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A000963
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A ternary continued fraction.
(Formerly M2660 N1062)
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1
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0, 1, 0, 3, 7, 16, 49, 104, 322, 683, 2114, 4485, 13881, 29450, 91147, 193378, 598500, 1269781, 3929940, 8337783, 25805227, 54748516, 169445269, 359496044, 1112631142
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| 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
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| G.f.: (-2x^5 + 7x^4 - 4x^3 + x)/(-x^6 + 3x^4 - 7x^2 + 1)
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MAPLE
| A000963:=z*(-1+4*z**2-7*z**3+2*z**4)/(-1+7*z**2-3*z**4+z**6); [Conjectured by S. Plouffe in his 1992 dissertation.]
a:= n-> (Matrix([[16, 7, 3, 0, 1, 0]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [0, 7, 0, -3, 0, 1][i] else 0 fi)^n)[1, 6]: seq (a(n), n=0..24); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 26 2008]
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CROSSREFS
| Sequence in context: A129045 A005312 A143817 * A133593 A191147 A058887
Adjacent sequences: A000960 A000961 A000962 * A000964 A000965 A000966
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KEYWORD
| nonn,cofr
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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