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A033497 a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2, a(3) = 4.

%I A033497 #21 Sep 08 2022 08:44:51
%S A033497 1,2,4,10,22,48,100,210,430,882,1786,3620,7288,14676,29452,59114,
%T A033497 118438,237306,475042,950966,1902814,3807414,7616614,15236848,
%U A033497 30477316,60961920,121931128,243876932,487768540,975566532,1951162516,3902384146,7804827406,15609773250
%N A033497 a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2, a(3) = 4.
%H A033497 Harvey P. Dale, <a href="/A033497/b033497.txt">Table of n, a(n) for n = 1..1000</a>
%p A033497 A033497 := proc(n) option remember; if n <= 3 then 2^(n-1) else A033497(n-1)+A033497(round(2*(n-1)/2))+A033497(round((n-1)/2)); fi; end;
%t A033497 a[1]=1;a[2]=2;a[3]=4;a[n_]:=a[n]=2a[n-1]+a[Floor[n/2]]; Array[a,40] (* _Harvey P. Dale_, Aug 08 2019 *)
%t A033497 a[n_]:= a[n]= If[n<4, 2^(n-1), 2*a[n-1] + a[Floor[n/2]]]; Table[a[n], {n, 40}] (* _G. C. Greubel_, Oct 14 2019 *)
%o A033497 (PARI) a=vector(99,i,i*(i-1)/2+1);for(n=4,#a,a[n]=2*a[n-1]+a[n\2]);a \\ _Charles R Greathouse IV_, Nov 29 2011
%o A033497 (Magma) a:= func< n | n lt 4 select 2^(n-1) else 2*Self(n-1) + Self(Floor(n/2)) >;
%o A033497 [a(n): n in [1..40]]; // _G. C. Greubel_, Oct 14 2019
%o A033497 (Sage)
%o A033497 @CachedFunction
%o A033497 def a(n):
%o A033497     if (n<4): return 2^(n-1)
%o A033497     else: return 2*a(n-1) +a(floor(n/2))
%o A033497 [a(n) for n in (1..40)] # _G. C. Greubel_, Oct 14 2019
%o A033497 (GAP)
%o A033497 a:= function(n)
%o A033497     if n<4 then return 2^(n-1);
%o A033497     else return 2*a(n-1) + a(Int(n/2));
%o A033497     fi;
%o A033497   end;
%o A033497 List([1..40], n-> a(n) ); # _G. C. Greubel_, Oct 14 2019
%Y A033497 Cf. A033489, A033490.
%K A033497 nonn,easy
%O A033497 1,2
%A A033497 _N. J. A. Sloane_