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Search: id:A083564
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| 3, 21, 72, 329, 1353, 5796, 24447, 103729, 439128, 1860621, 7880997, 33385604, 141421803, 599075421, 2537719272, 10749959329, 45537545553, 192900159396, 817138154247, 3461452823129, 14662949371128, 62113250430021
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n+1)/a(n) -> (phi)^3 = [(1 + sqrt5)/2]^3 = 4.236067...
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FORMULA
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a(n) = 3a(n-1)+6a(n-2)-3a(n-3)-a(n-4); a(n) = Fib(4n)/Fib(n) = A000045(4n)/A000045(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003
a(n) = Lucas(3n) + (-1)^n*Lucas(n).
a(n) = 2*[2-sqrt(5)]^n-(1/2)*[ -1/2-(1/2)*sqrt(5)]^n-(1/2)*[ -1/2-(1/2)*sqrt(5)]^n*sqrt(5)+2*[2 +sqrt(5)]^n+(1/2)*sqrt(5)*[ -1/2+(1/2)*sqrt(5)]^n-(1/2)*[ -1/2+(1/2)*sqrt(5)]^n+[2 +sqrt(5)]^n*sqrt(5)-[2-sqrt(5)]^n*sqrt(5), with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 12 2008
G.f.: x(3+12x-9x^2-4x^3)/((1+x-x^2)(1-4x-x^2)). a(n) = A061084(n+1)+2*A001077(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 27 2008]
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EXAMPLE
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a(4) = 329 = (7)(47) = (L4)(L8).
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CROSSREFS
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Third row of array A028412.
Sequence in context: A117984 A050615 A145658 this_sequence A054646 A109721 A067002
Adjacent sequences: A083561 A083562 A083563 this_sequence A083565 A083566 A083567
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 12 2003
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 30 2003
More terms from Ralf Stephan (ralf(AT)ark.in-berlin.de), Feb 03 2005
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