Lines from HC3N and isotopic substituted species in ground and vibrationally excited states produce crowded millimeter and submillimeter wave spectra in the C-rich protoplanetary nebula CRL618. The complete sequence of HC3N rotational lines from J=9-8 to J=30-29 has been observed with the IRAM 30m telescope toward this object. Lines from a total of 15 different vibrational states (including the fundamental), with energies up to 1100 cm^-1, have been detected for the main HC3N isotopomer. In addition, the CSO telescope has been used to complement this study in the range J=31-30 to J=39-38, with detections in five of these states, all of them below 700 cm^-1. Vibrationally excited HC3N rotational lines exhibit P-Cygni profiles at 3 mm, evolving to pure emission lineshapes at shorter wavelengths. This evolution of the line profile shows little dependence on the vibrational state from which they rotational lines arise. The absorption features are formed against the continuum emission, which has been successfully characterized in this work due to the large frequency coverage. The HC3N column density in front of the the continuum source has been determined by comparing the output of an array of models to the data. The best fits are obtained for column densities in the range 2.0-3.5 10$^17 cm^-2, consistent with previous estimates from ISO data, and TK in the range 250 to 275 K, in very good agreement with estimates made from the same ISO data.Peer reviewed