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

Author

Paul Curtz, May 21 2010

Keywords

• sign
• easy
• less

Comments

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

Links

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

Crossrefs

Cf. A069705, A070365, A132954, A153727.

Programs

Magma

&cat [[4, -1, 2, -4, 1, 2]^^20]; // Wesley Ivan Hurt, Jun 23 2016

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 *)

PARI

a(n)=[1,5,4,6,2,3][n%5+1] \\ Charles R Greathouse IV, Jun 02 2011

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)

Extensions

New name from Wesley Ivan Hurt, Jun 23 2016