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%I #20 Jul 07 2017 03:28:41
%S 1,1,2,4,8,17,32,64,129,256,513,1024,2051,4093,8192,16381,32746,65523,
%T 131082,262168,524262,1048547,2097100,4194345,8388733,16777351,
%U 33554669,67109796,134219275,268437750,536872179
%N Number of 1s in the first 2^n entries of the Kolakoski sequence, A000002.
%H Richard P. Brent, <a href="/A289322/b289322.txt">Table of n, a(n) for n = 0..64</a>
%H Richard P. Brent and Judy-anne H. Osborn, <a href="https://maths-people.anu.edu.au/~brent/pd/Kolakoski-ACCMCC.pdf">A fast algorithm for the Kolakoski sequence</a>, Dec. 2016
%H J. Nilsson, <a href="http://arxiv.org/abs/1110.4228">A Space Efficient Algorithm for the Calculation of the Digit Distribution in the Kolakoski Sequence</a>, arXiv preprint arXiv:1110.4228 [math.CO], 2011.
%H M. Rao, <a href="http://www.arthy.org/kola/kola.php">Trucs et bidules sur la séquence de Kolakoski</a>, Oct. 2012.
%F a(n) = (2^n + A088568(2^n))/2 = (2^n - A289323(n))/2.
%e The first 32 entries of the Kolakoski sequence, A000002, are 12211212212211211221211212211211. From this we see that a(5)=17, since among the first 2^5 letters, 17 of them are 1s.
%Y Cf. A000002. Analogous for powers of ten is A195206. Equivalent but with smaller entries is A289323. Closely related are A054353, A074286, A088568, A156077.
%K nonn
%O 0,3
%A _Richard P. Brent_, Jul 05 2017
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