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%I M2662 #52 Oct 21 2023 19:57:53
%S 1,3,7,17,39,85,183,389,815,1693,3495,7173,14655,29837,60567,122645,
%T 247855,500061,1007495,2027493,4076191,8188333,16437623,32978613,
%U 66132495,132562173,265628263,532110981,1065670783,2133798221,4271762007,8550587221,17113150959
%N Expansion of 1/((1-2*x)*(1-x-2*x^3)).
%D D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976. See links in A003229 for an earlier version.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A003478/b003478.txt">Table of n, a(n) for n = 0..1000</a>
%H D. E. Daykin, <a href="/A003229/a003229.pdf">Letter to N. J. A. Sloane, Mar 1974</a>.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,2,-4)
%F G.f.: 1/((1-2*x)*(1-x-2*x^3)).
%p A003478:=1/(2*z-1)/(-1+z+2*z**3); # Conjectured by _Simon Plouffe_ in his 1992 dissertation
%t CoefficientList[Series[1/((1-2x)(1-x-2x^3)), {x,0,50}],x] (* _Harvey P. Dale_, Mar 14 2011 *)
%o (PARI) Vec(1/((1-2*x)*(1-x-2*x^3))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Harvey P. Dale_, Mar 14 2011
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