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Search: id:A131713
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| A131713 |
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Period 3: repeat 1, -2, 1. |
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+0
6
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| 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2, 1, -2, 1
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Second differences of A131534. Binomial transform of 1, -3,6, -9, 9, 0 ..., A057083 signed.
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FORMULA
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a(n)={-[(n+1) mod 3]+[(n+2) mod 3]}, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Oct 02 2007
G.f.: -(x-1)/(x^2+x+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=2cos((2n+1)pi/3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Nov 23 2008]
a(n)=1/3*(-1/2-(1/2*I)*sqrt(3))^(-2)*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2+(1/2*I) *sqrt(3))^(-2)*(-1/2+(1/2*I)*sqrt(3))^n+1/3*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2 +(1/2*I)*sqrt(3))^n-2/3*(-1/2-(1/2*I)*sqrt(3))^(-1)*(-1/2-(1/2*I)*sqrt(3))^n-2/3 *(-1/2+(1/2*I)*sqrt(3))^(-1)*(-1/2+(1/2*I)*sqrt(3))^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 27 2008]
G.f.: (1-x)/(1+x+x^2) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 24 2009]
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PROGRAM
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(PARI) a(n)=[1, -2, 1][1+n%3] [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 24 2009]
(PARI) a(n)=1-3*(n%3==1) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 24 2009]
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CROSSREFS
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Cf. A131534, A057083, A061347, A131556.
Sequence in context: A115576 A115572 A152847 this_sequence A152846 A152845 A115571
Adjacent sequences: A131710 A131711 A131712 this_sequence A131714 A131715 A131716
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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), Sep 14 2007
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