A204671 a(n) = n^n (mod 6).

1, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4, 3, 4, 5, 0, 1, 4

Offset: 0

Author

José María Grau Ribas, Jan 18 2012

Keywords

• nonn
• easy

Comments

For n>0, periodic with period 6 = A174824: repeat [1, 4, 3, 4, 5, 0].

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Crossrefs

Cf. A000312, A010875, A174824, A204690.

Programs

Magma

[1] cat &cat [[1, 4, 3, 4, 5, 0]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Maple

A204671:=n->[1, 4, 3, 4, 5, 0][(n mod 6)+1]: 1, seq(A204671(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

Mathematica

Table[PowerMod[n,n,6], {n,0,140}]
Join[{1},LinearRecurrence[{0, 0, 0, 0, 0, 1},{1, 4, 3, 4, 5, 0},86]] (* Ray Chandler, Aug 26 2015 *)

PARI

a(n)=lift(Mod(n, 6)^n) \\ Andrew Howroyd, Feb 25 2018

Formula

G.f.: (x^6-5*x^5-4*x^4-3*x^3-4*x^2-x-1)/((x-1)*(x+1)*(x^2-x+1)*(x^2+x+1)). [Colin Barker, Jul 20 2012]

From Wesley Ivan Hurt, Jun 23 2016: (Start)

a(n) = a(n-6) for n>5.

a(0) = 1, a(n) = (17 - cos(n*Pi) - 8*cos(n*Pi/3) - 8*cos(2*n*Pi/3) - 4*sqrt(3)*sin(n*Pi/3) - 4*sqrt(3)*sin(2*n*Pi/3))/6 for n>0. (End)

a(n) = A010875(A000312(n)). - Michel Marcus, Jun 27 2016