  We study recurrence relations for various Wigner 3nj-symbols and the
non-topological 10j-symbol. For the 6j-symbol and the 15j-symbols which
correspond to basic amplitudes of 3d and 4d topological spin foam models,
recurrence relations are obtained from the invariance under Pachner moves and
can be interpreted as quantizations of the constraints of the underlying
classical field theories. We also derive recurrences from the action of
holonomy operators on spin network functionals, making a more precise link
between the topological Pachner moves and the classical constraints.
Interestingly, our recurrence relations apply to any SU(2) invariant symbol,
depending on the cycles of the corresponding spin network graph. Another method
is used for non-topological objects such as the 10j-symbol and pseudo-isoceles
6j-symbols. The recurrence relations are also interpreted in terms of
elementary geometric properties. Finally, we discuss the extension of the
recurrences to take into account boundary states which leads to equations
similar to Ward identities for correlation functions in the Barrett-Crane
model.
