### Electronic Research Archive

2021, Issue 5: 3489-3507. doi: 10.3934/era.2021049

# Identities for linear recursive sequences of order $2$

• Received: 01 January 2021 Revised: 01 July 2021 Published: 22 July 2021
• Primary: 11B83, 05A19; Secondary: 05A05, 05A15, 11B39

• 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.

Citation: Tian-Xiao He, Peter J.-S. Shiue. Identities for linear recursive sequences of order $2$[J]. Electronic Research Archive, 2021, 29(5): 3489-3507. doi: 10.3934/era.2021049

### Related Papers:

• 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.

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