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1, 1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Starting from the 4th term, every succeeding term is twice the preceding term. I.e. a(n+1) = 2a(n).
Number of binary words of length n-2 that do not start with 01 (n>=2). Example: a(5)=6 because we have 000,001,100,101,110 and 111. Except for the initial term, column 0 of A119440. - Emeric Deutsch (deutsch(AT)duke.poly.edu), May 19 2006
a(n) written in base 2: a(1) = 1, a(2) = 1, a(3) = 10, a(n) for n >= 4: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, (n-4) times 0 (see A003953(n-3). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 17 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (2).
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FORMULA
| G.f.: x*(1-x-x^3)/(1-2*x). - Paul Barry, Feb 17 2005
a(n) = 3*2^(n-4) for n>3; a(1)=a(2)=1, a(3)=2. - Emeric Deutsch, May 19 2006
a(n) = 2^(n-4)+2^(n-3) for n>3. - Jaroslav Krizek, Aug 17 2009
a(0) = 1, a(2) = 1, a(3) = 2, for n>3: a(n) = sum_(i=2..n-1) a(i). - Jaroslav Krizek, Nov 16 2009
a(n)=A042950(n-3). - From DELEHAM Philippe, Oct 17 2011.
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MAPLE
| a:=proc(n) if n=1 or n=2 then 1 elif n=3 then 2 else 3*2^(n-4) fi end: seq(a(n), n=1..37); - Emeric Deutsch, May 19 2006
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MATHEMATICA
| Table[ Ceiling[3*2^(n - 4)], {n, 34}] (* or *)
Rest@CoefficientList[Series[x(1 - x - x^3)/(1 - 2x), {x, 0, 33}], x] (from Robert G. Wilson v, Jul 08 2006)
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CROSSREFS
| Cf. A119440.
Sequence in context: A049890 A042950 * A110164 A035055 A119559 A045761
Adjacent sequences: A098008 A098009 A098010 * A098012 A098013 A098014
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KEYWORD
| nonn,easy
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AUTHOR
| Ray G. Opao (1260(AT)email.com), Sep 09 2004
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EXTENSIONS
| More terms from Emeric Deutsch, May 19 2006
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