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A369179 Irregular triangle read by rows: row n lists the number of I characters for each of the distinct derivable strings in the MIU formal system that are n characters long.

%I A369179 #29 Mar 04 2024 01:05:16
%S A369179 1,1,1,2,1,1,2,1,2,2,1,1,2,1,2,2,1,2,2,2,4,1,1,2,1,2,2,1,2,2,2,4,1,2,
%T A369179 2,2,4,2,4,4,4,5,1,1,2,1,2,2,1,2,2,2,4,1,2,2,2,4,2,4,4,4,5,1,2,2,2,4,
%U A369179 2,4,4,4,5,2,4,4,4,5,4,4,5,4,5,5
%N A369179 Irregular triangle read by rows: row n lists the number of I characters for each of the distinct derivable strings in the MIU formal system that are n characters long.
%C A369179 See A368946 for the description of the MIU formal system and A369173 for the triangle of the corresponding derivable strings.
%D A369179 Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
%H A369179 Paolo Xausa, <a href="/A369179/b369179.txt">Table of n, a(n) for n = 2..10922</a> (rows 2..14 of the triangle, flattened).
%H A369179 Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.
%H A369179 <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.
%F A369179 T(n,k) = A268643(A369173(n,k)).
%F A369179 T(n,k) = n - 1 - A369174(n,k).
%F A369179 T(n,k) mod 3 > 0.
%e A369179 Triangle begins:
%e A369179   [2] 1;
%e A369179   [3] 1 1 2;
%e A369179   [4] 1 1 2 1 2 2;
%e A369179   [5] 1 1 2 1 2 2 1 2 2 2 4;
%e A369179   [6] 1 1 2 1 2 2 1 2 2 2 4 1 2 2 2 4 2 4 4 4 5;
%e A369179   ...
%t A369179 A369179row[n_] := Select[Map[Count[#, 1]&, Tuples[{0, 1}, n - 1]], !Divisible[#, 3]&]; Array[A369179row, 6, 2]
%Y A369179 Cf. A024495 (row lengths), A268643, A368946, A369173, A369174 (number of zeros).
%K A369179 nonn,base,tabf,easy
%O A369179 2,4
%A A369179 _Paolo Xausa_, Jan 16 2024