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

1,5

Links

Table of n, a(n) for n=1..87.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A025453 A094215 A329040 * A236000 A114139 A195679

Adjacent sequences: A296975 A296976 A296977 * A296979 A296980 A296981

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 22 2017

Status

approved