, number = {4}, pages = {95-98}, doi = {10.11648/j.ajmcm.20170204.11}, url = {https://doi.org/10.11648/j.ajmcm.20170204.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20170204.11}, abstract = {Recently, some combinatorial properties for the the Catalan-Larcombe-French numbers have been proved by Sun and Wu, and Zhao. Recently, Z. W. Sun conjectured that the root of the Catalan-Larcombe-French numbers is log-concave. In this paper, we confirm Sun's conjecture by establishing the lower and upper bound for the ratios of the Catalan-Larcombe-French numbers.}, year = {2017} }
TY - JOUR T1 - On the Log-Concavity of the Root of the Catalan-Larcombe-French Numbers AU - Yang Wen Y1 - 2017/04/17 PY - 2017 N1 - https://doi.org/10.11648/j.ajmcm.20170204.11 DO - 10.11648/j.ajmcm.20170204.11 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 95 EP - 98 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20170204.11 AB - Recently, some combinatorial properties for the the Catalan-Larcombe-French numbers have been proved by Sun and Wu, and Zhao. Recently, Z. W. Sun conjectured that the root of the Catalan-Larcombe-French numbers is log-concave. In this paper, we confirm Sun's conjecture by establishing the lower and upper bound for the ratios of the Catalan-Larcombe-French numbers. VL - 2 IS - 4 ER -