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A156872 Period 12: 1,3,-1,3,1,0,-1,-3,1,-3,-1,0 repeated. 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, -1, -3, 1, -3, -1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

First differences of A154811.

LINKS

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

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

a(n)=(1/12)/{-(n mod 12)-[(n+1) mod 12]-2*[(n+2) mod 12]+4*[(n+3) mod 12]-4*[(n+4) mod 12]+2*[(n+5) mod 12]+[(n+6) mod 12]+[(n+7) mod 12]+2*[(n+8) mod 12]-2*[(n+9) mod 12]+4*[(n+10) mod 12]-2*[(n+11) mod 12]}, with n>=0 [From Paolo P. Lava, Feb 20 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

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Last modified April 21 20:59 EDT 2019. Contains 322328 sequences. (Running on oeis4.)