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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
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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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Table of n, a(n) for n=0..41.
R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86.
Russ Chamberlain, Sam Ginsburg and Chi Zhang, Generating Functions and Wilf-equivalence on Theta_k-embeddings, University of Wisconsin, April 2012.
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]
V. C. Harris, C. C. Styles, A generalization of Fibonacci numbers, Fib. Quart. 2 (1964) 277-289, sequence u(n,3,2).
Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 425
Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1).
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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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Sequence in context: A062433 A317910 A065095 * A212364 A320591 A129339
Adjacent sequences: A005250 A005251 A005252 * A005254 A005255 A005256
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Harvey P. Dale, Mar 14 2018
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STATUS
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approved
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