A search for leptoquarks produced singly and in pairs in proton-proton collisions is presented. We consider the leptoquark (LQ) to be a scalar particle of charge -1/3e coupling to a top quark plus a tau lepton (t tau) or a bottom quark plus a neutrino (b nu), or a vector particle of charge +2/3e, coupling to t nu or b tau. These choices are motivated by models that can explain a series of anomalies observed in the measurement of B meson decays. In this analysis the signatures t tau nu b and t tau nu are probed, using data recorded by the CMS experiment at the CERN LHC at root s = 13 TeV and that correspond to an integrated luminosity of 137 fb(-1). These signatures have not been previously explored in a dedicated search. The data are found to be in agreement with the standard model prediction. Lower limits at 95% confidence level are set on the LQ mass in the range 0.98-1.73 TeV, depending on the LQ spin and its coupling lambda to a lepton and a quark, and assuming equal couplings for the two LQ decay modes considered. These are the most stringent constraints to date on the existence of leptoquarks in this scenario. (C) 2021 The Author(s). Published by Elsevier B.V.