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

Author

N. J. A. Sloane, Jul 10 2012

Keywords

• nonn

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

Crossrefs

Cf. A001285, A010060, A005942.

Programs

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)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 *)