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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.
3
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, 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, 4, 2, 2, 2, 1, 4, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1
OFFSET
2,5
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) = A055641(A369173(n,k)).
T(n,k) = n - 1 - A369179(n,k).
EXAMPLE
Triangle begins:
[2] 0;
[3] 1 1 0;
[4] 2 2 1 2 1 1;
[5] 3 3 2 3 2 2 3 2 2 2 0;
[6] 4 4 3 4 3 3 4 3 3 3 1 4 3 3 3 1 3 1 1 1 0;
...
MATHEMATICA
A369174row[n_] := n - 1 - Select[Map[Count[#, 1]&, Tuples[{0, 1}, n - 1]], !Divisible[#, 3]&]; Array[A369174row, 6, 2]
CROSSREFS
Cf. A024495 (row lengths), A055641, A368946, A369173, A369179 (number of ones).
Sequence in context: A352942 A180312 A178819 * A355855 A046816 A352248
KEYWORD
nonn,base,tabf,easy
AUTHOR
Paolo Xausa, Jan 15 2024
STATUS
approved