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Let Y denote a d-class symmetric association scheme, with d = 3. We show the following: If Y admits a P-polynomial structure with intersection numbers pijh and Y is 1-thin with respect to at least one vertex, then plll=0 ? plii=0 1 = i = - 1. If Y admits a Q-polynomial structure with Krein parameters qijh, and Y is dual 1-thin with respect to at least one vertex, then qlll = 0 ? qlii = 01 = i = d-1.

A Note on Thin P-Polynomial and Dual-Thin Q-Polynomial Symmetric Association Schemes