A151847 a(0)=1; a(1)=0; a(2)=1; for n>=3 if n=2^i + j with 0<=j<2^i then a(n)=a(j) + a(j + 1) except we add 1 if j=2^i-1.

1, 0, 1, 2, 1, 1, 3, 4, 1, 1, 3, 3, 2, 4, 7, 6, 1, 1, 3, 3, 2, 4, 7, 5, 2, 4, 6, 5, 6, 11, 13, 8, 1, 1, 3, 3, 2, 4, 7, 5, 2, 4, 6, 5, 6, 11, 13, 7, 2, 4, 6, 5, 6, 11, 12, 7, 6, 10, 11, 11, 17, 24, 21, 10, 1, 1, 3, 3, 2, 4, 7, 5, 2, 4, 6, 5, 6, 11, 13, 7, 2, 4, 6, 5, 6, 11, 12, 7, 6, 10, 11, 11, 17, 24, 21

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

I would very much like a g.f. for this sequence!

Maple

f:= proc(n) option remember; local i, j;
  i:= ilog2(n);
  j:= n - 2^i;
  if j = 2^i-1 then procname(j)+procname(j+1)+1
    else procname(j)+procname(j+1)
    fi
end proc:
f(0):= 1: f(1):=0: f(2):= 1:
map(f, [$0..100]); # Robert Israel, Oct 30 2017

Crossrefs

Cf. A151843-A151874.

Sequence in context: A300508 A120013 A344180 * A349593 A179743 A113749

Adjacent sequences: A151844 A151845 A151846 * A151848 A151849 A151850

Keyword

nonn

Author

N. J. A. Sloane, Jul 17 2009

Extensions

Name corrected by Robert Israel, Oct 30 2017

Status

approved