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%I #17 Jul 29 2023 03:16:51
%S 0,1,1,2,2,4,3,4,4,7,5,8,6,7,10,11,10,8,13,12,12,14,16,17,11,14,17,20,
%T 16,17,19,21,23,17,17,19,24,24,25,18,29,26,29,26,26,29,35,29,26,40,29,
%U 33,33,38,36,34,28,38,42,40,37,34,40,27,45,35,37,41,40,44,48,45,41,45
%N Number of 1's in the binary representation of A000129(n).
%H Amiram Eldar, <a href="/A166267/b166267.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A000120(A000129(n)). - _R. J. Mathar_, Oct 28 2009
%t Clear[a,b,c,f,n,lst] f[n_]:=Plus@@IntegerDigits[n,2]; a=1;b=0;c=0;lst={b}; Do[c=a+b+c;AppendTo[lst,f[c]];a=b;b=c,{n,5!}];lst
%t DigitCount[LinearRecurrence[{2, 1}, {0, 1}, 100], 2, 1] (* _Amiram Eldar_, Jul 29 2023 *)
%o (Python)
%o def A000129(n):
%o if n <=1:
%o return n
%o else:
%o return 2*A000129(n-1)+A000129(n-2)
%o def A000120(n):
%o a=0
%o sh=n
%o while sh > 0:
%o a += sh & 1
%o sh >>= 1
%o return a
%o def A166267(n):
%o return A000120(A000129(n))
%o print([A166267(n) for n in range(30)])
%o # _R. J. Mathar_, Oct 18 2009
%Y Cf. A000120, A000129.
%K nonn,base,easy
%O 0,4
%A _Vladimir Joseph Stephan Orlovsky_, Oct 10 2009
%E Keyword:base added by _R. J. Mathar_, Oct 28 2009
%E Offset changed to 0 by _Georg Fischer_, Dec 19 2020
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