Search: id:A007777
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%I A007777
%S A007777 1,2,4,6,10,14,20,24,30,36,44,48,60,60,62,72,82,88,96,112,120,120,136,
%T A007777 148,164,152,154,148,162,176,190,196,210,216,224,228,248,272,284,296,
%U A007777 300,296,320,332,356,356,376,400,416,380,382,376,382,356,374,392,410
%N A007777 Number of overlap-free binary words of length n.
%D A007777 J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. 
               Computer Sci., 307 (2003), 3-29.
%D A007777 J. Cassaigne, Counting overlap-free binary words, pp. 216-225 of STACS 
               '93, Lect. Notes Comput. Sci., Springer-Verlag, 1993.
%D A007777 J. Cassaigne, Motifs \'evitables et r\'egularit\'es dans les mots (Th\`ese 
               de Doctorat), Tech. Rep. LITP-TH 94-04, Institut Blaise Pascal, Paris, 
               1994.
%D A007777 Raphael M. Jungers, Vladimir Yu. Protasov and Vincent D. Blondel, Computing 
               the Growth of the Number of Overlap-Free Words with Spectra of Matrices, 
               in LATIN 2008: Theoretical Informatics, Lecture Notes in Computer 
               Science, Volume 4957/2008, [From N. J. A. Sloane, Jul 10 2009]
%H A007777 J.-P. Allouche and J. Shallit, <a href="http://www.lri.fr/~allouche/kreg2.ps">
               The Ring of k-regular Sequences, II</a>
%H A007777 J. Cassaigne, <a href="http://iml.univ-mrs.fr/~cassaign/publis/overlap.ps.gz">
               Counting overlap-free binary words</a>
%H A007777 K. Jarhumaki and J. Shallit, <a href="http://arXiv.org/abs/math.CO/0304095">
               Polynomial vs Exponential Growth in Repetition-Free Binary Words</
               a>
%H A007777 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               OverlapfreeWord.html">Link to a section of The World of Mathematics.</
               a>
%p A007777 delta:=linalg[matrix](4,4,[0,0,1,1,0,0,0,0,0,1,0,0,1,0,0,0]); iota:=linalg[matrix](4,
               4,[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0]); kappa:=linalg[matrix](4,4,[0,
               0,1,1,1,1,0,0,0,0,0,0,0,0,0,0]);
%p A007777 V:=proc(n) options remember: if n>7 and n mod 2 =1 then RETURN(evalm(kappa 
               &* V((n+1)/2) &* transpose(delta) + delta &* V((n+1)/2) &* transpose(kappa))) 
               elif n=5 then RETURN(linalg[matrix](4,4,[2,0,0,0,0,0,0,0,0,0,0,0,
               0,0,0,0])) elif n=7 then RETURN(linalg[matrix](4,4,[0,0,2,0,0,2,0,
               0,2,0,0,0,0,0,0,0])) else RETURN(linalg[matrix](4,4,0)) fi: end;
%p A007777 U:=proc(n) options remember: if n>7 and n mod 2 =1 then RETURN(evalm(iota 
               &* V((n+1)/2) &* transpose(delta) + delta &* V((n+1)/2) &* transpose(iota) 
               + (kappa+iota) &* U((n+1)/2) &* transpose(delta) + delta &* U((n+1)/
               2) &* transpose(kappa+iota))) elif n>7 and n mod 2 =0 then RETURN(evalm(iota 
               &* V(n/2) &* transpose(iota) + delta &* V(n/2+1) &* transpose(delta) 
               + (kappa+iota) &* U(n/2) &* transpose(kappa+iota) + delta &* U(n/
               2+1) &* transpose(delta))) elif n=4 then RETURN(linalg[matrix](4,
               4,[2,0,2,0,0,2,0,0,2,0,0,0,0,0,0,2])) elif n=5 then RETURN(linalg[matrix](4,
               4,[0,2,2,0,2,0,0,2,2,0,2,0,0,2,0,0])) elif n=6 then RETURN(linalg[matrix](4,
               4,[2,2,0,2,2,2,2,0,0,2,2,0,2,0,0,2])) elif n=7 then RETURN(linalg[matrix](4,
               4,[4,2,0,2,2,0,2,2,0,2,0,2,2,2,2,0])) fi: end;
%p A007777 a:=proc(n) if n<4 then RETURN([1,2,4,6][n+1]) else RETURN(add(add(U(n)[i,
               j],i=1..4),j=1..4)) fi: end; seq(a(n),n=0..100); (Pab Terr)
%Y A007777 Cf. A038952, A028445, A082379, A082380.
%Y A007777 Sequence in context: A036641 A062425 A121386 this_sequence A082379 A167379 
               A094589
%Y A007777 Adjacent sequences: A007774 A007775 A007776 this_sequence A007778 A007779 
               A007780
%K A007777 nonn,easy,nice
%O A007777 0,2
%A A007777 cassaign(AT)clipper.ens.fr (Julien Cassaigne)
%E A007777 More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 09 2005

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