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%I M3343 N1345 #32 Feb 06 2019 02:00:01
%S 0,0,1,1,4,8,25,53,164,348,1077,2285,7072,15004,46437,98521,304920,
%T 646920,2002201,4247881,13147084,27892928,86327905,183153773,
%U 566856284,1202645508,3722157357,7896950165,24440860552,51853868404,160486408077
%N The convergent sequence C_n for the ternary continued fraction (3,1;2,2) of period 2.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A000964/b000964.txt">Table of n, a(n) for n = 0..1000</a>
%H D. N. Lehmer, <a href="https://www.jstage.jst.go.jp/article/tmj1911/37/0/37_0_436/_article/-char/en">On ternary continued fractions</a>, Tohoku Math. J., 37 (1933), 436-445.
%H D. N. Lehmer, <a href="/A000962/a000962.pdf">On ternary continued fractions</a> (Annotated scanned copy)
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 7, 0, -3, 0, 1).
%F G.f.: (x^5 - 3x^4 + x^3 + x^2)/(-x^6 + 3x^4 - 7x^2 + 1).
%F 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
%p 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
%t LinearRecurrence[{0,7,0,-3,0,1},{0,0,1,1,4,8},31] (* _Harvey P. Dale_, Jun 29 2011 *)
%t 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 *)
%Y Cf. A000962, A000964.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, Apr 22 2006