OFFSET
1,1
COMMENTS
Also compositions matching the pattern (2,1).
A composition of n is a finite sequence of positive integers summing to n. 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
EXAMPLE
The sequence of terms together with the corresponding compositions begins:
5: (2,1)
9: (3,1)
11: (2,1,1)
13: (1,2,1)
17: (4,1)
18: (3,2)
19: (3,1,1)
21: (2,2,1)
22: (2,1,2)
23: (2,1,1,1)
25: (1,3,1)
27: (1,2,1,1)
29: (1,1,2,1)
33: (5,1)
34: (4,2)
35: (4,1,1)
MATHEMATICA
stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]];
Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___}/; x>y]&]
CROSSREFS
The complement A225620 is the avoiding version.
The (1,2)-matching version is A335485.
Patterns matching this pattern are counted by A002051 (by length).
Permutations of prime indices matching this pattern are counted by A008480(n) - 1.
These compositions are counted by A056823 (by sum).
Combinatory separations are counted by A269134.
Patterns matched by standard compositions are counted by A335454.
Minimal patterns avoided by a standard composition are counted by A335465.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 18 2020
STATUS
approved