Lucas Sequence Calculator
Generate Lucas numbers (2, 1, 3, 4, 7, 11, 18, ...) and explore their properties.
Parameters
Lucas Sequence (First 15 Terms)
L(0)=2L(1)=1L(2)=3L(3)=4L(4)=7L(5)=11L(6)=18L(7)=29L(8)=47L(9)=76L(10)=123L(11)=199L(12)=322L(13)=521L(14)=843
L(10)
123
= φ^10 + ψ^10
Sum of 15 Terms
2,206
Comparison with Fibonacci
| n | F(n) | L(n) | F(n-1)+F(n+1) |
|---|---|---|---|
| 1 | 1 | 1 | 1 |
| 2 | 1 | 3 | 3 |
| 3 | 2 | 4 | 4 |
| 4 | 3 | 7 | 7 |
| 5 | 5 | 11 | 11 |
| 6 | 8 | 18 | 18 |
| 7 | 13 | 29 | 29 |
| 8 | 21 | 47 | 47 |
| 9 | 34 | 76 | 76 |
Notice that L(n) = F(n-1) + F(n+1) for all n ≥ 1
L(0)
2
Starting value
L(1)
1
Starting value
Properties & Formulas
Recurrence
L(n) = L(n-1) + L(n-2)
L(0) = 2, L(1) = 1
Closed Form
L(n) = φ^n + ψ^n
Fibonacci Relation
L(n) = F(n-1) + F(n+1)
Product Identity
L(n) × F(n) = F(2n)