OFFSET
0,2
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
Row n is the A357134(n)-th composition in standard order.
EXAMPLE
Triangle begins:
0:
1: 1
2: 2
3: 1 1
4: 1 1
5: 2 1
6: 1 2
7: 1 1 1
8: 3
9: 1 1 1
10: 2 2
11: 2 1 1
12: 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;
Join@@Table[Join@@stc/@stc[n], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 26 2022
STATUS
approved