On integrality and periodicity of the Motzkin numbers

Autores: Martin Klazar , Florian Luca
Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 69, Nº. 1-2, 2005, págs. 68-75
Idioma: inglés
DOI: 10.1007/s00010-004-2734-x
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Resumen
- In this note we investigate arithmetic properties of the Motzkin numbers. We prove that among all fractional sequences of Motzkin type, the only integral ones are integral multiples of the sequence of Motzkin numbers; in fact, we prove a stronger result. We also show that the sequence of Motzkin numbers is nonperiodic modulo any positive integer larger than one.