  Partitions without sequences of consecutive integers as parts have been
studied recently by many authors, including Andrews, Holroyd, Liggett, and
Romik, among others. Their results include a description of combinatorial
properties, hypergeometric representations for the generating functions, and
asymptotic formulas for the enumeration functions. We complete a similar
investigation of partitions into distinct parts without sequences, which are of
particular interest due to their relationship with the Rogers-Ramanujan
identities. Our main results include a double series representation for the
generating function, an asymptotic formula for the enumeration function, and
several combinatorial inequalities.
