Search: id:A005253
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%I A005253 M1044
%S A005253 1,1,1,1,2,4,7,11,16,23,34,52,81,126,194,296,450,685,1046,1601,2452,3753,
%T A005253 5739,8771,13404,20489,31327,47904,73252,112004,171245,261813,400285
%N A005253 Number of binary words not containing ..01110...
%D A005253 R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. 
               Quart., 16 (1978), 84-86.
%D A005253 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005253 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005253 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005253 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=425">
               Encyclopedia of Combinatorial Structures 425</a>
%F A005253 G.f. : (1-x+x^4)/(1-2x+x^2-x^5); a(n-1)=sum{k=0..floor(n/5), binomial(n-3k, 
               2k)}. - Paul Barry (pbarry(AT)wit.ie), Sep 16 2004
%p A005253 A005253:=-(1-z+z**4)/(-1+2*z-z**2+z**5); [Conjectured by S. Plouffe in 
               his 1992 dissertation.]
%Y A005253 Sequence in context: A000601 A062433 A065095 this_sequence A129339 A011912 
               A063676
%Y A005253 Adjacent sequences: A005250 A005251 A005252 this_sequence A005254 A005255 
               A005256
%K A005253 nonn
%O A005253 0,5
%A A005253 N. J. A. Sloane (njas(AT)research.att.com).

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