Catalan and Motzkin numbers modulo 4 and 8

  • Authors:

  • Sen-Peng Eu;Shu-Chung Liu;Yeong-Nan Yeh

  • Affiliations:

  • Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung, Taiwan;Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu City, Taiwan;Institute of Mathematics, Academia Sinica, Taipei, Taiwan

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2008

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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.