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Search: id:A128588
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| 1, 2, 4, 6, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080
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OFFSET
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1,2
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COMMENT
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a(n)/a(n-1) tends to phi, 1.618...
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LINKS
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B. Winterfjord, Binary strings and substring avoidance.
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FORMULA
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Binomial transform of A128587; a(n+2) = a(n+1) + a(n), n>3.
Apart from the initial term, double the Fibonacci numbers. O.g.f.: x*(1+x+x^2)/(1-x-x^2). a(n) gives the number of binary strings of length n-1 avoiding the substrings 000 and 111. a(n) also gives the number of binary strings of length n-1 avoiding the substrings 010 and 101. - Peter Bala (pbala(AT)toucansurf.com), Jan 22 2008
a(n)=A068922(n-1), n>2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 14 2008
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EXAMPLE
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a(4) = 6 = 1*1 + 3*1 + 3*1 + 1*(-1); where A128587 = (1, 1, 1, -1, 3, -5, 9,...).
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CROSSREFS
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Cf. A128587, A128586, A007318.
Cf. A006355, A055389.
Sequence in context: A028488 A080432 A094985 this_sequence A023613 A065795 A000801
Adjacent sequences: A128585 A128586 A128587 this_sequence A128589 A128590 A128591
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 11 2007
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EXTENSIONS
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More terms from Peter Bala (pbala(AT)toucansurf.com), Jan 22 2008
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