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a(0)=1; a(1)=1; a(2)=2; 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.
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%I #4 May 19 2020 07:24:59

%S 1,1,2,4,2,3,6,7,2,3,6,6,5,9,13,10,2,3,6,6,5,9,13,9,5,9,12,11,14,22,

%T 23,13,2,3,6,6,5,9,13,9,5,9,12,11,14,22,23,12,5,9,12,11,14,22,22,14,

%U 14,21,23,25,36,45,36,16,2,3,6,6,5,9,13,9,5,9,12,11,14,22,23,12,5,9,12,11,14

%N a(0)=1; a(1)=1; a(2)=2; 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.

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

%Y Cf. A151843-A151874.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 17 2009