A Classification of Motzkin Numbers Modulo 8

  • Ying Wang
  • Guoce Xin
Keywords: Motzkin numbers, Congruence classes


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.

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