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

0,2

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

Table of n, a(n) for n=0..11.

Wikipedia, MU Puzzle.

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

Formula

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

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]]]]

Crossrefs

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

Partial sums of A368947.

Sequence in context: A018011 A025208 A245774 * A049941 A219634 A252696

Adjacent sequences: A369145 A369146 A369147 * A369149 A369150 A369151

Keyword

nonn,hard,more

Author

Paolo Xausa, Jan 14 2024

Status

approved