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

Author

Paul Curtz, Feb 17 2009

Keywords

• sign
• easy
• less

Comments

First differences of A154811.

Links

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

Programs

Mathematica

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

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

Extensions

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