cp's OEIS Frontend

A369206 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.

%I A369206 #20 Jan 18 2024 10:51:07
%S A369206 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 A369206 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 A369206 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,4,3,4,4
%N A369206 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 A369206 See A368946 for the description of the MIU formal system and the triangle of corresponding strings.
%D A369206 Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
%H A369206 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 A369206 Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.
%H A369206 <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.
%F A369206 T(n,k) = A055641(A368946(n,k)).
%F A369206 T(n,k) = A369172(n,k) - A369207(n,k) - 1.
%e A369206 Triangle begins:
%e A369206   [0] 0;
%e A369206   [1] 1 0;
%e A369206   [2] 2 1 0;
%e A369206   [3] 4 2 1 0 1 1;
%e A369206   [4] 8 4 2 2 2 1 0 1 1 1 1 1 1 2 2 2;
%e A369206   ...
%t A369206 MIUStepOW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, "111" -> "0"], StringReplaceList[#, "00" -> ""]}&, s]];
%t A369206 With[{rowmax = 5}, Map[StringCount[#, "0"]&, NestList[MIUStepOW3, {"1"}, rowmax]]]
%Y A369206 Cf. A055641, A368946, A368947 (row lengths), A369172, A369207 (number of ones).
%K A369206 nonn,base,tabf
%O A369206 0,4
%A A369206 _Paolo Xausa_, Jan 16 2024