We use genome-wide nucleosome maps to study sequence specificity of intrinsic histone-DNA interactions. In contrast with previous approaches, we employ an analogy between a classical one-dimensional fluid of finite-size particles in an arbitrary external potential and arrays of DNA-bound histone octamers. We derive an analytical solution to infer free energies of nucleosome formation directly from nucleosome occupancies measured in high-throughput experiments. The sequence-specific part of free energies is then captured by fitting them to a sum of energies assigned to individual nucleotide motifs. We have developed hierarchical models of increasing complexity and spatial resolution, establishing that nucleosome occupancies can be explained by systematic differences in mono- and dinucleotide content between nucleosomal and linker DNA sequences, with periodic dinucleotide distributions and longer sequence motifs playing a minor role. Furthermore, similar sequence signatures are exhibited by control experiments in which nucleosome-free genomic DNA is either sonicated or digested with micrococcal nuclease, making it possible that current predictions based on high-throughput nucleosome-positioning maps are biased by experimental artifacts.