|
| |
|
|
A076895
|
|
a(1) = 1, a(n) = n - a(ceil(n/2)).
|
|
2
|
|
|
|
1, 1, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 12, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 20, 20, 21, 22, 23, 23, 24, 25, 26, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 34, 35, 36, 37, 37, 38, 38, 39, 39, 40, 41, 42, 42, 43, 43, 44, 44, 45, 46, 47, 47, 48, 48
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
LINKS
|
Table of n, a(n) for n=1..73.
|
|
|
FORMULA
|
a(n) is asymptotic to (2/3)*n.
a(n) = A050292(n-1) + (1+(1-2*(C(n)-F(n)))*(-1)^F(n))/2 where C(n)=ceil(log[2](n)); F(n)=floor(log[2](n)) and A050292(n) (with A050292(0)=0) is the maximum cardinality of a double-free subset of {1, 2, ..., n}. So using Wang's asymptotic formula for A050292, a(n) = (2/3)*n+O(log[4](n)). Series expansion: (1/(x-1)) * ( 1/(x-1) + Sum(i=1, infinity, (-1)^i*( x^(2^i)/(x^(2^i)-1) - x^(2^(i-1)) ) ). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 17 2003
a(n+1) = b(n) with b(0)=0, b(2n) = -b(n)+2n+1, b(2n+1) = -b(n)+2n+2-[n==0]. Also a(n+1) = A050292(n) + A030301(n). - Ralf Stephan, Oct 28 2003
|
|
|
PROG
|
(PARI) a(n)=if(n<2, 1, n-a(ceil(n/2)))
|
|
|
CROSSREFS
|
Cf. A050292, A079411.
Sequence in context: A096386 A135671 A079420 * A029086 A070046 A130120
Adjacent sequences: A076892 A076893 A076894 * A076896 A076897 A076898
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Benoit Cloitre, Nov 26 2002
|
|
|
EXTENSIONS
|
Edited by Ralf Stephan, Sep 01 2004
|
|
|
STATUS
|
approved
|
| |
|
|
