Three families of $q$-Lommel polynomials

Three $q$-versions of Lommel polynomials are studied. Included are explicit representations, recurrences, continued fractions, and connections to associated Askey–Wilson polynomials. Combinatorial results are emphasized, including a general theorem when $R_I$ moments coincide with orthogonal polynomial moments. The combinatorial results use weighted Motzkin paths, Schr"oder paths, and parallelogram polyominoes.