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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A033489, A033490.

Programs

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

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;

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 *)

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

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