%I M0705 #44 Oct 21 2023 19:24:06

%S 1,2,3,5,9,15,25,43,73,123,209,355,601,1019,1729,2931,4969,8427,14289,

%T 24227,41081,69659,118113,200275,339593,575819,976369,1655555,2807193,

%U 4759931,8071041,13685427,23205289,39347371,66718225,113128803,191823545,325259995

%N a(n) = a(n-1) + 2*a(n-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 Unpublished, 1976.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 T. D. Noe, <a href="/A003476/b003476.txt">Table of n, a(n) for n = 1..500</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 Kevin Ryde, <a href="http://user42.tuxfamily.org/dragon/index.html">Iterations of the Dragon Curve</a>, see index "RQ", "BQ", and "S".

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2).

%F a(n) = A003229(n-1) + A052537(n-2).

%F a(n) = (1/4)*abs(A078044(n+2)).

%p A003476:=-(1+z+z**2)/(-1+z+2*z**3); # _Simon Plouffe_ in his 1992 dissertation

%t LinearRecurrence[{1,0,2},{1,2,3},30] (* _Harvey P. Dale_, Jun 01 2020 *)

%o (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 Cf. A003229, A052537, A078044.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_