Get Math Help

Home / Get Math Help

Perrin Sequence

Alternate name

Sequence description

sequence defined by a_n = a_(n - 2) + a_(n - 3)

Sequence terms

3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39, 51, 68, 90, 119, 158, 209, 277, 367, ...

Formula

$a_n = sum_({ω: ω^3 - ω - 1 = 0}) ω^n$

Recurrence relation

a_0 = 3

a_1 = 0

a_2 = 2

a_n = a_(n - 3) + a_(n - 2)

Ordinary generating function

sum_(n=0)^∞a_nx^n = (x^2 - 3)/(x^3 + x^2 - 1)

Program

$a_n = LinearRecurrence[{0, 1, 1}, {3, 0, 2}, n + 1][[-1]]$

Table program

LinearRecurrence[{0, 1, 1}, {3, 0, 2}, n + 1]

Plot