I've written an extension using Py_LIMITED_API, and I've created a type using PyType_FromSpec with the slot "Py_sq_length" defined. The slot is not being picked up, i.e. len(MyType()) fails. I can see that tp_as_sequence has not been set, which explains why. All is well if I set it manually (without Py_LIMITED_API defined), like so:
  MyType->tp_as_sequence = &((PyHeapTypeObject*)MyType)->as_sequence;

As far as I can see (docs are lacking), there's no way of setting tp_as_number, tp_as_sequence or tp_as_mapping in types created with PyType_FromSpec. I would expect the presence of any Py_sq_* slots to set tp_as_sequence (likewise for number and mapping).

For 3.3, this is fixed in bb6df3781edb. However, this needs to be backported to 3.2.