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.

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, 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, 3, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 1, 1

Offset: 1

Author

Gus Wiseman, Dec 22 2017

Keywords

• nonn
• tabf

Examples

			Triangle of normal sequences begins:
1,
11,12,21,
111,112,121,122,123,132,211,212,213,221,231,312,321.
		

Crossrefs

Cf. A000670, A095684, A124734, A228369, A296772, A296975, A296976, A296977.

Programs

Mathematica

normseqs[n_]:=Union@@Permutations/@Function[s,Array[Count[s,y_/;y<=#]+1&,n]]/@Subsets[Range[n-1]+1];
Array[normseqs,5,1,Join]

Formula

Row n is formed by A000670(n) sequences and has total length n * A000670(n).