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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033489, A033497.

Programs

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

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;

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

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