Human influenza A (subtype H3N2) is characterized genetically by the limited standing diversity of its hemagglutinin and antigenically by clusters that emerge and replace each other within 2 to 8 years. By introducing an epidemiological model that allows for differences between the genetic and antigenic properties of the virus's hemagglutinin, we show that these patterns can arise from cluster-specific immunity alone. Central to the formulation is a genotype-to-phenotype mapping, based on neutral networks, with antigenic phenotypes, not genotypes, determining the degree of strain cross-immunity. The model parsimoniously explains well-known, as well as previously unremarked, features of interpandemic influenza dynamics and evolution. It captures the observed boom-and-bust pattern of viral evolution, with periods of antigenic stasis during which genetic diversity grows, and with episodic contraction of this diversity during cluster transitions.