A151845 a(0)=0; a(1)=1; 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.

0, 1, 1, 3, 1, 2, 4, 5, 1, 2, 4, 4, 3, 6, 9, 7, 1, 2, 4, 4, 3, 6, 9, 6, 3, 6, 8, 7, 9, 15, 16, 9, 1, 2, 4, 4, 3, 6, 9, 6, 3, 6, 8, 7, 9, 15, 16, 8, 3, 6, 8, 7, 9, 15, 15, 9, 9, 14, 15, 16, 24, 31, 25, 11, 1, 2, 4, 4, 3, 6, 9, 6, 3, 6, 8, 7, 9, 15, 16, 8, 3, 6, 8, 7, 9, 15, 15, 9, 9, 14, 15, 16, 24, 31, 25

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):= 0: f(1):=1: f(2):= 1:
map(f, [$0..100]); # Robert Israel, Oct 30 2017

Crossrefs

Cf. A151843-A151874.

Sequence in context: A074585 A183312 A108038 * A230448 A201653 A230765

Adjacent sequences: A151842 A151843 A151844 * A151846 A151847 A151848

Keyword

nonn

Author

N. J. A. Sloane, Jul 17 2009

Extensions

Name corrected by Robert Israel, Oct 30 2017

Status

approved