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A131713
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Period 3: repeat 1, -2, 1.
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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, 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, 1, -2, 1, 1, -2, 1, 1, -2, 1, 1, -2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Second differences of A131534. Binomial transform of 1, -3,6, -9, 9, 0 ..., A057083 signed.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (-1,-1).
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FORMULA
| a(n) = b(2*n + 1) where b(n) is multiplicative with b(2^n) = 0^n, b(3^n) = 3 * 0^n - 2, b(p^n) = 1 if p > 3. - Michael Somos, Jan 02 2011
a(n)={-[(n+1) mod 3]+[(n+2) mod 3]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 02 2007
G.f.: (1-x)/(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 (paoloplava(AT)gmail.com), Nov 27 2008]
a(n) = A117188(2*n). - R. J. Mathar, Jun 13 2011
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MATHEMATICA
| f[n_] := If[ Mod[n, 3] == 1, -2, 1]; Array[f, 105, 0]
CoefficientList[Series[(1 - x)/(1 + x + x^2), {x, 0, 104}], x]
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PROG
| (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
| Sequence in context: A057559 A205375 A016010 * A099837 A100051 A122876
Adjacent sequences: A131710 A131711 A131712 * A131714 A131715 A131716
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KEYWORD
| sign,easy,less
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Sep 14 2007
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EXTENSIONS
| Corrected and extended by Michael Somos, Jan 02 2011
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