A369148 In the MIU formal system, total number (including duplicates) of strings up to n steps distant from the MI string.

1, 3, 6, 12, 28, 88, 444, 3671, 47981, 976631, 29554002, 1326494644

Offset: 0

Author

Paolo Xausa, Jan 14 2024

Keywords

• nonn
• hard
• more

Comments

See A368946 for the description of the MIU formal system.

References

• Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41.

Links

• Wikipedia, MU Puzzle.
• Index entries for sequences from "Goedel, Escher, Bach".

Crossrefs

Cf. A331536 (without duplicates), A368946, A369173 (all MIU strings).

Partial sums of A368947.

Programs

Mathematica

MIUStepW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, {"111" -> "0", "00" -> ""}]}&, s]];
With[{rowmax = 9}, Accumulate[Map[Length, NestList[MIUStepW3, {"1"}, rowmax]]]]

Formula

a(n) >= A331536(n+1).