Catalan and Motzkin numbers modulo 4 and 8

Sen Peng Eu; Shu Chung Liu; Yeong Nan Yeh

doi:10.1016/j.ejc.2007.06.019

Catalan and Motzkin numbers modulo 4 and 8

Sen Peng Eu^*
, Shu Chung Liu
, Yeong Nan Yeh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of 8.

Original language	English
Pages (from-to)	1449-1466
Number of pages	18
Journal	European Journal of Combinatorics
Volume	29
Issue number	6
DOIs	https://doi.org/10.1016/j.ejc.2007.06.019
Publication status	Published - 2008 Aug
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2007.06.019

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title = "Catalan and Motzkin numbers modulo 4 and 8",

abstract = "In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of 8.",

author = "Eu, \{Sen Peng\} and Liu, \{Shu Chung\} and Yeh, \{Yeong Nan\}",

note = "Funding Information: The authors would like to thank Bruce Sagan for his valuable suggestions which led to a great improvement on the earlier version of this paper. S.-P. Eu was partially supported by NSC 95-2115-M-390-005. S.-C. Liu was partially supported by NSC 95-2115-M-163-002 and Y.-N. Yeh was partially supported by NSC 95-2115-M-001-009. ",

year = "2008",

month = aug,

doi = "10.1016/j.ejc.2007.06.019",

language = "English",

volume = "29",

pages = "1449--1466",

journal = "European Journal of Combinatorics",

issn = "0195-6698",

publisher = "Academic Press",

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TY - JOUR

T1 - Catalan and Motzkin numbers modulo 4 and 8

AU - Eu, Sen Peng

AU - Liu, Shu Chung

AU - Yeh, Yeong Nan

N1 - Funding Information: The authors would like to thank Bruce Sagan for his valuable suggestions which led to a great improvement on the earlier version of this paper. S.-P. Eu was partially supported by NSC 95-2115-M-390-005. S.-C. Liu was partially supported by NSC 95-2115-M-163-002 and Y.-N. Yeh was partially supported by NSC 95-2115-M-001-009.

PY - 2008/8

Y1 - 2008/8

N2 - In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of 8.

AB - In this paper, we compute the congruences of Catalan and Motzkin numbers modulo 4 and 8. In particular, we prove the conjecture proposed by Deutsch and Sagan that no Motzkin number is a multiple of 8.

UR - https://www.scopus.com/pages/publications/43849089253

UR - https://www.scopus.com/pages/publications/43849089253#tab=citedBy

U2 - 10.1016/j.ejc.2007.06.019

DO - 10.1016/j.ejc.2007.06.019

M3 - Article

AN - SCOPUS:43849089253

SN - 0195-6698

VL - 29

SP - 1449

EP - 1466

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 6

ER -

Catalan and Motzkin numbers modulo 4 and 8

Abstract

ASJC Scopus subject areas

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