A289322 Number of 1s in the first 2^n entries of the Kolakoski sequence, A000002.

1, 1, 2, 4, 8, 17, 32, 64, 129, 256, 513, 1024, 2051, 4093, 8192, 16381, 32746, 65523, 131082, 262168, 524262, 1048547, 2097100, 4194345, 8388733, 16777351, 33554669, 67109796, 134219275, 268437750, 536872179

Offset: 0

Author

Richard P. Brent, Jul 05 2017

Keywords

• nonn

Examples

			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.
		

Links

• Richard P. Brent, Table of n, a(n) for n = 0..64
• Richard P. Brent and Judy-anne H. Osborn, A fast algorithm for the Kolakoski sequence, Dec. 2016
• J. Nilsson, A Space Efficient Algorithm for the Calculation of the Digit Distribution in the Kolakoski Sequence, arXiv preprint arXiv:1110.4228 [math.CO], 2011.
• M. Rao, Trucs et bidules sur la séquence de Kolakoski, Oct. 2012.

Crossrefs

Cf. A000002. Analogous for powers of ten is A195206. Equivalent but with smaller entries is A289323. Closely related are A054353, A074286, A088568, A156077.

Formula

a(n) = (2^n + A088568(2^n))/2 = (2^n - A289323(n))/2.