1) Given:Lucas number:
2) Fibonacci number:Definition from any book or internet
3) Tablen Lucas number Fibonacci number
0 Lo = 2 Fo = 0
1 L1 = 1 F1 = 1
2 L2 = 1 + 2 = 3 F2 = 1 + 0 = 1 ⇒ L2 = F1 + F3 = 1 + 2 = 3
3 L3 = 3 + 1 = 4 F3 = 1 + 1 = 2 ⇒ L3 = F2 + F4 = 1 + 3 = 4
4 L4 = 4 + 3 = 7 F4 = 1 + 2 = 3 ⇒ L4 = F3 + F5 = 2 + 5 = 7
5) L5 = 7 + 4 = 11 F5 = 4 + 3 = 5 ⇒ L5 = F4 + F6 = 3 + 8 = 11
6) L6 = 11 + 7 = 18 F6 = 3 + 7 = 10 ⇒ L6 = F5 + F7 = 5 + 13 = 18
From that you can see that the relation continues.