A369206 - OEIS

%I #20 Jan 18 2024 10:51:07

%S 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,

%T 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,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,3,4,4

%N 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.

%C See A368946 for the description of the MIU formal system and the triangle of corresponding strings.

%D Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.

%H Paolo Xausa, <a href="/A369206/b369206.txt">Table of n, a(n) for n = 0..3670</a> (rows 0..7 of the triangle, flattened).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.

%H <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.

%F T(n,k) = A055641(A368946(n,k)).

%F T(n,k) = A369172(n,k) - A369207(n,k) - 1.

%e Triangle begins:

%e   [0] 0;

%e   [1] 1 0;

%e   [2] 2 1 0;

%e   [3] 4 2 1 0 1 1;

%e   [4] 8 4 2 2 2 1 0 1 1 1 1 1 1 2 2 2;

%e   ...

%t MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];

%t With[{rowmax = 5}, Map[StringCount[#, "0"]&, NestList[MIUStepOW3, {"1"}, rowmax]]]

%Y Cf. A055641, A368946, A368947 (row lengths), A369172, A369207 (number of ones).

%K nonn,base,tabf

%O 0,4

%A _Paolo Xausa_, Jan 16 2024