Search: id:A000962
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%I A000962 M1473 N0582
%S A000962 1,0,0,1,2,5,15,32,99,210,650,1379,4268,9055,28025,59458,184021,390420,
%T A000962 1208340,2563621,7934342,16833545,52099395,110534372,342101079,725803590
%N A000962 A ternary continued fraction.
%D A000962 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000962 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000962 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.
%D A000962 D. N. Lehmer, On ternary continued fractions, Tohoku Math. J., 37 (1933), 
               436-445.
%H A000962 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A000962 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A000962 G.f.: (-2x^5 + 5x^4 + x^3 - 7x^2 + 1)/(-x^6 + 3x^4 - 7x^2 + 1)
%p A000962 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.]
%p A000962 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]
%Y A000962 Sequence in context: A077686 A034499 A006451 this_sequence A118387 A034522 
               A148339
%Y A000962 Adjacent sequences: A000959 A000960 A000961 this_sequence A000963 A000964 
               A000965
%K A000962 nonn
%O A000962 0,5
%A A000962 N. J. A. Sloane (njas(AT)research.att.com).

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