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A156872
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Period 12: 1,3,-1,3,1,0,-1,-3,1,-3,-1,0 repeated.
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0
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| First differences of A154811.
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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 (mathar(AT)strw.leidenuniv.nl), 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 (paoloplava(AT)gmail.com), Feb 20 2009]
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CROSSREFS
| Sequence in context: A174233 A079530 A020815 * A132301 A073272 A175623
Adjacent sequences: A156869 A156870 A156871 * A156873 A156874 A156875
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KEYWORD
| sign,easy,less
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Feb 17 2009
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EXTENSIONS
| Edited, formulas commenting other sequences removed, by R. J. Mathar (mathar(AT)strw.leidenunvi.nl), Feb 23 2009
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