The geometries of the BnH+ clusters for n=1-13 have been optimized at the B3LYP level of theory. Excluding B2H+, the ground states of all clusters are low-spin coupled. The structures appear to be related to the bare B-n(+) clusters in two ways : (1) an H atom is added to the B-n(+) cluster or (2) a BH is added to the B-n-1(+) cluster. The B-n(+)-H binding energies are computed at the B3LYP level of theory, and calibrated using the CCSD(T) level of theory. The computed results tend to fall between the experimental best estimates and the experimental lower bounds. The B-n-1(+)-H binding energies show an inverse correspondence with the B-n-1(+)-B values, while the (+)(Bn-1)-B and to parallel each other.