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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)/a(n-1) tends to phi, 1.618...
From A014217=1,1,2,4,6,. Which leads to A153819=16,34,88,. Inverse binomial transform of A069403=1,3,9,25,67. [From Paul Curtz, Jan 03 2009]
Variation on "Narayana's Cows". One cow at step n=1. At any subsequent step any cow generates another one but after two steps dies. The sequence gives the total number of cows at any steps. [From Paolo P. Lava, Oct 07 2009]
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LINKS
| B. Winterfjord, Binary strings and substring avoidance.
J.-P. Allouche and T. Johnson, Narayana's Cows and Delayed Morphisms.
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FORMULA
| 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, Jan 22 2008
a(n)=A068922(n-1), n>2. - R. J. Mathar, Jun 14 2008
G.f.: (-1+x+x^2+x^3+x^4+x^5)/(x^2*(1-x-x^2)). - Paul Weisenhorn, Oct 30 2011
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EXAMPLE
| 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
| Cf. A128587, A128586, A007318.
Cf. A006355, A055389.
Sequence in context: A028488 A080432 A094985 * A023613 A065795 A000801
Adjacent sequences: A128585 A128586 A128587 * A128589 A128590 A128591
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 11 2007
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EXTENSIONS
| More terms from Peter Bala (pbala(AT)toucansurf.com), Jan 22 2008
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