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1, 3, 8, 19, 42, 89, 184, 375, 758, 1525, 3060, 6131, 12274, 24561, 49136, 98287, 196590, 393197, 786412, 1572843, 3145706, 6291433, 12582888, 25165799, 50331622, 100663269, 201326564, 402653155, 805306338, 1610612705, 3221225440
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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Row sums of A132110. - Gary W. Adamson, Aug 09 2007
Consider the infinite sequence of strings x(1) = a, x(2) = aba, x(3) = ababbaba,..., where x(n+1) = x(n).b.x(n), for n >= 1. Each x(n), for n >= 2, has borders x(1), x(2),...,x(n-1), none of which cover x(n). The length of x(n+1) is 3*2^n-n-2. [William F. Smyth, Feb 29 2012]
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REFERENCES
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T. Flouri, C.S. Iliopoulos, S.P. Pissis and W.F. Smyth, On Approximate String Matching, submitted to COCOON-12.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Tomas Flouri, Costas S. Iliopoulos, Solon P. Pissis, W. F. Smyth, On approximate string covering (draft, 2012).
Index to sequences with linear recurrences with constant coefficients, signature (4,-5,2).
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FORMULA
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a(0)=1, a(n)=2*a(n-1)+n;
Binomial transform of [1, 2, 3, 3, 3,...]. - Gary W. Adamson, Aug 09 2007
G.f.: (x^2-x+1)/((1-2*x)*(1-x)^2)=3*U(0)x; where U(k)= 1 - (k+2)/(3*2^k - 18*x*4^k/(6*x*2^k - (k+2)/U(k+1))); (continued fraction, 3-step). - Sergei N. Gladkovskii, Jul 04 2012
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MATHEMATICA
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lst={}; Do[AppendTo[lst, 3*2^n-n-2], {n, 0, 4!}]; lst [From Vladimir Joseph Stephan Orlovsky, Oct 25 2008]
LinearRecurrence[{4, -5, 2}, {1, 3, 8}, 40] (* Vincenzo Librandi, Jun 23 2012 *)
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PROG
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(PARI) a(n)=3<<n-n-2 \\ Charles R Greathouse IV, Feb 29 2012
(MAGMA) I:=[1, 3, 8]; [n le 3 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 23 2012
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CROSSREFS
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Cf. A000295, A132110.
Sequence in context: A074839 A002318 A095681 * A099050 A065352 A161993
Adjacent sequences: A079580 A079581 A079582 * A079584 A079585 A079586
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Benoit Cloitre, Jan 25 2003
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STATUS
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approved
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