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A033490 a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2.

%I A033490 #14 Sep 08 2022 08:44:51
%S A033490 1,2,5,12,26,57,119,250,512,1050,2126,4309,8675,17469,35057,70364,
%T A033490 140978,282468,565448,1131946,2264942,4532010,9066146,18136601,
%U A033490 36277511,72563697,145136069,290289607,580596683,1161228423,2322491903,4645054170,9290178704,18580498386
%N A033490 a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2.
%H A033490 G. C. Greubel, <a href="/A033490/b033490.txt">Table of n, a(n) for n = 1..1000</a>
%p A033490 A033490 := proc(n) option remember; if n <= 2 then n else A033490(n-1)+A033490(round(2*(n-1)/2))+A033490(round((n-1)/2)); fi; end;
%t A033490 a[n_]:= a[n]= If[n<3, 2^(n-1), 2*a[n-1] + a[Floor[n/2]]]; Table[a[n], {n, 40}] (* _G. C. Greubel_, Oct 14 2019 *)
%o A033490 (PARI) a=vector(99,i,i);for(n=3,#a,a[n]=2*a[n-1]+a[n\2]);a \\ _Charles R Greathouse IV_, Nov 29 2011
%o A033490 (Magma) a:= func< n | n lt 3 select 2^(n-1) else 2*Self(n-1) + Self(Floor(n/2)) >;
%o A033490 [a(n): n in [1..40]]; // _G. C. Greubel_, Oct 14 2019
%o A033490 (Sage)
%o A033490 @CachedFunction
%o A033490 def a(n):
%o A033490     if (n<3): return 2^(n-1)
%o A033490     else: return 2*a(n-1) +a(floor(n/2))
%o A033490 [a(n) for n in (1..40)] # _G. C. Greubel_, Oct 14 2019
%o A033490 (GAP)
%o A033490 a:= function(n)
%o A033490     if n<3 then return 2^(n-1);
%o A033490     else return 2*a(n-1) + a(Int(n/2));
%o A033490     fi;
%o A033490   end;
%o A033490 List([1..40], n-> a(n) ); # _G. C. Greubel_, Oct 14 2019
%Y A033490 Cf. A033489, A033497.
%K A033490 nonn,easy
%O A033490 1,2
%A A033490 _N. J. A. Sloane_
%E A033490 Terms a(30) onward added by _G. C. Greubel_, Oct 14 2019