Periodic Solutions to a Third-Order Conditional Difference Equation over the Integers

Table 3

𝐋4	𝒫𝐋4(𝑟)	Roots of 𝒫𝐋4(𝑟)=0
𝐃^4	3𝑟^4+6𝑟^2+8𝑟^3−1	1⁄3, −1(triple)
3𝐃s1𝐂	5𝑟^3+9𝑟^2+3𝑟−1	1⁄5, −1(double)
2𝐃s2𝐂s	8𝑟^2+8𝑟	−1(double)
1𝐃3𝐂s	12𝑟+4	−1/3
𝐂^4	16	⧵