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A296978 List of normal sequences ordered first by length and then lexicographically, where a finite sequence is normal if it spans an initial interval of positive integers.

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%I A296978 #7 Dec 28 2017 21:36:29
%S A296978 1,1,1,1,2,2,1,1,1,1,1,1,2,1,2,1,1,2,2,1,2,3,1,3,2,2,1,1,2,1,2,2,1,3,
%T A296978 2,2,1,2,3,1,3,1,2,3,2,1,1,1,1,1,1,1,1,2,1,1,2,1,1,1,2,2,1,1,2,3,1,1,
%U A296978 3,2,1,2,1,1,1,2,1,2,1,2,1,3,1,2,2,1,1
%N A296978 List of normal sequences ordered first by length and then lexicographically, where a finite sequence is normal if it spans an initial interval of positive integers.
%F A296978 Row n is formed by A000670(n) sequences and has total length n * A000670(n).
%e A296978 Triangle of normal sequences begins:
%e A296978 1,
%e A296978 11,12,21,
%e A296978 111,112,121,122,123,132,211,212,213,221,231,312,321.
%t A296978 normseqs[n_]:=Union@@Permutations/@Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];
%t A296978 Array[normseqs,5,1,Join]
%Y A296978 Cf. A000670, A095684, A124734, A228369, A296772, A296975, A296976, A296977.
%K A296978 nonn,tabf
%O A296978 1,5
%A A296978 _Gus Wiseman_, Dec 22 2017