2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62338We present a new identity involving compositions (i.e. ordered partitions of natural numbers). The Formula has its origin in complex dynamical systems and appears when counting, in the polynomial family $\{f_c:z \mapsto z^d + c \}$, periodic critical orbits with equivalent itineraries. We give two different proofs of the identity; one following the original approach in dynamics and another with purely combinatorial methods.8 pages, 1 figureCombinatoricsDynamical Systems05A17,11P81,37F10,37F45text