132-avoiding two-stack sortable permutations, Fibonacci numbers, and Pell numbers

We describe the recursive structures of the set of two-stack sortable permutations which avoid 132 and the set of two-stack sortable permutations which contain 132 exactly once. Using these results and standard generating function techniques, we enumerate two-stack sortable permutations which avoid (or contain exactly once) 132 and which avoid (or contain exactly once) an arbitrary permutation τ . In most cases the number of such permutations is given by a simple formula involving Fibonacci or Pell numbers.