  This paper shows a new phenomenon in higher cluster tilting theory. For each
positive integer d, we exhibit a triangulated category C with the following
properties.
  On the one hand, the d-cluster tilting subcategories of C have very simple
mutation behaviour: Each indecomposable object has exactly d mutations. On the
other hand, the weakly d-cluster tilting subcategories of C which lack
functorial finiteness can have much more complicated mutation behaviour: For
each 0 <= \ell <= d-1, we show a weakly d-cluster tilting subcategory T_{\ell}
which has an indecomposable object with precisely \ell mutations.
  The category C is the algebraic triangulated category generated by a
(d+1)-spherical object and can be thought of as a higher cluster category of
Dynkin type A infinity.
