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A204671 a(n) = n^n (mod 6). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)