%I #19 Feb 07 2023 12:44:22
%S 2,3,3,5,5,9,9,17,17,33,33,65,65,129,129,257,257,513,513,1025,1025,
%T 2049,2049,4097,4097,8193,8193,16385,16385,32769,32769,65537,65537,
%U 131073,131073,262145,262145,524289,524289,1048577,1048577,2097153
%N Summatory Rudin-Shapiro sequence for 2^(n-1).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rudin-ShapiroSequence.html">Rudin-Shapiro Sequence.</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2).
%F Apart from leading term, just A000051 (2^n + 1) doubled up.
%F G.f.: -x*(-2 - x + 4*x^2)/((x - 1)*(2*x^2 - 1)). - _R. J. Mathar_, Jul 15 2016
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3). - _Wesley Ivan Hurt_, Aug 19 2022
%F E.g.f.: cosh(x) + cosh(sqrt(2)*x) + sinh(x) + sinh(sqrt(2)*x)/sqrt(2) - 2. - _Stefano Spezia_, Feb 05 2023
%t d2n[n_]:=Module[{x=2^n+1},{x,x}];Join[{2},Flatten[Array[d2n,30]]] (* _Harvey P. Dale_, May 26 2011 *)
%Y Cf. A014081, A020985, A020986, A000051.
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_