A358525 - OEIS

%I #6 Nov 21 2022 22:01:49

%S 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,

%T 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,

%U 2,6,6,4,2,3,3,12,3,12,12,5,2,6,3,12,3,4

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

%C 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.

%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>

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

%t stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];

%t Table[Length[Permutations[stc[n]]],{n,0,100}]

%Y See link for sequences related to standard compositions.

%Y Positions of 1's are A272919.

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

%K nonn

%O 0,6

%A _Gus Wiseman_, Nov 21 2022