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%I #9 Jun 30 2020 01:55:59
%S 21,43,45,53,73,85,86,87,91,93,107,109,117,146,147,149,153,165,169,
%T 171,172,173,174,175,181,182,183,187,189,201,213,214,215,219,221,235,
%U 237,245,273,277,293,294,295,297,299,301,306,307,309,313,325,329,331,333
%N Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,2,1).
%C 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.
%C We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H Gus Wiseman, <a href="/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%e The sequence of terms together with the corresponding compositions begins:
%e 21: (2,2,1)
%e 43: (2,2,1,1)
%e 45: (2,1,2,1)
%e 53: (1,2,2,1)
%e 73: (3,3,1)
%e 85: (2,2,2,1)
%e 86: (2,2,1,2)
%e 87: (2,2,1,1,1)
%e 91: (2,1,2,1,1)
%e 93: (2,1,1,2,1)
%e 107: (1,2,2,1,1)
%e 109: (1,2,1,2,1)
%e 117: (1,1,2,2,1)
%e 146: (3,3,2)
%e 147: (3,3,1,1)
%t stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t Select[Range[0,100],MatchQ[stc[#],{___,x_,___,x_,___,y_,___}/;x>y]&]
%Y The complement A335524 is the avoiding version.
%Y The (1,2,2)-matching version is A335475.
%Y Patterns matching this pattern are counted by A335509 (by length).
%Y Permutations of prime indices matching this pattern are counted by A335453.
%Y These compositions are counted by A335472 (by sum).
%Y Constant patterns are counted by A000005 and ranked by A272919.
%Y Permutations are counted by A000142 and ranked by A333218.
%Y Patterns are counted by A000670 and ranked by A333217.
%Y Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y Combinatory separations are counted by A269134.
%Y Patterns matched by standard compositions are counted by A335454.
%Y Minimal patterns avoided by a standard composition are counted by A335465.
%Y Cf. A034691, A056986, A108917, A114994, A238279, A333224, A333257, A335446, A335456, A335458.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jun 18 2020
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