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1, 2, 3, 5, 8, 13, 22, 39, 72, 137, 266, 523, 1036, 2061, 4110, 8207, 16400, 32785, 65554, 131091, 262164, 524309, 1048598, 2097175, 4194328, 8388633, 16777242
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OFFSET
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1,2
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COMMENTS
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a(n+1)/a(n)-> 2.
Appears to be the same as A052968 (apart from the offset). - R. J. Mathar, Jun 14 2017
This conjecture is proved in A288381. - Michel Dekking, Feb 18 2021
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LINKS
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Table of n, a(n) for n=1..27.
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FORMULA
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a(n) = -1 + A288133(n-1) for n >= 2.
Conjectures from Colin Barker, Jun 10 2017: (Start)
G.f.: x*(1 - 2*x + x^3 - x^4) / ((1 - x)^2*(1 - 2*x)).
a(n) = -1 + 2^(n-3) + n for n>2.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>5.
(End)
Barker's conjectures are implied by Mathar's conjecture. - Michel Dekking, Feb 18 2021
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MATHEMATICA
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s = {0, 0}; w[0] = StringJoin[Map[ToString, s]];
w[n_] := StringReplace[w[n - 1], {"00" -> "0001", "1" -> "11"}]
Table[w[n], {n, 0, 8}]
st = ToCharacterCode[w[11]] - 48 (* A288381 *)
Flatten[Position[st, 0]] (* A288382 *)
Flatten[Position[st, 1]] (* A288383 *)
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CROSSREFS
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Cf. A288381, A288383.
Sequence in context: A173404 A325473 A213710 * A052968 A206720 A018067
Adjacent sequences: A288379 A288380 A288381 * A288383 A288384 A288385
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling, Jun 10 2017
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STATUS
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approved
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