cp's OEIS Frontend

A335523 Numbers k such that the k-th composition in standard order (A066099) avoids the pattern (2,1,1).

%I A335523 #11 Jun 30 2020 01:54:47
%S A335523 0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,17,18,20,21,22,24,25,26,28,29,
%T A335523 30,31,32,33,34,36,37,38,40,41,42,44,48,49,50,52,53,54,56,57,58,60,61,
%U A335523 62,63,64,65,66,68,69,70,72,73,76,80,81,82,84,85,86,88,90
%N A335523 Numbers k such that the k-th composition in standard order (A066099) avoids the pattern (2,1,1).
%C A335523 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 A335523 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 A335523 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335523 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H A335523 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%t A335523 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335523 Select[Range[0,100],!MatchQ[stc[#],{___,x_,___,y_,___,y_,___}/;x>y]&]
%Y A335523 Patterns avoiding this pattern are counted by A001710 (by length).
%Y A335523 Permutations of prime indices avoiding this pattern are counted by A335449.
%Y A335523 These compositions are counted by A335471 (by sum).
%Y A335523 The complement A335478 is the matching version.
%Y A335523 The (1,1,2)-avoiding version is A335522.
%Y A335523 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335523 Permutations are counted by A000142 and ranked by A333218.
%Y A335523 Patterns are counted by A000670 and ranked by A333217.
%Y A335523 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335523 Combinatory separations are counted by A269134.
%Y A335523 Patterns matched by standard compositions are counted by A335454.
%Y A335523 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335523 Cf. A034691, A056986, A108917, A114994, A238279, A333224, A333257, A335446, A335456, A335458.
%K A335523 nonn
%O A335523 1,3
%A A335523 _Gus Wiseman_, Jun 18 2020