Interpre'tation bijective d'une re'currence des nombres de Motzkin

The purpose of this note is to give a combinatorial proof of the three-term linear recurrence for Motzkin numbers. The present work is inspired by Remy's combinatorial proof of the linear recurrence for Catalan numbers (RAIRO Inform. Theor. 19(2) (1985) 179) and the more recent proof given by Foata and Zeilberger (J. Combin. Theory Ser. A 80(2) (1997) 380) for Schroder numbers (Z. Math. Phys. 15 (1870) 361).

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