  We propose a new topological invariant of unlabeled trees of N nodes. The
invariant is a set of Nx2 matrices of integers, with sum_j k^{d_{i,j}} and v_i
as the matrix elements, where d_{i,j} are the elements of the distance matrix
and v_i denotes i-th node's degree and k in N. To compare the invariant
calculated for possibly different graphs, the matrix rows are ordered with
respect to first column, and -- if necessary -- with respect to the second one.
We use the new invariant to evaluate from below the number of topologically
different unlabeled trees up to N=17. The results slightly exceed the
asymptotic evaluation of Otter.
