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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.
2
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 17 2009
EXTENSIONS
Name corrected by Robert Israel, Oct 30 2017
STATUS
approved