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Search: id:A132951
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| A132951 |
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Period 6: 1, 3, 1, -1, -3, -1. |
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+0
2
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| 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1, 1, 3, 1, -1, -3, -1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Same recurrence as A132868 and A132353. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
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FORMULA
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a(n) = 3a(n-1)-a(n-3)+3a(n-4).
O.g.f.: (1+3*x+x^2)/((x+1)*(x^2-x+1)) = -(1/3)/(x+1)+(1/3)*(4*x+4)/(x^2-x+1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 28 2007
a(n)=(1/3)*{-(n mod 6)-[(n+1) mod 6]+[(n+2) mod 6]+[(n+3) mod 6]+[(n+4) mod 6]-[(n+5) mod 6]} - Paolo P. Lava (ppl(AT)spl.at), Nov 30 2007
a(n)=-(1/3)*(-1)^n+(4/3)*cos(Pi*n/3)+(4*3^0.5/3)*sin(Pi*n/3). - Richard Choulet (richardchoulet(AT)yahoo.fr), Jan 02 2008
a(n)=a(n-6)=A131531(n+3)+A131531(n+1)+3*A131531(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
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CROSSREFS
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Cf. A109007.
Sequence in context: A087283 A111625 A109007 this_sequence A101685 A049653 A060266
Adjacent sequences: A132948 A132949 A132950 this_sequence A132952 A132953 A132954
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KEYWORD
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sign
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Nov 22 2007
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EXTENSIONS
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Edited by njas, May 16 2008 at the suggestion of R. J. Mathar.
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