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Search: id:A140514
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| A140514 |
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Subtraction of two basic sequences to get a semi-chaotic sequence: a(n)=padovan(n);b(n)=thuemorse(n); c(n)=a(n)-b(n). |
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1
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| 0, 0, 0, 1, 1, 2, 3, 3, 4, 7, 9, 11, 16, 20, 27, 37, 48, 65, 86, 113, 151, 199, 264, 351, 465, 615, 815, 1081, 1431, 1897, 2513, 3328, 4409, 5842, 7739, 10251, 13581, 17990, 23832, 31572, 41824, 55404, 73395, 97229, 128800, 170625, 226030, 299425, 396655
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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Thue Morse Function from notebook downloaded from:
http://mathworld.wolfram.com/notebooks/IntegerSequences/Thue-MorseSequence.nb.
Limit[c[n+1]/c[n],n->Infinity=Real Root of [x^3-x-1=0]->1.32472.
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REFERENCES
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Weisstein, Eric W. "Thue-Morse Sequence." http : // mathworld.wolfram.com/Thue - MorseSequence.html
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FORMULA
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a(n) = a(n-2)+a(n-3); b(n)=Substitution({0 -> {0, 1}, 1 -> {1, 0}}); c(n)=a(n)-b(n).
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MATHEMATICA
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(*A000931*) a[0] = 0; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; (*A010060*) b = ThueMorse[7, 0][[7]]; c = Table[a[n], {n, 0, Length[b] - 1}]; d = c - b
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CROSSREFS
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Cf. A000931, A010060.
Sequence in context: A152980 A035535 A154309 this_sequence A047079 A156353 A130743
Adjacent sequences: A140511 A140512 A140513 this_sequence A140515 A140516 A140517
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 01 2008
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