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A054349 Successive generations of the variant of the Kolakoski sequence described in A042942. 7
2, 22, 2211, 221121, 221121221, 22112122122112, 2211212212211211221211, 221121221221121122121121221121121, 2211212212211211221211212211211212212211212212112 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..8.

Bertran Steinsky, A Recursive Formula for the Kolakoski Sequence A000002, J. Integer Sequences, Vol. 9 (2006), Article 06.3.7.

CROSSREFS

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

Word lengths give A042942.

Sequence in context: A104149 A113761 A319620 * A182293 A222000 A261400

Adjacent sequences:  A054346 A054347 A054348 * A054350 A054351 A054352

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 07 2000

EXTENSIONS

More terms from David Wasserman, Mar 04 2002

STATUS

approved

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Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)