A178141 Period 6: repeat [4, -1, 2, -4, 1, 2].

4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2, 4, -1, 2, -4, 1, 2

Offset

0,1

Comments

Differences of the period 6: repeat [1, 5, 4, 6, 2, 3] (A070365).

Links

Table of n, a(n) for n=0..77.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Formula

Mix A153727(n+1) with -A153727(n).

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

G.f.: (4-x+2*x^2-4*x^3+x^4+2*x^5)/(1-x^6).

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

a(n) = (2 + 5*cos(n*Pi) + 7*cos(n*Pi/3) - 2*cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3))/3. (End)

Maple

A178141:=n->[4, -1, 2, -4, 1, 2][(n mod 6)+1]: seq(A178141(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

Mathematica

PadRight[{}, 100, {4, -1, 2, -4, 1, 2}] (* Wesley Ivan Hurt, Jun 23 2016 *)

Prog

(PARI) a(n)=[1, 5, 4, 6, 2, 3][n%5+1] \\ Charles R Greathouse IV, Jun 02 2011
(Magma) &cat [[4, -1, 2, -4, 1, 2]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Crossrefs

Cf. A069705, A070365, A132954, A153727.

Sequence in context: A100353 A366397 A080508 * A063987 A236269 A010126

Adjacent sequences: A178138 A178139 A178140 * A178142 A178143 A178144

Keyword

sign,easy,less

Author

Paul Curtz, May 21 2010

Extensions

New name from Wesley Ivan Hurt, Jun 23 2016

Status

approved