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%I #13 Feb 14 2016 18:52:52
%S 0,1,3,4,8,10,12,13,21,25,29,31,35,37,39,40,56,64,72,76,84,88,92,94,
%T 102,106,110,112,116,118,120,121,153,169,185,193,209,217,225,229,245,
%U 253,261,265,273,277,281,283,299,307,315,319,327,331,335,337
%N a(0)=0; thereafter a(2n+1)=3*a(n)+1, a(2n)=2*a(n)+a(n-1)+1.
%H Colin Barker, <a href="/A268514/b268514.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = Sum{i=1..n} 2^{number of 0's in binary expansion of i}.
%F a(n) = (A064194(n+1)-1)/2.
%o (PARI) a(n) = sum(i=1, n, b=binary(i); 2^(#b-norml2(b))) \\ _Colin Barker_, Feb 08 2016
%Y Cf. A064194, A023416 (no. of 0's in n).
%Y First differences are (essentially) A080100.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Feb 07 2016