Perrin number

In mathematics, the Perrin numbers are defined by the recurrence relation

P(n) = P(n − 2) + P(n − 3) for n > 2,

with initial values

P(0) = 3, P(1) = 0, P(2) = 2.

The sequence of Perrin numbers starts with

3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39 ... (sequence A001608 in the OEIS)

The number of different maximal independent sets in an n-vertex cycle graph is counted by the nth Perrin number for n > 1. [1]

History

This sequence was mentioned implicitly by Édouard Lucas (1876). In 1899, the same sequence was mentioned explicitly by François Olivier Raoul Perrin. [2] The most extensive treatment of this sequence was given by Adams and Shanks (1982).

Other Languages
Deutsch: Perrin-Folge
français: Nombre de Perrin
한국어: 페린 넘버
日本語: ペラン数
svenska: Perrintal
中文: 佩蘭數列