|
%I #20 Jan 18 2024 07:47:43
%S 1,3,6,12,28,88,444,3671,47981,976631,29554002,1326494644
%N In the MIU formal system, total number (including duplicates) of strings up to n steps distant from the MI string.
%C See A368946 for the description of the MIU formal system.
%D Douglas R. Hofstadter, Gödel, Escher, Bach: an Eternal Golden Braid, Basic Books, 1979, pp. 33-41.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/MU_puzzle">MU Puzzle</a>.
%H <a href="/index/Go#GEB">Index entries for sequences from "Goedel, Escher, Bach"</a>.
%F a(n) >= A331536(n+1).
%t MIUStepW3[s_] := Flatten[Map[{If[StringEndsQ[#, "1"], # <> "0", Nothing], # <> #, StringReplaceList[#, {"111" -> "0", "00" -> ""}]}&, s]];
%t With[{rowmax = 9}, Accumulate[Map[Length, NestList[MIUStepW3, {"1"}, rowmax]]]]
%Y Cf. A331536 (without duplicates), A368946, A369173 (all MIU strings).
%Y Partial sums of A368947.
%K nonn,hard,more
%O 0,2
%A _Paolo Xausa_, Jan 14 2024
|
