

A060973


a(2*n+1) = a(n+1)+a(n), a(2*n) = 2*a(n), with a(1)=0 and a(2)=1.


4



0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,4


LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000
R. Stephan, Some divideandconquer sequences ...
R. Stephan, Table of generating functions


FORMULA

a(n) = nA006165(n) = A006165(n)A053646(n) = (nA053646(n))/2 [for n>1 ]. If n = 2*2^m+k with 0< = k< = 2^m, then a(n) = 2^m; if n = 3*2^m+k with 0< = k< = 2^m, then a(n) = 2^m+k.
G.f. x/(1x) + x/(1x)^2 * (1 + sum(k>=0, t^2(t1), t=x^2^k)).  Ralf Stephan, Sep 12 2003


EXAMPLE

a(6)=2*a(3)=2*1=2. a(7)=a(3)+a(4)=1+2=3.


MAPLE

A060973 := proc(n)
option remember;
if n <= 2 then
return n1;
fi;
if n mod 2 = 0 then
2*procname(n/2)
else
procname((n1)/2)+procname((n+1)/2);
fi;
end proc:


CROSSREFS

Sequence in context: A228482 A091822 A173022 * A097915 A029131 A162351
Adjacent sequences: A060970 A060971 A060972 * A060974 A060975 A060976


KEYWORD

nonn


AUTHOR

Henry Bottomley, May 09 2001


STATUS

approved



