HCCNC and HNC3 are less commonly found isomers of cyanoacetylene, HC3N, a molecule that is widely found in diverse astronomical sources. We want to know if HNC3 is present in sources other than the dark cloud TMC-1 and how its abundance is relative to that of related molecules. We used the Astrochemical Studies At IRAM unbiased spectral survey at IRAM 30 m towards the prototypical pre-stellar core L1544 to search for HNC3 and HCCNC which are by-product of the HC3NH+ recombination, previously detected in this source. We performed a combined analysis of published HNC3 microwave rest frequencies with thus far unpublished millimetre data because of issues with available rest frequency predictions. We determined new spectroscopic parameters for ...