Using real-space self-consistent field theory calculations (SCFT), directed self-assembly of block copolymers was explored on sparsely nanopatterned substrates. In this study, the lamellar structure forming block copolymers are confined between two surfaces. The top surface is strictly neutral, and the bottom one is periodically patterned with neutral interspacing (nanopattern), which forms a sparsely nanopatterned substrate. The dimension of nanopatterns is commensurate with periods of lamellar structure of the block copolymers self-assembling in bulk. By systematically varying the film thickness and interspacing between nanopatterns, the density multiplication of nanopattern in the film was investigated, and a variety of nanostructures not available in bulk (nonbulk structures) were observed.