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It is shown that the   h  ‐vectors of Stanley–Reisner rings of three classes of matroids are pure  O ‐sequences. The classes are (a) matroids that are truncations of matroids, or more generally of Cohen–Macaulay complexes, (b) matroids whose dual is    (  rank  +  2  )   ‐partite, and (c) matroids of Cohen–Macaulay type at most 5. Consequences for the computational search for a counterexample to a conjecture of Stanley are discussed.

Generic and special constructions of pure O ‐sequences