Counting (3 + 1)-avoiding permutations

A poset is (3+1)-free   if it contains no induced subposet isomorphic to the disjoint union of a 3-element chain and a 1-element chain. These posets are of interest because of their connection with interval orders and their appearance in the (3+1)-free Conjecture of Stanley and Stembridge. The dimension 2 posets PP are exactly the ones which have an associated permutation ππ where i≺ji≺j in PP if and only if i