A156346 -id:A156346 - cp's OEIS frontend

A156872 Period 12: 1,3,-1,3,1,0,-1,-3,1,-3,-1,0 repeated.

1, 3, -1, 3, 1, 0, -1, -3, 1, -3, -1, 0, 1, 3, -1, 3, 1, 0, -1, -3, 1, -3, -1, 0, 1, 3, -1, 3, 1, 0, -1, -3, 1, -3, -1, 0, 1, 3, -1, 3, 1, 0, -1, -3, 1, -3, -1, 0, 1, 3, -1, 3, 1, 0, -1, -3, 1, -3, -1, 0

Offset: 0

Paul Curtz, Feb 17 2009

First differences of A154811.

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

PadRight[{},70,{1,3,-1,3,1,0,-1,-3,1,-3,-1,0}] (* Harvey P. Dale, Sep 23 2012 *)

Palindromic properties: a(n+6)= -a(n). a(12k+i)=a(12k+4-i), i=0..2. a(12k+5+i)=a(12k+11-i), i=0..3.
a(n) = A156194(n+1)-A156194(n+7) = A156194(n+1)-A156199(n+1).
a(n) = A156227(n+1) (mod 9).
a(n+1) -a(n)= A156346(n+1).
a(n)=A056594(n)+3*A014021(n-1). G.f.: (1+3*x-x^2+3*x^3+x^4)/((1+x^2)*(x^4-x^2+1)). - R. J. Mathar, Feb 23 2009

Edited, formulas commenting other sequences removed, by R. J. Mathar, Feb 23 2009

A158137 Period 9: repeat [-2,4,-2,4,-2,-2,1,1,-2].

Original entry on oeis.org

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

Offset: 0

Paul Curtz, Mar 13 2009

Rotated by 7 places, the period is palindromic: 1,-2,-2,4,-2,4,-2,-2,1.

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

Cf. A156346.

PadRight[{},120,{-2,4,-2,4,-2,-2,1,1,-2}] (* Harvey P. Dale, Dec 11 2018 *)

a(n)=[-2,4,-2,4,-2,-2,1,1,-2][n%9+1] \\ Charles R Greathouse IV, Jul 13 2016

a(n)= A158090(n)-2 = A158090(n)-A007395(n+1).

G.f.: (-2+2*x+4*x^3+x^6+2*x^4+2*x^7)/((1+x+x^2)*(x^6+x^3+1)). a(n)= -a(n-1)-a(n-2)-a(n-3)-a(n-4)-a(n-5)-a(n-6)-a(n-7)-a(n-8). - R. J. Mathar, Apr 09 2009

Edited and extended by R. J. Mathar, Apr 09 2009

cp's OEIS Frontend

A156872 Period 12: 1,3,-1,3,1,0,-1,-3,1,-3,-1,0 repeated.

Views

Author

Keywords

Comments

Links

Programs

Mathematica

Formula

Extensions