| 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 1, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2
(list; graph; listen)
|
|
|
OFFSET
|
1,10
|
|
|
COMMENT
|
Number of i such that d(i)<d(i-1), where Sum{d(i)*2^i: i=0,1,....,m} is base 2 representation of n.
|
|
LINKS
|
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
FORMULA
|
G.f.: 1/(1-x) * sum(k>=0, t^2/(1+t)/(1+t^2), t=x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 10 2003
a(n) = A069010(n) - (n mod 2). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 10 2003
a(4n) = a(4n+1) = a(2n), a(4n+2) = a(n)+1, a(4n+3) = a(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 20 2003
|
|
CROSSREFS
|
Cf. A014081, A014082, A037800, A056974, A056975, A056976, A056977, A056978, A056979, A056980.
a(n) = A005811(n) - ceiling(A005811(n)/2) = A005811(n) - A069010(n).
Equals (A072219(n+1)-1)/2.
Sequence in context: A047988 A037818 A087116 this_sequence A080234 A136049 A135694
Adjacent sequences: A033261 A033262 A033263 this_sequence A033265 A033266 A033267
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
