OFFSET
0,8
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. See also A000120, A059893, A070939, A114994, A225620.
LINKS
EXAMPLE
The 83rd composition in standard order is (2,3,1,1), with strong nonexcedances {3,4}, so a(83) = 2.
MATHEMATICA
stc[n_]:=Differences[Prepend[Join@@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
pa[y_]:=Length[Select[Range[Length[y]], #>y[[#]]&]];
Table[pa[stc[n]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 22 2022
STATUS
approved