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A005253
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Number of binary words not containing ..01110...
(Formerly M1044)
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5
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1, 1, 1, 1, 2, 4, 7, 11, 16, 23, 34, 52, 81, 126, 194, 296, 450, 685, 1046, 1601, 2452, 3753, 5739, 8771, 13404, 20489, 31327, 47904, 73252, 112004, 171245, 261813, 400285, 612009, 935737, 1430710, 2187496, 3344567, 5113647, 7818464, 11953991, 18277014
(list;
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listen;
history;
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OFFSET
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0,5
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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R. K. Guy, Anyone for Twopins?, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission]
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FORMULA
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G.f.: (1-x+x^4)/(1-2x+x^2-x^5). - Simon Plouffe in his 1992 dissertation.
a(n-1) = Sum{k=0..floor(n/5)} binomial(n-3k, 2k). - Paul Barry, Sep 16 2004
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MATHEMATICA
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LinearRecurrence[{2, -1, 0, 0, 1}, {1, 1, 1, 1, 2}, 50] (* Harvey P. Dale, Mar 14 2018 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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