1,3

Mathematica in flatten a sequence truncates the nulls instead of making zeros

of them as I have been doing. I'm entering this code as it didn't come up in a search an appears to be interesting as a sequence that appears to be chaotic.

http://south.rotol.ramk.fi/keranen/ias2002/NewAbelianSquare-FreeDT0L-LanguagesOver4Letters.nb

S. Wolfram. A New Kind of Science. Wolfram Media, 2002.

Mathematica substitution code...see references: Mathematica section.

Triangular form with "nulls":

{{}},

{{0}, {1}, {2}},

{{0, 1}, {0, 2},

{1, 0}, {1, 2}, {2, 0}, {2, 1}},

{{0, 1, 0}, {0, 1, 2}, {0, 2, 0}, {0, 2, 1}, {1, 0, 1}, {1, 0, 2}, {1, 2,

0}, {1, 2, 1}, {2, 0, 1}, {2, 0, 2}, {2, 1, 0}, {2, 1, 2}},

{{0, 1,0, 2}, {0, 1, 2, 0}, {0, 1, 2, 1}, {0, 2,

0, 1}, {0, 2, 1, 0}, {0, 2, 1, 2}, {1, 0, 1, 2}, {1, 0, 2, 0}, {1,

0, 2, 1}, {1, 2, 0, 1}, {1, 2, 0, 2}, {1, 2,

1, 0}, {2, 0, 1, 0}, {2, 0, 1, 2}, {2, 0, 2, 1}, {2, 1, 0, 1}, {2,

1, 0, 2}, {2, 1, 2, 0}},

{{0, 1, 0, 2, 0}, {0, 1, 0, 2, 1}, {0, 1, 2, 0, 1}, {0, 1, 2, 0, 2}, {0, 1, 2, 1, 0}, {0, 2, 0,1, 0}, {0, 2, 0, 1, 2}, {0, 2, 1, 0, 1}, {0, 2, 1, 0,2}, {0, 2, 1, 2, 0}, {1, 0,1, 2, 0}, {1, 0, 1, 2, 1}, {1, 0, 2, 0, 1}, {1, 0, 2, 1, 0}, {1, 0, 2, 1, 2}, {1, 2, 0, 1, 0}, {1, 2, 0, 1, 2}, {1, 2, 0, 2, 1}, {1, 2, 1, 0, 1}, {1, 2, 1, 0, 2}, {2, 0,1, 0, 2}, {2, 0, 1, 2, 0}, {2, 0, 1, 2, 1}, {2, 0, 2,1, 0}, {2, 0, 2, 1, 2}, {2,1, 0, 1, 2}, {2, 1, 0, 2, 0}, {2, 1, 0, 2, 1}, {2, 1, 2, 0, 1}, {2, 1, 2, 0, 2}},

{{0, 1, 0, 2, 0, 1}, {0, 1, 0, 2, 1, 0}, {0, 1,0, 2, 1, 2}, {0, 1, 2, 0, 1, 0}, {0, 1, 2, 1, 0, 1}, {0, 2, 0, 1, 0, 2}, {0, 2, 0, 1, 2, 0}, {0, 2, 0, 1, 2, 1}, {0, 2, 1, 0, 2, 0}, {0, 2, 1, 2, 0, 2}, {1, 0, 1, 2, 0, 1}, {1, 0, 1, 2, 0, 2}, {1, 0, 1, 2, 1, 0}, {1, 0, 2, 0, 1, 0}, {1, 0, 2, 1, 0, 1}, {1, 2, 0, 1, 2, 1}, {1, 2, 0, 2, 1, 2}, {1, 2, 1, 0, 1, 2}, {1, 2, 1, 0, 2, 0}, {1, 2, 1, 0, 2, 1}, {2, 0, 1, 0, 2, 0}, {2, 0, 1, 2, 0, 2}, {2, 0, 2, 1, 0, 1}, {2, 0, 2, 1, 0, 2}, {2, 0, 2, 1, 2, 0}, {2, 1, 0, 1, 2, 1}, {2, 1, 0, 2, 1, 2}, {2, 1, 2, 0, 1, 0}, {2, 1, 2, 0, 1, 2}, {2, 1, 2, 0, 2, 1}}, {{0, 1, 0, 2, 0, 1, 0}, {0,1, 0, 2, 1, 0, 1}, {0, 1, 2, 1, 0, 1, 2}, {0, 2, 0, 1, 0, 2, 0}, {0, 2, 0, 1, 2, 0, 2}, {0, 2, 1, 2, 0, 2, 1}, {1, 0, 1, 2, 0, 1, 0}, {1, 0, 1, 2, 1, 0, 1}, {1,

0, 2, 0, 1, 0, 2}, {1, 2, 0, 2, 1, 2, 0}, {1, 2, 1, 0, 1, 2, 1}, {1, 2, 1, 0, 2, 1, 2}, {2, 0, 1, 0, 2, 0, 1}, {2, 0, 2,1, 0, 2, 0}, {2, 0, 2, 1, 2, 0, 2}, {2,1, 0, 1, 2, 1, 0}, {2, 1, 2, 0, 1, 2, 1}, {2, 1, 2, 0, 2, 1, 2}},

{}

Clear[a]; a = With[{n = 8, k = 3}, NestList[DeleteCases[Flatten[Map[Table[Append[ #, i - 1], {i, k}] &, # ], 1], {___, u__, v__} /; Sort[{u}] == Sort[{v}]] &, {{}}, n]]; Flatten[a]

Cf. A007413, A001285.

Sequence in context: A156667 A110914 A127505 this_sequence A086372 A089650 A085513

Adjacent sequences: A138033 A138034 A138035 this_sequence A138037 A138038 A138039

nonn,uned,tabf

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 02 2008