A033490 a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 2.
1, 2, 5, 12, 26, 57, 119, 250, 512, 1050, 2126, 4309, 8675, 17469, 35057, 70364, 140978, 282468, 565448, 1131946, 2264942, 4532010, 9066146, 18136601, 36277511, 72563697, 145136069, 290289607, 580596683, 1161228423, 2322491903, 4645054170, 9290178704, 18580498386
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
Programs
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GAP
a:= function(n) if n<3 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 3 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
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;
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Mathematica
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 *) -
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
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Sage
@CachedFunction def a(n): if (n<3): 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
Extensions
Terms a(30) onward added by G. C. Greubel, Oct 14 2019