卢卡斯数列是斐波那契数和卢卡斯数的推广,以法国数学家爱德华·卢卡斯命名。
给定两个整数P和Q,满足:

则第一类卢卡斯数列Un(P,Q)和第二类卢卡斯数列Vn(P,Q)由以下递推关系定义:



以及



卢卡斯数列的特征方程是:

它的判别式是
,它的根是:

注意a和b是不同的,因为
卢卡斯数列的项可以用a和b的项定义如下:


从中我们可以推出以下关系:


不少斐波那契数和卢卡斯数所满足的关系,在卢卡斯数列中也有类似的形式。例如:
一般 |
P=1, Q=-1
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 |
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 |
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 |
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 |
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 |
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 |
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对于某些P和Q的值,卢卡斯数列有特殊名称:
- Un(1,−1):斐波那契数
- Vn(1,−1):卢卡斯数
- Un(2,−1):佩尔数
- Un(1,−2):Jacobsthal数