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Search: id:A005253
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| A005253 |
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Number of binary words not containing ..01110...
(Formerly M1044)
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+0
4
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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
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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R. Austin and R. K. Guy, Binary sequences without isolated ones, Fib. Quart., 16 (1978), 84-86.
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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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 425
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FORMULA
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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
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MAPLE
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A005253:=-(1-z+z**4)/(-1+2*z-z**2+z**5); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A000601 A062433 A065095 this_sequence A129339 A011912 A063676
Adjacent sequences: A005250 A005251 A005252 this_sequence A005254 A005255 A005256
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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