A214215 List of subwords (or factors) of the Thue-Morse "1,2"-word A001285.

1, 2, 11, 12, 21, 22, 112, 121, 122, 211, 212, 221, 1121, 1122, 1211, 1212, 1221, 2112, 2121, 2122, 2211, 2212, 11212, 11221, 12112, 12122, 12211, 12212, 21121, 21122, 21211, 21221, 22112, 22121, 112122, 112211, 112212, 121121, 121122, 121221, 122112, 122121

Offset

1,2

Comments

The number of factors of length m is given by A005942(m).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10200

Maple

b:= proc(n) option remember; local r;
      `if`(n=0, 1, `if`(n<4, 2*n, `if`(irem(n, 2, 'r')=0,
       b(r)+b(r+1), 2*b(r+1))))
    end:
m:= proc(n) option remember; local r;
      `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, m(r), 3-m(r)))
    end:
T:= proc(n) local k, s; s:={};
      for k while nops(s)<b(n) do
        s:= s union {parse(cat(seq(m(i), i=k..k+n-1)))}
      od; sort([s[]])[]
    end:
seq(T(n), n=1..10);  # Alois P. Heinz, Jul 19 2012

Mathematica

b[n_] := b[n] = Module[{r}, If[n == 0, 1, If[n < 4, 2n, r = Quotient[n, 2]; If[Mod[n, 2] == 0, b[r] + b[r + 1], 2b[r + 1]]]]];
m[n_] := m[n] = Module[{r}, If[n == 0, 1, r = Quotient[n, 2]; If[Mod[n, 2] == 0, m[r], 3 - m[r]]]];
T[n_] := Module[{k, s = {}}, For[k = 1,  Length[s] < b[n], k++, s = s  ~Union~ {FromDigits[#]}& @ Table[m[i], {i, k, k + n - 1}]]; Sort[s]];
Array[T, 10] // Flatten (* Jean-François Alcover, Nov 22 2020, after Alois P. Heinz *)

Crossrefs

Cf. A001285, A010060, A005942.

Sequence in context: A007931 A136407 A376677 * A376637 A136999 A271372

Adjacent sequences: A214212 A214213 A214214 * A214216 A214217 A214218

Keyword

nonn

Author

N. J. A. Sloane, Jul 10 2012

Status

approved