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Search: id:A006355
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| A006355 |
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Number of binary vectors of length n containing no singletons. |
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+0
21
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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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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 (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
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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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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 (pbarry(AT)wit.ie), May 04 2005
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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); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 18 2008]
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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.
Adjacent sequences: A006352 A006353 A006354 this_sequence A006356 A006357 A006358
Sequence in context: A139582 A034410 A050194 this_sequence A055389 A084202 A053637
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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 (reinhard.zumkeller(AT)gmail.com), May 20 2006
Corrected by T. D. Noe (noe(AT)sspectra.com), Oct 31 2006
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