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A369207 Irregular triangle read by rows: row n lists the number of I 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.

%I A369207 #18 Jan 18 2024 10:50:55
%S A369207 1,1,2,2,2,4,4,4,4,8,1,1,8,8,8,1,1,8,16,5,5,5,5,5,5,1,2,2,16,16,16,5,
%T A369207 5,5,5,2,2,1,16,5,5,5,5,5,5,16,32,13,13,13,13,13,13,13,13,13,13,13,13,
%U A369207 13,13,5,10,2,2,2,5,10,2,2,5,10,2,5,10,2,5,10,2,2,10,2,2,2,2,2,4,4
%N A369207 Irregular triangle read by rows: row n lists the number of I 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.
%C A369207 See A368946 for the description of the MIU formal system and the triangle of corresponding strings.
%D A369207 Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
%H A369207 Paolo Xausa, <a href="/A369207/b369207.txt">Table of n, a(n) for n = 0..3670</a> (rows 0..7 of the triangle, flattened).
%H A369207 Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.
%H A369207 <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.
%F A369207 T(n,k) = A268643(A368946(n,k)).
%F A369207 T(n,k) = A369172(n,k) - A369206(n,k) - 1.
%e A369207 Triangle begins:
%e A369207   [0] 1;
%e A369207   [1] 1 2;
%e A369207   [2] 2 2 4;
%e A369207   [3] 4 4 4 8 1 1;
%e A369207   [4] 8 8 8 1 1 8 16 5 5 5 5 5 5 1 2 2;
%e A369207   ...
%t A369207 MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];
%t A369207 With[{rowmax = 5}, Map[StringCount[#, "1"]&, NestList[MIUStepOW3, {"1"}, rowmax]]]
%Y A369207 Cf. A268643, A368946, A368947 (row lengths), A369172, A369206 (number of zeros).
%K A369207 nonn,base,tabf
%O A369207 0,3
%A A369207 _Paolo Xausa_, Jan 16 2024