The well-known Motzkin numbers were conjectured by Deutsch and Sagan to be nonzero when modulo $8$. The conjecture was first proved by Sen-Peng Eu, Shu-chung Liu and Yeong-Nan Yeh by using the factorial representation of the Catalan numbers. We present a short proof by finding a recursive formula for Motzkin numbers modulo $8$. Moreover, such a recursion leads to a full classification of Motzkin numbers modulo $8$. An addendum was added on April 3 2018.
@article{10_37236_7092,
author = {Ying Wang and Guoce Xin},
title = {A classification of {Motzkin} numbers modulo 8},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {1},
doi = {10.37236/7092},
zbl = {1391.05022},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7092/}
}
TY - JOUR
AU - Ying Wang
AU - Guoce Xin
TI - A classification of Motzkin numbers modulo 8
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/7092/
DO - 10.37236/7092
ID - 10_37236_7092
ER -
%0 Journal Article
%A Ying Wang
%A Guoce Xin
%T A classification of Motzkin numbers modulo 8
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/7092/
%R 10.37236/7092
%F 10_37236_7092
Ying Wang; Guoce Xin. A classification of Motzkin numbers modulo 8. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7092
