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 A000964 The convergent sequence C_n for the ternary continued fraction (3,1;2,2) of period 2. (Formerly M3343 N1345) 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES 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). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 D. N. Lehmer, On ternary continued fractions, Tohoku Math. J., 37 (1933), 436-445. D. N. Lehmer, On ternary continued fractions (Annotated scanned copy) Index entries for linear recurrences with constant coefficients, signature (0, 7, 0, -3, 0, 1). FORMULA G.f.: (x^5 - 3x^4 + x^3 + x^2)/(-x^6 + 3x^4 - 7x^2 + 1). a(n) = 7*a(n-2) - 3*a(n-4) + a(n-6); a(0)=0, a(1)=0, a(2)=1, a(3)=1, a(4)=4, a(5)=8. - Harvey P. Dale, Jun 29 2011 MAPLE 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 MATHEMATICA LinearRecurrence[{0, 7, 0, -3, 0, 1}, {0, 0, 1, 1, 4, 8}, 31] (* Harvey P. Dale, Jun 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 *) CROSSREFS Cf. A000962, A000964. Sequence in context: A185615 A068367 A292548 * A297458 A328038 A107840 Adjacent sequences:  A000961 A000962 A000963 * A000965 A000966 A000967 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Emeric Deutsch, Apr 22 2006 STATUS approved

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Last modified April 11 00:03 EDT 2021. Contains 342877 sequences. (Running on oeis4.)