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

%I A214215 #12 Nov 22 2020 12:22:32
%S A214215 1,2,11,12,21,22,112,121,122,211,212,221,1121,1122,1211,1212,1221,
%T A214215 2112,2121,2122,2211,2212,11212,11221,12112,12122,12211,12212,21121,
%U A214215 21122,21211,21221,22112,22121,112122,112211,112212,121121,121122,121221,122112,122121
%N A214215 List of subwords (or factors) of the Thue-Morse "1,2"-word A001285.
%C A214215 The number of factors of length m is given by A005942(m).
%H A214215 Alois P. Heinz, <a href="/A214215/b214215.txt">Table of n, a(n) for n = 1..10200</a>
%p A214215 b:= proc(n) option remember; local r;
%p A214215       `if`(n=0, 1, `if`(n<4, 2*n, `if`(irem(n, 2, 'r')=0,
%p A214215        b(r)+b(r+1), 2*b(r+1))))
%p A214215     end:
%p A214215 m:= proc(n) option remember; local r;
%p A214215       `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, m(r), 3-m(r)))
%p A214215     end:
%p A214215 T:= proc(n) local k, s; s:={};
%p A214215       for k while nops(s)<b(n) do
%p A214215         s:= s union {parse(cat(seq(m(i), i=k..k+n-1)))}
%p A214215       od; sort([s[]])[]
%p A214215     end:
%p A214215 seq(T(n), n=1..10);  # _Alois P. Heinz_, Jul 19 2012
%t A214215 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]]]]];
%t A214215 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 A214215 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]];
%t A214215 Array[T, 10] // Flatten (* _Jean-François Alcover_, Nov 22 2020, after _Alois P. Heinz_ *)
%Y A214215 Cf. A001285, A010060, A005942.
%K A214215 nonn
%O A214215 1,2
%A A214215 _N. J. A. Sloane_, Jul 10 2012