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A006355
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Number of binary vectors of length n containing no singletons.
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71
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1, 0, 2, 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, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634
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OFFSET
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0,3
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COMMENTS
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Number of cvtemplates at n-2 letters given <= 2 consecutive consonants or vowels (n >= 4).
Number of (n,2) Freiman-Wyner sequences.
Diagonal sums of the Riordan array ((1-x+x^2)/(1-x), x/(1-x)), A072405 (where this begins 1,0,1,1,1,1,...). - Paul Barry, May 04 2005
a(n) = A119457(n-1,n-2) for n>2. - Reinhard Zumkeller, May 20 2006
Central terms of the triangle in A094570. - Reinhard Zumkeller, Mar 22 2011
Pisano period lengths: 1, 1, 8, 3, 20, 8, 16, 6, 24, 20, 10, 24, 28, 16, 40, 12, 36, 24, 18, 60,... - R. J. Mathar, Aug 10 2012
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REFERENCES
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I. F. Blake, The enumeration of certain run length sequences, Information and Control, 55 (1982), 222-237.
Enoch Haga, Room for Expansion, Word Ways, 33 (No. 2, 2000), pp. 106-113 (see p. 110).
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 16,51.
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 0..4786 (next term has 1001 digits)
Index entries for sequences related to linear recurrences with constant coefficients
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 898
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FORMULA
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a(n+2) = F(n-1) + F(n+2), for n>0.
G.f.: (1-x+x^2)/(1-x-x^2). - Paul Barry, May 04 2005
a(n) = 2*F(n-1) for n>0, F(n)=A000045(n) and a(0)=1. [Mircea Merca, Jun 28 2012]
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MAPLE
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a:= n-> if n=0 then 1 else (Matrix([[2, -2]]). Matrix([[1, 1], [1, 0]])^n) [1, 1] fi: seq (a(n), n=0..38); # Alois P. Heinz, Aug 18 2008
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MATHEMATICA
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lst={1}; Do[AppendTo[lst, Fibonacci[n+3]-Fibonacci[n]], {n, -1, 4*4!}]; lst [From Vladimir Orlovsky, Jun 11 2009]
lst={1}; a=2; s=3; Do[a=s-(a+1); AppendTo[lst, a]; s+=a, {n, 5!}]; lst [From Vladimir Orlovsky, Oct 27 2009]
Join[{1}, Last[#]-First[#]&/@Partition[Fibonacci[Range[-1, 40]], 4, 1]] (* From Harvey P. Dale, Sep 30 2011 *)
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PROG
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(PARI) a(n)=if(n, 2*fibonacci(n-1), 1) \\ Charles R Greathouse IV, Mar 14, 2012
(Haskell)
a006355 n = a006355_list !! n
a006355_list = 1 : fib2s where
fib2s = 0 : map (+ 1) (scanl (+) 1 fib2s)
-- Reinhard Zumkeller, Mar 20 2013
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CROSSREFS
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Except for initial term, = 2*Fibonacci numbers (A000045).
Essentially the same as A055389.
Cf. A097925, A097926.
Essentially the same as A047992, A068922, A054886 and A090991.
Sequence in context: A034410 A192682 A050194 * A055389 A163733 A198834
Adjacent sequences: A006352 A006353 A006354 * A006356 A006357 A006358
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KEYWORD
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nonn,easy,nice
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AUTHOR
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David M. Bloom.
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EXTENSIONS
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More terms from Reinhard Zumkeller, May 20 2006
Corrected by T. D. Noe, Oct 31 2006
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STATUS
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approved
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