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.

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

Author

Paolo Xausa, Jan 15 2024

Keywords

• nonn
• base
• tabf
• easy

Comments

See A368946 for the description of the MIU formal system and A369173 for the triangle of the corresponding derivable strings.

Examples

			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;
  ...
		

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".

Crossrefs

Cf. A024495 (row lengths), A055641, A368946, A369173, A369179 (number of ones).

Programs

Mathematica

A369174row[n_] := n - 1 - Select[Map[Count[#, 1]&, Tuples[{0, 1}, n - 1]], !Divisible[#, 3]&]; Array[A369174row, 6, 2]

Formula

T(n,k) = A055641(A369173(n,k)).

T(n,k) = n - 1 - A369179(n,k).