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.

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.

Index entries for sequences from "Goedel, Escher, Bach".

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

Adjacent sequences: A369176 A369177 A369178 * A369180 A369181 A369182

Keyword

nonn,base,tabf,easy

Author

Paolo Xausa, Jan 16 2024

Status

approved