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

0,2

Comments

First differences of A154811.

Links

Table of n, a(n) for n=0..59.

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

Formula

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

Mathematica

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

Crossrefs

Sequence in context: A280725 A243328 A243332 * A263526 A132301 A073272

Adjacent sequences: A156869 A156870 A156871 * A156873 A156874 A156875

Keyword

sign,easy,less

Author

Paul Curtz, Feb 17 2009

Extensions

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

Status

approved