Incomplete 𝑘-Fibonacci and 𝑘-Lucas Numbers

Table 2

The numbers 𝐿^𝑙_𝑘,𝑛, for 1⩽𝑛⩽9.

𝑛⧵𝑙	0	1	2	3	4
1	k
2	𝑘^2	𝑘^2+2
3	𝑘^3	𝑘^3+3𝑘
4	𝑘^4	𝑘^4+4𝑘^2	𝑘^4+4𝑘^2+2
5	𝑘^5	𝑘^5+5𝑘^3	𝑘^5+5𝑘^3+5𝑘
6	𝑘^6	𝑘^6+6𝑘^4	𝑘^6+6𝑘^4+9𝑘^2	𝑘^6+6𝑘^4+9𝑘^2+2
7	𝑘^7	𝑘^7+7𝑘^5	𝑘^7+7𝑘^5+14𝑘^3	𝑘^7+7𝑘^5+14𝑘^3+7𝑘
8	𝑘^8	𝑘^8+8𝑘^6	𝑘^8+8𝑘^6+20𝑘^4	𝑘^8+8𝑘^6+20𝑘^4+16𝑘^2	𝑘^8+8𝑘^6+20𝑘^4+16𝑘^2+2
9	𝑘^9	𝑘^9+9𝑘^7	𝑘^9+9𝑘^7+27𝑘^5	𝑘^9+9𝑘^7+27𝑘^5+30𝑘^3	𝑘^9+9𝑘^7+27𝑘^5+30𝑘^3+9𝑘