A358525 Number of distinct permutations of the n-th composition in standard order.

1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 3, 2, 3, 3, 1, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 1, 1, 2, 2, 3, 1, 6, 6, 4, 2, 6, 1, 6, 6, 6, 6, 5, 2, 3, 6, 4, 6, 6, 6, 5, 3, 4, 6, 5, 4, 5, 5, 1, 1, 2, 2, 3, 2, 6, 6, 4, 2, 3, 3, 12, 3, 12, 12, 5, 2, 6, 3, 12, 3, 4

Offset

0,6

Comments

The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

Links

Table of n, a(n) for n=0..85.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

Example

The a(45) = 6 permutations are: (2121), (2112), (2211), (1221), (1212), (1122).

Mathematica

stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Table[Length[Permutations[stc[n]]], {n, 0, 100}]

Crossrefs

See link for sequences related to standard compositions.

Positions of 1's are A272919.

Cf. A000120, A048896, A070939, A329395, A333766, A358371, A358372, A358379, A358505, A358507, A358508.

Sequence in context: A255350 A104482 A333632 * A209332 A020945 A231734

Adjacent sequences: A358522 A358523 A358524 * A358526 A358527 A358528

Keyword

nonn

Author

Gus Wiseman, Nov 21 2022

Status

approved