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Search: id:A102283
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| A102283 |
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Period 3: repeat (0,1,-1). |
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+0
6
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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
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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M. N. Huxley, Area, Lattice Points and Exponential Sums, Oxford, 1996; p. 236.
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FORMULA
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a(n)=-a(n-1)-a(n-2); a(0)=0, a(1)=1. G.f.: x/(1+x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=-(1/3)*{(n mod 3)-2*[(n+1) mod 3]+[(n+2) mod 3]}, with n>=0. a(n)=-(1/3)*I*sqrt(3)*[ -1/2+(1/2)*I*sqrt(3)]^n+(1/3)*I*sqrt(3)*[ -1/2-(1/2)*I *sqrt(3)]^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 06 2008]
a(n) = -2*sin(4*pi*n/3)/sqrt(3) = 2*sin(8*pi*n/3)/sqrt(3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 05 2008]
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MAPLE
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ch:=n-> if n mod 3 = 0 then 0; elif n mod 3 = 1 then 1; else -1; fi;
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CROSSREFS
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Sequence in context: A094217 A092220 A011655 this_sequence A128834 A022928 A000494
Adjacent sequences: A102280 A102281 A102282 this_sequence A102284 A102285 A102286
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 02 2008
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