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

0,3

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).

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

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 *)

Prog

(Magma) [1] cat &cat [[1, 4, 3, 4, 5, 0]^^20]; // Wesley Ivan Hurt, Jun 23 2016
(PARI) a(n)=lift(Mod(n, 6)^n) \\ Andrew Howroyd, Feb 25 2018

Crossrefs

Cf. A000312, A010875, A174824, A204690.

Sequence in context: A332472 A049788 A002558 * A204816 A204818 A099634

Adjacent sequences: A204668 A204669 A204670 * A204672 A204673 A204674

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 18 2012

Status

approved