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A369174 Irregular triangle read by rows: row n lists the number of U characters for each of the distinct derivable strings in the MIU formal system that are n characters long.

%I A369174 #32 Jan 18 2024 10:51:27
%S A369174 0,1,1,0,2,2,1,2,1,1,3,3,2,3,2,2,3,2,2,2,0,4,4,3,4,3,3,4,3,3,3,1,4,3,
%T A369174 3,3,1,3,1,1,1,0,5,5,4,5,4,4,5,4,4,4,2,5,4,4,4,2,4,2,2,2,1,5,4,4,4,2,
%U A369174 4,2,2,2,1,4,2,2,2,1,2,2,1,2,1,1
%N A369174 Irregular triangle read by rows: row n lists the number of U characters for each of the distinct derivable strings in the MIU formal system that are n characters long.
%C A369174 See A368946 for the description of the MIU formal system and A369173 for the triangle of the corresponding derivable strings.
%D A369174 Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
%H A369174 Paolo Xausa, <a href="/A369174/b369174.txt">Table of n, a(n) for n = 2..10922</a> (rows 2..14 of the triangle, flattened).
%H A369174 Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.
%H A369174 <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.
%F A369174 T(n,k) = A055641(A369173(n,k)).
%F A369174 T(n,k) = n - 1 - A369179(n,k).
%e A369174 Triangle begins:
%e A369174   [2] 0;
%e A369174   [3] 1 1 0;
%e A369174   [4] 2 2 1 2 1 1;
%e A369174   [5] 3 3 2 3 2 2 3 2 2 2 0;
%e A369174   [6] 4 4 3 4 3 3 4 3 3 3 1 4 3 3 3 1 3 1 1 1 0;
%e A369174   ...
%t A369174 A369174row[n_] := n - 1 - Select[Map[Count[#, 1]&, Tuples[{0, 1}, n - 1]], !Divisible[#, 3]&]; Array[A369174row, 6, 2]
%Y A369174 Cf. A024495 (row lengths), A055641, A368946, A369173, A369179 (number of ones).
%K A369174 nonn,base,tabf,easy
%O A369174 2,5
%A A369174 _Paolo Xausa_, Jan 15 2024