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A357135
Take the k-th composition in standard order for each part k of the n-th composition in standard order; then concatenate.
10
1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1
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.
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
See link for sequences related to standard compositions.
Row n is the A357134(n)-th composition in standard order.
The version for Heinz numbers of partitions is A357139, cf. A003963.
Row sums are A357186, differences A357187.
Sequence in context: A193348 A263723 A354974 * A367987 A370077 A370080
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 26 2022
STATUS
approved