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A111091
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Successive generations of a Kolakoski(3,1) rule starting with 1 (see A066983).
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0
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OFFSET
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1,2
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COMMENTS
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Terms are palindromic. If b_3(n) denotes the number of 3's in a(n) then b(n) satisfies the recursion: b_3(1)=0, b_3(2)=1 and b_3(n) = b_3(n-1) + b_3(n-2) + (-1)^n so that b_3(2n)=A055588(n) and b_3(2n+1)=A027941(n). If b_1(n) denotes the number of 1's: b_1(1)=1, b_1(2)=0 and b_1(n) = b_1(n-1) + b_1(n-2) - 2*(-1)^n so that b_1(2n)=A004146(n) and b_1(2n+1) = A000032(n-2) - 2.
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LINKS
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FORMULA
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As n grows, a(2n-1) converges toward A095345 (read as a word) and a(2n) converges toward A095346.
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EXAMPLE
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1 --> 3 --> 111 --> 313 --> 1113111 --> 313111313
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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