"Vajda's identity" is really Tagiuro's identity: A. Tagiuri, Di alcune successioni ricorrenti a termini interi e positivi, Periodico di Matematica 16 (1900–1901), 1–12. See also https://math.stackexchange.com/questions/1356391/is-there-a-name-for-this-fibonacci-identity.
Ira Gessel
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