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A054349 Successive generations of the variant of the Kolakoski sequence described in A042942. 7

%I

%S 2,22,2211,221121,221121221,22112122122112,2211212212211211221211,

%T 221121221221121122121121221121121,

%U 2211212212211211221211212211211212212211212212112

%N Successive generations of the variant of the Kolakoski sequence described in A042942.

%C For n >= 0, let f_1(n) be the number of 1's in a(n) (sequence begins: 0, 0, 2, 3, 4, 6, 11, 17, 24, ...) and f_2(n) be the number of 2's (sequence begins: 1, 2, 2, 3, 5, 8, 11, 16, 25, ...). Then there is a simple relation between f_1 and f_2, namely: f_1(n) = 1 - f_2(n) + f_2(n-1) + f_2(n-2) + ... + f_2(0). i.e. f_1(7) = 17 and 1 - f_2(7) + f_2(6) + ... + f_2(0) = 1 - 16 + 11 + 8 + 5 + 3 + 2 + 2 + 1 = 17. - _Benoit Cloitre_, Oct 11 2005

%H Bertran Steinsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Steinsky/steinsky5.html">A Recursive Formula for the Kolakoski Sequence A000002</a>, J. Integer Sequences, Vol. 9 (2006), Article 06.3.7.

%Y Cf. A000002, A054348, A054350, A054351, A111123, A111124.

%Y Word lengths give A042942.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, May 07 2000

%E More terms from _David Wasserman_, Mar 04 2002

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Last modified April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)