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

Table 4

𝐋5	𝒫𝐋5(𝑟)	Rational roots of 𝒫𝐋5(𝑟)=0
𝐃^5	3𝑟^5+5𝑟^4+10𝑟^3+5𝑟^2−1	1/3
4𝐃s1𝐂	4𝑟^4+8𝑟^3+9𝑟^2+2𝑟−1	⧵
3𝐃s2𝐂s	6𝑟^3+10𝑟^2+7𝑟−1	⧵
2𝐃s3𝐂s	9𝑟^2+12𝑟+1	⧵
1𝐃4𝐂s	15𝑟+7	−7/15
𝐂^5	22	⧵