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A005253 Number of binary words not containing ..01110...
(Formerly M1044)

%I M1044

%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="http://www.emis.ams.org/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="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 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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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)