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A369206
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Irregular triangle read by rows: row n lists the number of U characters for each of the strings of the MIU formal system at the n-th level of the tree generated by recursively applying the system rules, starting from the MI string.
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4
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0, 1, 0, 2, 1, 0, 4, 2, 1, 0, 1, 1, 8, 4, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 16, 8, 4, 3, 3, 3, 3, 4, 4, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 3, 4, 4
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OFFSET
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0,4
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COMMENTS
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See A368946 for the description of the MIU formal system and the triangle of corresponding strings.
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REFERENCES
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Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
[0] 0;
[1] 1 0;
[2] 2 1 0;
[3] 4 2 1 0 1 1;
[4] 8 4 2 2 2 1 0 1 1 1 1 1 1 2 2 2;
...
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MATHEMATICA
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MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];
With[{rowmax = 5}, Map[StringCount[#, "0"]&, NestList[MIUStepOW3, {"1"}, rowmax]]]
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CROSSREFS
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KEYWORD
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nonn,base,tabf
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AUTHOR
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STATUS
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approved
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