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Finding certain posets in SAGE

Distributive lattices can be characterised as lattices having no sublattice isomorphic to the diamond or the pentagon (see for example ). Now I try to obtain in SAGE all connected posets with a global maximum and a global minimum that do not contain the diamond or the pentagon as a subposet. How to do that in SAGE in the quickest possible way? And do such (maybe not necessarily connected) posets have a name or are enumerated in the OEIS?