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%I #19 Aug 25 2021 10:15:45
%S 1,2,4,7,14,28,55,110,220,439,878,1756,3511,7022,14044,28087,56174,
%T 112348,224695,449390,898780,1797559,3595118,7190236,14380471,
%U 28760942,57521884,115043767,230087534,460175068,920350135,1840700270,3681400540
%N Expansion of (1-2*x^3)/(1-2*x-x^3+2*x^4).
%H Kevin Ryde, <a href="http://user42.tuxfamily.org/dragon/index.html">Iterations of the Dragon Curve</a>, see index "JN".
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1,-2).
%F G.f.: (1-2*x^3)/(1-2*x-x^3+2*x^4).
%F a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 7, a(n) = 2*a(n-1) + a(n-3) - 2*a(n-4) for n > 3. - _Jinyuan Wang_, Apr 08 2020
%F a(n) = ceiling((6/7)*2^n) = (6*2^n + 2^(n mod 3))/7. - _Kevin Ryde_, Aug 25 2021
%t LinearRecurrence[{2, 0, 1, -2}, {1, 2, 4, 7}, 30] (* _Jinyuan Wang_, Apr 07 2020 *)
%o (PARI) Vec((1-2*x^3)/(1-2*x-x^3+2*x^4) + O(x^50)) \\ _Michel Marcus_, Dec 09 2014
%Y Cf. A033129, A294627 (first differences).
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 30 2000