Identities for linear recursive sequences of order <inline-formula><tex-math id="M1">$ 2 $</tex-math></inline-formula>

We present here a general rule of construction of identities for recursive sequences by using sequence transformation techniques developed in [ 16 ]. Numerous identities are constructed, and many well known identities can be proved readily by using this unified rule. Various Catalan-like and Cassini-like identities are given for recursive number sequences and recursive polynomial sequences. Sets of identities for Diophantine quadruple are shown.