A033497 a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2, a(3) = 4.
1, 2, 4, 10, 22, 48, 100, 210, 430, 882, 1786, 3620, 7288, 14676, 29452, 59114, 118438, 237306, 475042, 950966, 1902814, 3807414, 7616614, 15236848, 30477316, 60961920, 121931128, 243876932, 487768540, 975566532, 1951162516, 3902384146, 7804827406, 15609773250
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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GAP
a:= function(n) if n<4 then return 2^(n-1); else return 2*a(n-1) + a(Int(n/2)); fi; end; List([1..40], n-> a(n) ); # G. C. Greubel, Oct 14 2019 -
Magma
a:= func< n | n lt 4 select 2^(n-1) else 2*Self(n-1) + Self(Floor(n/2)) >; [a(n): n in [1..40]]; // G. C. Greubel, Oct 14 2019
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Maple
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;
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Mathematica
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 *) 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 *)
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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
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Sage
@CachedFunction def a(n): if (n<4): return 2^(n-1) else: return 2*a(n-1) +a(floor(n/2)) [a(n) for n in (1..40)] # G. C. Greubel, Oct 14 2019