Catalan's identity and sum of k -Lucas sequence

Jye Ying Sia; Chee Kit Ho

doi:10.1063/1.4937073

Catalan's identity and sum of k -Lucas sequence

Sunway University
University Utara Malaysia

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We proved the Catalan's Identity and obtained the sum using the same generating matrix for the k-Lucas sequence, L_n+1 = kL_n + L_n-1 with the initial values, L₀ = k, L₁ = 2 when n and k are both positive.

Original language	English
Title of host publication	Innovation and Analytics Conference and Exhibition, IACE 2015
Subtitle of host publication	Proceedings of the 2nd Innovation and Analytics Conference and Exhibition
Editors	Nazihah Ahmad, Jafri Zulkepli, Adyda Ibrahim, Nazrina Aziz, Syariza Abdul-Rahman
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735413382
DOIs	https://doi.org/10.1063/1.4937073
Publication status	Published - 11 Dec 2015
Externally published	Yes
Event	2nd Innovation and Analytics Conference and Exhibition, IACE 2015 - Alor Setar, Kedah, Malaysia Duration: 29 Sept 2015 → 1 Oct 2015

Publication series

Name	AIP Conference Proceedings
Volume	1691
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	2nd Innovation and Analytics Conference and Exhibition, IACE 2015
Country/Territory	Malaysia
City	Alor Setar, Kedah
Period	29/09/15 → 1/10/15

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10.1063/1.4937073

Cite this

Sia, J. Y., & Ho, C. K. (2015). Catalan's identity and sum of k -Lucas sequence. In N. Ahmad, J. Zulkepli, A. Ibrahim, N. Aziz, & S. Abdul-Rahman (Eds.), Innovation and Analytics Conference and Exhibition, IACE 2015: Proceedings of the 2nd Innovation and Analytics Conference and Exhibition Article 040023 (AIP Conference Proceedings; Vol. 1691). American Institute of Physics Inc.. https://doi.org/10.1063/1.4937073

Sia, Jye Ying ; Ho, Chee Kit. / Catalan's identity and sum of k -Lucas sequence. Innovation and Analytics Conference and Exhibition, IACE 2015: Proceedings of the 2nd Innovation and Analytics Conference and Exhibition. editor / Nazihah Ahmad ; Jafri Zulkepli ; Adyda Ibrahim ; Nazrina Aziz ; Syariza Abdul-Rahman. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

@inproceedings{7c948e6bf2f64ae7a2b7c1f750d1b0b7,

title = "Catalan's identity and sum of k -Lucas sequence",

abstract = "We proved the Catalan's Identity and obtained the sum using the same generating matrix for the k-Lucas sequence, Ln+1 = kLn + Ln-1 with the initial values, L0 = k, L1 = 2 when n and k are both positive.",

author = "Sia, \{Jye Ying\} and Ho, \{Chee Kit\}",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; 2nd Innovation and Analytics Conference and Exhibition, IACE 2015 ; Conference date: 29-09-2015 Through 01-10-2015",

year = "2015",

month = dec,

day = "11",

doi = "10.1063/1.4937073",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Nazihah Ahmad and Jafri Zulkepli and Adyda Ibrahim and Nazrina Aziz and Syariza Abdul-Rahman",

booktitle = "Innovation and Analytics Conference and Exhibition, IACE 2015",

}

Sia, JY & Ho, CK 2015, Catalan's identity and sum of k -Lucas sequence. in N Ahmad, J Zulkepli, A Ibrahim, N Aziz & S Abdul-Rahman (eds), Innovation and Analytics Conference and Exhibition, IACE 2015: Proceedings of the 2nd Innovation and Analytics Conference and Exhibition., 040023, AIP Conference Proceedings, vol. 1691, American Institute of Physics Inc., 2nd Innovation and Analytics Conference and Exhibition, IACE 2015, Alor Setar, Kedah, Malaysia, 29/09/15. https://doi.org/10.1063/1.4937073

Catalan's identity and sum of k -Lucas sequence. / Sia, Jye Ying ; Ho, Chee Kit.
Innovation and Analytics Conference and Exhibition, IACE 2015: Proceedings of the 2nd Innovation and Analytics Conference and Exhibition. ed. / Nazihah Ahmad; Jafri Zulkepli; Adyda Ibrahim; Nazrina Aziz; Syariza Abdul-Rahman. American Institute of Physics Inc., 2015. 040023 (AIP Conference Proceedings; Vol. 1691).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Ho, Chee Kit

PY - 2015/12/11

Y1 - 2015/12/11

N2 - We proved the Catalan's Identity and obtained the sum using the same generating matrix for the k-Lucas sequence, Ln+1 = kLn + Ln-1 with the initial values, L0 = k, L1 = 2 when n and k are both positive.

AB - We proved the Catalan's Identity and obtained the sum using the same generating matrix for the k-Lucas sequence, Ln+1 = kLn + Ln-1 with the initial values, L0 = k, L1 = 2 when n and k are both positive.

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DO - 10.1063/1.4937073

M3 - Conference contribution

AN - SCOPUS:84984572013

T3 - AIP Conference Proceedings

BT - Innovation and Analytics Conference and Exhibition, IACE 2015

A2 - Ahmad, Nazihah

A2 - Zulkepli, Jafri

A2 - Ibrahim, Adyda

A2 - Aziz, Nazrina

A2 - Abdul-Rahman, Syariza

PB - American Institute of Physics Inc.

T2 - 2nd Innovation and Analytics Conference and Exhibition, IACE 2015

Y2 - 29 September 2015 through 1 October 2015

ER -

Sia JY , Ho CK. Catalan's identity and sum of k -Lucas sequence. In Ahmad N, Zulkepli J, Ibrahim A, Aziz N, Abdul-Rahman S, editors, Innovation and Analytics Conference and Exhibition, IACE 2015: Proceedings of the 2nd Innovation and Analytics Conference and Exhibition. American Institute of Physics Inc. 2015. 040023. (AIP Conference Proceedings). doi: 10.1063/1.4937073

Catalan's identity and sum of k -Lucas sequence

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