0,2

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

J. Cassaigne, Counting overlap-free binary words, pp. 216-225 of STACS '93, Lect. Notes Comput. Sci., Springer-Verlag, 1993.

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.

J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II

J. Cassaigne, Counting overlap-free binary words

K. Jarhumaki and J. Shallit, Polynomial vs Exponential Growth in Repetition-Free Binary Words

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

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]);

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;

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;

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)

Cf. A038952, A028445, A082379, A082380.

Adjacent sequences: A007774 A007775 A007776 this_sequence A007778 A007779 A007780

Sequence in context: A036641 A062425 A121386 this_sequence A082379 A094589 A071425

nonn,easy,nice

cassaign(AT)clipper.ens.fr (Julien Cassaigne)

More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 09 2005