

A282166


a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings of length greater than 1, and every number different from its neighbors.


4



1, 3, 4, 7, 8, 12, 13, 17, 18, 22, 24, 28, 30, 35, 37, 42, 44, 49, 51, 56, 59
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OFFSET

1,2


COMMENTS

For example, [1,1] is not a valid sequence because 1 is selfadjacent; [1,2,3,1,2] is not valid because the substring [1,2] appears twice.


LINKS



EXAMPLE

a(1) = 1 via [1];
a(2) = 3 via [1,2];
a(3) = 4 via [1,2,1];
a(4) = 7 via [1,2,1,3];
a(5) = 8 via [1,2,1,3,1];
a(6) = 12 via [1,2,1,3,1,4];
a(7) = 13 via [1,2,1,3,1,4,1];
a(8) = 17 via [1,2,1,3,1,4,2,3];
a(9) = 18 via [1,2,1,3,2,3,1,4,1];
a(10) = 22 via [1,2,1,3,1,4,2,3,4,1];
a(11) = 24 via [1,2,1,3,2,3,1,4,1,5,1].


MATHEMATICA

Table[Module[{s = Select[Permutations[Range@ n  1, n], Length@ # > 1 &]}, Total@ First@ MinimalBy[#, Total] &@ DeleteCases[#, w_ /; Apply[Times, If[Length@ # > 0, Rest@ #, #] &@ Union@ Map[SequenceCount[w, #] &, s]] > 1] &@ Apply[Join, Map[MinimalBy[#, Total] &, Table[Select[Tuples[Range@ k, n], Function[w, Times @@ Boole@ {Length@ Union@ w == k, First@ #, If[n > 2, Xor @@ Rest@ #, True]} == 1 &@ Map[Length@ Split@ # == Length@ # &, {w, w[[1 ;; 1 ;; 2]], Rest[w][[1 ;; 1 ;; 2]]}]]], {k, n}]]]], {n, 7}] (* Michael De Vlieger, Mar 27 2017, Version 10 *)


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



