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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.
3
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, 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, 2, 4, 4, 4, 5, 2, 4, 4, 4, 5, 4, 4, 5, 4, 5, 5
OFFSET
2,4
COMMENTS
See A368946 for the description of the MIU formal system and A369173 for the triangle of the corresponding derivable strings.
REFERENCES
Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41 and pp. 261-262.
LINKS
Paolo Xausa, Table of n, a(n) for n = 2..10922 (rows 2..14 of the triangle, flattened).
Wikipedia, MU Puzzle.
FORMULA
T(n,k) = A268643(A369173(n,k)).
T(n,k) = n - 1 - A369174(n,k).
T(n,k) mod 3 > 0.
EXAMPLE
Triangle begins:
[2] 1;
[3] 1 1 2;
[4] 1 1 2 1 2 2;
[5] 1 1 2 1 2 2 1 2 2 2 4;
[6] 1 1 2 1 2 2 1 2 2 2 4 1 2 2 2 4 2 4 4 4 5;
...
MATHEMATICA
A369179row[n_] := Select[Map[Count[#, 1]&, Tuples[{0, 1}, n - 1]], !Divisible[#, 3]&]; Array[A369179row, 6, 2]
CROSSREFS
Cf. A024495 (row lengths), A268643, A368946, A369173, A369174 (number of zeros).
Sequence in context: A109374 A079706 A250005 * A319907 A357112 A078703
KEYWORD
nonn,base,tabf,easy
AUTHOR
Paolo Xausa, Jan 16 2024
STATUS
approved