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A000964
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A ternary continued fraction.
(Formerly M3343 N1345)
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2
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0, 0, 1, 1, 4, 8, 25, 53, 164, 348, 1077, 2285, 7072, 15004, 46437, 98521, 304920, 646920, 2002201, 4247881, 13147084, 27892928, 86327905, 183153773, 566856284, 1202645508, 3722157357, 7896950165, 24440860552, 51853868404, 160486408077
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OFFSET
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0,5
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REFERENCES
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D. N. Lehmer, On ternary continued fractions, Tohoku Math. J., 37 (1933), 436-445.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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FORMULA
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G.f.: (x^5 - 3x^4 + x^3 + x^2)/(-x^6 + 3x^4 - 7x^2 + 1)
a(0)=0, a(1)=0, a(2)=1, a(3)=1, a(4)=4, a(5)=8, a(n)=7*a(n-2)- 3*a(n-4)+ a(n-6) [From Harvey P. Dale, June 29 2011]
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MAPLE
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G:=(x^5-3*x^4+x^3+x^2)/(-x^6+3*x^4-7*x^2+1): Gser:=series(G, x=0, 35): seq(coeff(Gser, x, n), n=0..32); - Emeric Deutsch, Apr 22 2006
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MATHEMATICA
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LinearRecurrence[{0, 7, 0, -3, 0, 1}, {0, 0, 1, 1, 4, 8}, 31] (* From Harvey P. Dale, June 29 2011 *)
CoefficientList[Series[(x^5-3x^4+x^3+x^2)/(-x^6+3x^4-7x^2+1), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 11 2012 *)
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CROSSREFS
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Sequence in context: A154586 A185615 A068367 * A107840 A046736 A174171
Adjacent sequences: A000961 A000962 A000963 * A000965 A000966 A000967
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Emeric Deutsch, Apr 22 2006
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STATUS
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approved
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