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%I M0781 #47 Oct 21 2023 23:48:46
%S 1,2,3,6,11,18,31,54,91,154,263,446,755,1282,2175,3686,6251,10602,
%T 17975,30478,51683,87634,148591,251958,427227,724410,1228327,2082782,
%U 3531603,5988258,10153823,17217030,29193547,49501194,83935255,142322350
%N Expansion of 1/((1-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 Unpublished, 1976.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="/A003479/b003479.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 (2,-1,2,-2).
%F A003476(n+1) + A077949(n)/2 - 1/2. - _Ralf Stephan_, Sep 25 2004
%F a(n+1) - a(n) = A077949(n+1). - _R. J. Mathar_, Mar 22 2011
%p A003479:=1/(z-1)/(-1+z+2*z**3); # _Simon Plouffe_ in his 1992 dissertation
%t CoefficientList[Series[1/((1-x)*(1-x-2*x^3)),{x,0,40}],x] (* _Vincenzo Librandi_, Jun 12 2012 *)
%o (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -2,2,-1,2]^n*[1;2;3;6])[1,1] \\ _Charles R Greathouse IV_, Jun 23 2020
%Y Cf. A003229.
%K easy,nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003
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