Intransitive Trees

We study the class of treesTon the set {1, 2, …, n} such that for any 1⩽i<j<k⩽nthe pairs {i, j} and {j, k} cannot both be edges inT. We derive a formula for the number of such trees. We also give a functional equation and a differential equation for the generating function. We mention some additional combinatorial interpretations of these numbers.