OFFSET
0,3
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
FORMULA
EXAMPLE
The terms together with their corresponding standard compositions begin:
0: ()
1: (1)
2: (2)
3: (1,1)
3: (1,1)
5: (2,1)
6: (1,2)
7: (1,1,1)
4: (3)
7: (1,1,1)
10: (2,2)
11: (2,1,1)
7: (1,1,1)
13: (1,2,1)
14: (1,1,2)
15: (1,1,1,1)
MATHEMATICA
stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
stcinv[q_]:=Total[2^(Accumulate[Reverse[q]])]/2;
Table[stcinv[Join@@stc/@stc[n]], {n, 0, 30}]
CROSSREFS
See link for sequences related to standard compositions.
The version for Heinz numbers of partitions is A003963.
The vertex-degrees are A048896.
The a(n)-th composition in standard order is row n of A357135.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 24 2022
STATUS
approved