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Search: id:A000962
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| A000962 |
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A ternary continued fraction.
(Formerly M1473 N0582)
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+0
1
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| 1, 0, 0, 1, 2, 5, 15, 32, 99, 210, 650, 1379, 4268, 9055, 28025, 59458, 184021, 390420, 1208340, 2563621, 7934342, 16833545, 52099395, 110534372, 342101079, 725803590
(list; graph; listen)
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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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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
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G.f.: (-2x^5 + 5x^4 + x^3 - 7x^2 + 1)/(-x^6 + 3x^4 - 7x^2 + 1)
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MAPLE
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A000962:=(z+1)*(2*z**4-7*z**3+6*z**2+z-1)/(-1+7*z**2-3*z**4+z**6); [Conjectured by S. Plouffe in his 1992 dissertation.]
a:= n-> (Matrix([[5, 2, 1, 0, 0, 1]]). 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..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 26 2008]
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CROSSREFS
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Sequence in context: A077686 A034499 A006451 this_sequence A118387 A034522 A148339
Adjacent sequences: A000959 A000960 A000961 this_sequence A000963 A000964 A000965
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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