We investigate tricritical behavior of the O(n) model in two dimensions by means of transfer-matrix andfinite-size scaling methods. For this purpose we consider an O(n) symmetric spin model on the honeycomb latticewith vacancies; the tricritical behavior is associated with the percolation threshold of the vacancies. The vacancies are represented by face variables on the elementary hexagons of the lattice. We apply a mapping of the spin degreesof freedom model on a non-intersecting-loop model, in which the number n of spin components assumes the role of acontinuously variable parameter. This loop model serves as a suitable basis for the construction of the transfer matrix.Our results reveal the existence of a tricritical line, parametrized by n, which connects the known universality classes ofthe tricritical Ising model and the theta point describing the collapse of a polymer. On the other side of the Ising point,the tricritical line extends to the n = 2 point describing a tricritical O(2) model.