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A006355 Number of binary vectors of length n containing no singletons. +0
26
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 (list; graph; listen)
OFFSET

0,3

COMMENT

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 (pbarry(AT)wit.ie), May 04 2005

a(n) = A119457(n-1,n-2) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2006

REFERENCES

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.

LINKS

Index entries for sequences related to linear recurrences with constant coefficients

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 898

FORMULA

a(n+2) = F(n-1) + F(n+2), for n>0.

G.f.: (1-x+x^2)/(1-x-x^2) - Paul Barry (pbarry(AT)wit.ie), May 04 2005

MAPLE

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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 18 2008]

MATHEMATICA

lst={1}; Do[AppendTo[lst, Fibonacci[n+3]-Fibonacci[n]], {n, -1, 4*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 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 (4vladimir(AT)gmail.com), Oct 27 2009]

CROSSREFS

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: A139582 A034410 A050194 this_sequence A055389 A163733 A084202

Adjacent sequences: A006352 A006353 A006354 this_sequence A006356 A006357 A006358

KEYWORD

nonn,easy,nice

AUTHOR

David M. Bloom.

EXTENSIONS

More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2006

Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 31 2006

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Last modified December 19 21:04 EST 2009. Contains 171054 sequences.


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