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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, 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
| 1,3
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COMMENTS
| Inverse binomial transform of A057079. - Paul Barry (pbarry(AT)wit.ie), May 15 2003
The unsigned version, with g.f. (1+x+2x^2)/(1-x^3), has a(n)=4/3-cos(2*pi*n/3)/3-sqrt(3)sin(2*pi*n/3)/3=gcd(fib(n+4), fib(n+1)). - Paul Barry (pbarry(AT)wit.ie), Apr 02 2004
a(n) = L(n-2,-1), where L is defined as in A108299; see also A010892 for L(n,+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005
From the Taylor expansion of log(1+x+x^2) at x=1, sum(k>=1, a(k)/k ) = log(3) = A002391. This is case n=3 of the general expression sum(k>=1, (1-n*!(k%n))/k ) = log(n). [Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 16 2009]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,-1).
Tanya Khovanova, Recursive Sequences
Ralph E. Griswold, Shaft Sequences
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FORMULA
| a(0) = a(1) = 1; a(n)= - a(n-1) - a(n-2).
G.f.: (1+2x)/(1+x+x^2). a(n)=(-1)^Floor[2n/3]+((-1)^Floor[(2n-1)/3]+ (-1)^Floor[(2n+1)/3])/2 - Mario Catalani (mario.catalani(AT)unito.it), Jan 07 2003
a(n)=-(n mod 3)+(n+1) mod 3 - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 20 2006
a(n) = -2*cos(2*pi*n/3); - Jaume Oliver Lafont (joliverlafont(AT)gmail.com), May 06 2008
Dirichlet g.f. zeta(s)*(1-1/3^(s-1)). - R. J. Mathar, Feb 09 2011
a(n) = n*sum(k=1..n,binomial(k,n-k)/k*(-1)^(k+1)). [Dmitry Kruchinin, Jun 3 2011]
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PROG
| (PARI) a(n)=1-3*!(n%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 16 2009]
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CROSSREFS
| Apart from signs, same as A057079, A100063. Cf. A000045, A010892 for the rules a(n) = a(n - 1) + a(n - 2), a(n) = a(n - 1) - a(n - 2). a(n) = - a(n - 1) + a(n - 2) gives a signed version of Fibonacci numbers.
a(n)=A057079(2n)
Sequence in context: A101825 A177702 A131534 * A115579 A115573 A152851
Adjacent sequences: A061344 A061345 A061346 * A061348 A061349 A061350
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KEYWORD
| sign,easy,mult
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jun 07 2001
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