The Padovan numbers are defined as $P(0) = P(1) = P(2) = 1$ and $P(n) = P(n-2) + P(n-3)$ for $n \ge 3$. The first few terms are $1,1,1,2,2,3,4,7,9,12$ (OEIS A134816, A000931). One of the identities given on the Wikipedia page is $$ \sum_{m=0}^n P(m)P(m+2) = P(n+2)P(n+3)-1$$ contributed by user Gandalf61 in July 2005. Is there an earlier citation for this identity? (Note that I'm not requesting a proof.)
Some notes on the history: The sequence was named by Ian Stewart in a 1996 Scientific American column citing the world of architecture, specifically Richard Padovan who credits Gérard Cordonnier and Hans van der Laan. It arose earlier, without a particular name, in Thomas Green's 1968 "Recurrent sequences and Pascal's triangle" (Math. Mag. 41, 13-21) and Dov Jarden's 1966 Recurring Sequences with articles originally published in the late 1940s. However, I did not see that any of these, or articles that cite them, include the identity given above.