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A003476 a(n) = a(n-1) + 2*a(n-3).

%I A003476 M0705 #44 Oct 21 2023 19:24:06
%S A003476 1,2,3,5,9,15,25,43,73,123,209,355,601,1019,1729,2931,4969,8427,14289,
%T A003476 24227,41081,69659,118113,200275,339593,575819,976369,1655555,2807193,
%U A003476 4759931,8071041,13685427,23205289,39347371,66718225,113128803,191823545,325259995
%N A003476 a(n) = a(n-1) + 2*a(n-3).
%D A003476 D. E. Daykin and S. J. Tucker, Introduction to Dragon Curves. Unpublished, 1976. See links in A003229 for an earlier version.
%D A003476 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A003476 T. D. Noe, <a href="/A003476/b003476.txt">Table of n, a(n) for n = 1..500</a>
%H A003476 D. E. Daykin, <a href="/A003229/a003229.pdf">Letter to N. J. A. Sloane, Mar 1974</a>.
%H A003476 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 A003476 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A003476 Kevin Ryde, <a href="http://user42.tuxfamily.org/dragon/index.html">Iterations of the Dragon Curve</a>, see index "RQ", "BQ", and "S".
%H A003476 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2).
%F A003476 a(n) = A003229(n-1) + A052537(n-2).
%F A003476 a(n) = (1/4)*abs(A078044(n+2)).
%p A003476 A003476:=-(1+z+z**2)/(-1+z+2*z**3); # _Simon Plouffe_ in his 1992 dissertation
%t A003476 LinearRecurrence[{1,0,2},{1,2,3},30] (* _Harvey P. Dale_, Jun 01 2020 *)
%o A003476 (PARI) my(P=Mod('x,'x^3-'x^2-2)); a(n) = subst(lift(P^n),'x,2) >> 1; \\ _Kevin Ryde_, Oct 16 2021
%Y A003476 Cf. A003229, A052537, A078044.
%K A003476 nonn,easy
%O A003476 1,2
%A A003476 _N. J. A. Sloane_