Editing Lucas number (section)

== Definition ==
As with the Fibonacci numbers, each Lucas number is defined to be the sum of its two immediately previous terms, thereby forming a [[Generalizations of Fibonacci numbers#Fibonacci integer sequences|Fibonacci integer sequence]].  The first two Lucas numbers are <math>L_0=2</math> and <math>L_1=1</math>, which differs from the first two Fibonacci numbers <math>F_0=0</math> and <math>F_1=1</math>. Though closely related in definition, Lucas and Fibonacci numbers exhibit distinct properties.

The Lucas numbers may thus be defined as follows:
:<math> 
  L_n :=
  \begin{cases}
    2               & \text{if } n = 0; \\
    1               & \text{if } n = 1; \\
    L_{n-1}+L_{n-2} & \text{if } n > 1.
   \end{cases}
 </math>
(where ''n'' belongs to the [[natural number]]s)

All Fibonacci-like integer sequences appear in shifted form as a row of the [[Wythoff array]]; the Fibonacci sequence itself is the first row and the Lucas sequence is the second row. Also like all Fibonacci-like integer sequences, the ratio between two consecutive Lucas numbers [[limit of a sequence|converges]] to the [[golden ratio]].