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A095343 Length of n-th string generated by a Kolakoski(7,1) rule starting with a(1)=1. 5
1, 1, 7, 7, 31, 49, 145, 289, 727, 1591, 3775, 8545, 19873, 45505, 105127, 241639, 557023, 1281937, 2953009, 6798817, 15657847, 36054295, 83027839, 191190721, 440274241, 1013846401, 2334669127, 5376208327, 12380215711, 28508840689 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Each string is derived from the previous string using the Kolakoski(7,1) rule and the additional condition: "string begins with 1 if previous string ends with 5 and vice versa". The strings are 1 -> 7 -> 1111111 -> 7171717 -> 11111117111111171111111711111117 -> ... and each one contains 1,1,7,7,31,... elements.

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(1) = a(2) = 1, a(n) = a(n-1) + 3*a(n-2) - 3*(-1)^n.

Empirical G.f.: x*(1+x+3*x^2)/((1+x)*(1-x-3*x^2)). [Colin Barker, Jul 02 2012]

CROSSREFS

Cf. A000002, A066983, A095342, A095344.

Sequence in context: A255281 A255283 A140252 * A286830 A286862 A290683

Adjacent sequences:  A095340 A095341 A095342 * A095344 A095345 A095346

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 03 2004

STATUS

approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)