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A130196
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Period 3: repeat 1 2 2.
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16
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1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2009: (Start)
Denominator of x(n)=x(n-1)+x(n-2), x(0)=0, x(1)=1/2; numerator=A167808;
a(n) = A131534(n)+A022003(n) = A080425(n)-A131534(n)+2 = A153727(n)/A131534(n). (End)
Continued fraction expansion of (5+sqrt(85))/10 [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 07 2010]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,1).
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FORMULA
| a(0)=1,a(1)=a(2)=2,a(n+3)=a(n).
a(n)=(1/9)*{8*(n mod 3)+5*[(n+1) mod 3]+2*[(n+2) mod 3]}, with n>=0. - Paolo P. Lava (paoloplava(AT)gmail.com), Aug 28 2007
G.f.: -(1+2*x+2*x^2)/(x-1)/(x^2+x+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
Closed form: a(n)=5/3+(2/3)*[ -1/2-(1/2*I)*sqrt(3)]^(-2)*[ -1/2-(1/2*I)*sqrt(3)]^n+(2/3)*[ -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) - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 17 2008
a(n)=(5-2*cos(2*pi*n/3))/3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Nov 23 2008]
a(n) = 2 - 0^(n mod 3). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2009]
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PROG
| (PARI) a(n)=2-0^(n%3) \\ Charles R Greathouse IV, Jun 01 2011
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CROSSREFS
| Cf. A177347 (decimal expansion of (5+sqrt(85))/10). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 07 2010]
Sequence in context: A102297 A098398 A131714 * A158209 A119646 A024693
Adjacent sequences: A130193 A130194 A130195 * A130197 A130198 A130199
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Aug 05 2007
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EXTENSIONS
| More terms from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 07 2010
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