login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330257 Number of length-n ternary squarefree words having no occurrences of either 010 or 212. 3
1, 3, 6, 10, 14, 20, 24, 30, 36, 44, 48, 60, 60, 62, 72, 82, 88, 96, 112, 120, 120, 136, 148, 164, 152, 154, 148, 162, 176, 190, 196, 210, 216, 224, 228, 248, 272, 284, 296, 300, 296, 320, 332, 356, 356, 376, 400, 416, 380, 382, 376, 382, 356, 374, 392, 410 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

An example of such a word is A036577.

REFERENCES

A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Norske vid. Selsk. Skr. Mat. Nat. Kl. 1 (1912), 1-67. Reprinted in Selected Mathematical Papers of Axel Thue, T. Nagell, editor, Universitetsforlaget, Oslo, 1977, pp. 413-478.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1000

J. Berstel, Axel Thue's papers on repetitions in words: a translation, Publications du Laboratoire de Combinatoire et d'Informatique Mathématique, Vol. 20, Université du Québec à Montréal, February 1995.

MAPLE

filter:= proc(s) local n, j, cands;

  n:= length(s);

  if n >= 3 and (s[1..3] = "010" or s[1..3]="212") then return false fi;

  for j from 1 to min(n/2, 5) do

    if s[1..j] = s[j+1..2*j] then return false fi;

  od;

  if n >= 12 then

    cands:= select(j -> j > 1 and j <= ceil((1+n)/2), {StringTools:-SearchAll(s[1..6], s)});

    for j in cands do if s[1..j-1] = s[j..2*j-2] then return false fi       od;

  fi;

  true

end proc:

S[0]:= {""}:

for n from 1 to 100 do

  S[n]:= select(filter, map(t -> (cat("0", t), cat("1", t), cat("2", t)), S[n-1]));

od:

seq(nops(S[i]), i=0..100); # Robert Israel, Dec 10 2019

CROSSREFS

Cf. A036577, A330258, A330259.

Sequence in context: A310071 A330259 A024928 * A079552 A334454 A236758

Adjacent sequences:  A330254 A330255 A330256 * A330258 A330259 A330260

KEYWORD

nonn,look

AUTHOR

Jeffrey Shallit, Dec 07 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)