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A005253 Number of binary words not containing ..01110...
(Formerly M1044)
4
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; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

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.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 425

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1).

FORMULA

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

MATHEMATICA

LinearRecurrence[{2, -1, 0, 0, 1}, {1, 1, 1, 1, 2}, 50] (* Harvey P. Dale, Mar 14 2018 *)

CROSSREFS

Sequence in context: A062433 A317910 A065095 * A212364 A320591 A129339

Adjacent sequences:  A005250 A005251 A005252 * A005254 A005255 A005256

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Harvey P. Dale, Mar 14 2018

STATUS

approved

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Last modified November 20 22:59 EST 2018. Contains 317427 sequences. (Running on oeis4.)