login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A033490
a(n) = 2*a(n-1) + a(floor(n/2)), with a(1) = 1, a(2) = 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
1,2
LINKS
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 *)
PROG
(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
(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
(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
(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
CROSSREFS
Sequence in context: A228078 A125180 A073778 * A221950 A116716 A128812
KEYWORD
nonn,easy
EXTENSIONS
Terms a(30) onward added by G. C. Greubel, Oct 14 2019
STATUS
approved