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A128834
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Periodic sequence 0,1,1,0,-1,-1,...
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14
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0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1, 0, -1, -1, 0, 1, 1
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OFFSET
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0,1
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COMMENTS
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Unsigned version in A011655 .
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LINKS
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Table of n, a(n) for n=0..104.
Index entries for sequences related to Chebyshev polynomials.
Index to sequences with linear recurrences with constant coefficients, signature (1,-1).
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FORMULA
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a(0)=0, a(1)=1, a(n+1) = a(n)-a(n-1) for n>=1.
G.f.:x*(1+x)/(1+x^3).
Euler transform of length 6 sequence [ 1, -1, -1, 0, 0, 1]. - Michael Somos Apr 15 2007
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= v -u^2 +2*u*v -2*u^2*v . - Michael Somos Apr 15 2007
G.f. A(x) satisfies 0= f(A(x), A(x^3)) where f(u, v)= v -u^3 +3*u*v -3*u^3*v . - Michael Somos Apr 15 2007
a(n)=(1/6)*{-(n mod 6)+[(n+2) mod 6]+[(n+3) mod 6]-[(n+5) mod 6]}, with n>=0 - Paolo P. Lava, Jun 11 2007
a(n) = A010892(n-1) . - R. J. Mathar, Feb 08 2008
a(n) = A010892(n+5) [From Jaume Oliver Lafont, Dec 05 2008]
a(n) is multiplicative with a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 3), a(p^e) = (-1)^e if p == 2 (mod 3) . - Michael Somos Apr 15 2007
a(n)=2*sin(n*pi/3)/sqrt(3) [From Jaume Oliver Lafont, Dec 05 2008]
Contribution from Wolfdieter Lang, Jul 18 2010: (Start)
O.g.f.: x/(1-x+x^2) = x*S(x), with S(x) o.g.f. for Chebyshev S(n,1) = U(n,1/2) = A010892(n).
a(n) = S(n-1,1) = U(n-1,1/2) with S(-1,1)=0. (End)
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EXAMPLE
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x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 + x^14 - x^16 + ...
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PROG
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(PARI) {a(n)= [0, 1, 1, 0, -1, -1][n%6 +1]}
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CROSSREFS
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Sequence in context: A092220 A011655 A102283 * A022928 A000494 A022933
Adjacent sequences: A128831 A128832 A128833 * A128835 A128836 A128837
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KEYWORD
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sign,mult,easy
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AUTHOR
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Philippe DELEHAM, Apr 13 2007
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STATUS
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approved
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