Identities for linear recursive sequences of order $ 2 $

Abstract

<p style='text-indent:20px;'>We present here a general rule of construction of identities for recursive sequences by using sequence transformation techniques developed in [<xref ref-type="bibr" rid="b16">16</xref>]. 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.</p>