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A335468 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,1,2).

%I A335468 #8 Jun 30 2020 09:54:59
%S A335468 22,45,46,54,76,86,90,91,93,94,109,110,118,148,150,153,156,166,173,
%T A335468 174,178,180,181,182,183,186,187,189,190,204,214,218,219,221,222,237,
%U A335468 238,246,278,280,297,300,301,302,306,307,308,310,313,316,326,332,333,334
%N A335468 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,1,2).
%C A335468 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 A335468 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 A335468 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335468 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H A335468 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 A335468 The sequence together with the corresponding compositions begins:
%e A335468    22: (2,1,2)
%e A335468    45: (2,1,2,1)
%e A335468    46: (2,1,1,2)
%e A335468    54: (1,2,1,2)
%e A335468    76: (3,1,3)
%e A335468    86: (2,2,1,2)
%e A335468    90: (2,1,2,2)
%e A335468    91: (2,1,2,1,1)
%e A335468    93: (2,1,1,2,1)
%e A335468    94: (2,1,1,1,2)
%e A335468   109: (1,2,1,2,1)
%e A335468   110: (1,2,1,1,2)
%e A335468   118: (1,1,2,1,2)
%e A335468   148: (3,2,3)
%e A335468   150: (3,2,1,2)
%t A335468 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335468 Select[Range[0,100],MatchQ[stc[#],{___,x_,___,y_,___,x_,___}/;x>y]&];
%Y A335468 The complement A335469 is the avoiding version.
%Y A335468 The (1,2,1)-matching version is A335466.
%Y A335468 These compositions are counted by A335472.
%Y A335468 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335468 Permutations are counted by A000142 and ranked by A333218.
%Y A335468 Patterns are counted by A000670 and ranked by A333217.
%Y A335468 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335468 Combinatory separations are counted by A269134 and ranked by A334030.
%Y A335468 Patterns matched by standard compositions are counted by A335454.
%Y A335468 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335468 Cf. A034691, A056986, A108917, A114994, A238279, A333224, A333257, A335453, A335456, A335458, A335509.
%K A335468 nonn
%O A335468 1,1
%A A335468 _Gus Wiseman_, Jun 16 2020