The innermost valence electron levels of large molecular chains are subject to a strong breakdown of the orbital picture of ionization into particularly dense sets of shake-up lines with exceedingly small intensities, which give rise to correlation bands in the ionization spectrum. A suitable algorithm is required for a size-consistent investigation of such sets. In this work, we report the inclusion of the band-Lanczos approach in the final diagonalization step of a one-electron Green's function calculation in the algebraic diagrammatic construction scheme. From a first application to a series of oligomers CnH2n+2(n=2-9) converging to polyethylene, the C-2s correlation bands of large saturated hydrocarbons are shown to extend beyond 60 eV, and to represent, regardless of cross section effects, at least 20% of the total valence ionization intensity, and about 60% of the intensity found in the inner valence region [is an element of(b) = 18-70 eV]. With the band-Lanczos approach, the distribution of spectral intensity is nearly entirely recovered, with the exception of a tiny violation (2% for the n-nonane compound).