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%I M1044 #51 Apr 13 2022 13:25:17
%S 1,1,1,1,2,4,7,11,16,23,34,52,81,126,194,296,450,685,1046,1601,2452,
%T 3753,5739,8771,13404,20489,31327,47904,73252,112004,171245,261813,
%U 400285,612009,935737,1430710,2187496,3344567,5113647,7818464,11953991,18277014
%N Number of binary words not containing ..01110...
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H R. Austin and R. K. Guy, <a href="http://www.fq.math.ca/Scanned/16-1/austin.pdf">Binary sequences without isolated ones</a>, Fib. Quart., 16 (1978), 84-86.
%H Russ Chamberlain, Sam Ginsburg and Chi Zhang, <a href="http://digital.library.wisc.edu/1793/61870">Generating Functions and Wilf-equivalence on Theta_k-embeddings</a>, University of Wisconsin, April 2012.
%H R. K. Guy, <a href="/A005251/a005251_1.pdf">Anyone for Twopins?</a>, in D. A. Klarner, editor, The Mathematical Gardner. Prindle, Weber and Schmidt, Boston, 1981, pp. 2-15. [Annotated scanned copy, with permission]
%H V. C. Harris, C. C. Styles, <a href="http://www.fq.math.ca/Scanned/2-4/harris.pdf">A generalization of Fibonacci numbers</a>, Fib. Quart. 2 (1964) 277-289, sequence u(n,3,2).
%H Milan Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Janjic/janjic73.html">Binomial Coefficients and Enumeration of Restricted Words</a>, Journal of Integer Sequences, 2016, Vol 19, #16.7.3
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=425">Encyclopedia of Combinatorial Structures 425</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1).
%F G.f.: (1-x+x^4)/(1-2x+x^2-x^5). - _Simon Plouffe_ in his 1992 dissertation.
%F a(n-1) = Sum{k=0..floor(n/5)} binomial(n-3k, 2k). - _Paul Barry_, Sep 16 2004
%t LinearRecurrence[{2,-1,0,0,1},{1,1,1,1,2},50] (* _Harvey P. Dale_, Mar 14 2018 *)
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_.
%E More terms from _Harvey P. Dale_, Mar 14 2018
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