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A147678 Double, add 0, double, add 1, double, add 2, double, add 3, etc.

%I A147678 #21 Jan 30 2024 06:25:12
%S A147678 1,2,2,4,5,10,12,24,27,54,58,116,121,242,248,496,503,1006,1014,2028,
%T A147678 2037,4074,4084,8168,8179,16358,16370,32740,32753,65506,65520,131040,
%U A147678 131055,262110,262126,524252,524269,1048538,1048556,2097112,2097131
%N A147678 Double, add 0, double, add 1, double, add 2, double, add 3, etc.
%C A147678 A147675-A147678 are from a quiz that someone asked me to help them with.
%H A147678 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-5,0,2).
%F A147678 From _R. J. Mathar_, Apr 22 2009: (Start)
%F A147678 a(n) = 4*a(n-2) - 5*a(n-4) + 2*a(n-6).
%F A147678 G.f.: -x*(2*x+1)*(2*x^4 - 2*x^2 + 1)/((2*x^2-1)*(x-1)^2*(1+x)^2).
%F A147678 a(n)=(1 + (-1)^n)/2 + 2*A016116(n) - A105811(n+3)/4 - 3*(n+1)/4. (End)
%F A147678 a(n) = 2*a(n-1) - (n mod 2)*(a(n-1) - (n-3)/2). - _Reinhard Zumkeller_, Apr 22 2009
%t A147678 Transpose[NestList[Flatten[{Rest[#],2First[#]-5#[[3]]+ 4#[[5]]}]&,{1,2,2,4,5,10},40]][[1]] (* _Harvey P. Dale_, Mar 24 2011 *)
%t A147678 dp[a_,n_]:=Flatten[{{x=a},Table[{2x,x=2x+m},{m,0,n}]}]; A147678=dp[1,20] (* _Zak Seidov_, Mar 24 2011 *)
%t A147678 LinearRecurrence[{0, 4, 0, -5, 0, 2}, {1, 2, 2, 4, 5, 10}, 20] (* _T. D. Noe_, Mar 25 2011 *)
%K A147678 nonn,easy
%O A147678 1,2
%A A147678 _N. J. A. Sloane_, Apr 21 2009
%E A147678 More terms from _R. J. Mathar_, Apr 22 2009