cp's OEIS Frontend

A335481 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,1,3).

%I A335481 #10 Jun 29 2020 22:12:03
%S A335481 44,88,89,92,108,152,172,176,177,178,179,180,184,185,188,216,217,220,
%T A335481 236,296,300,304,305,312,332,344,345,348,352,353,354,355,356,357,358,
%U A335481 359,360,361,364,368,369,370,371,372,376,377,380,408,428,432,433,434,435
%N A335481 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (2,1,3).
%C A335481 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 A335481 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 A335481 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a>
%H A335481 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a>
%H A335481 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 A335481 The sequence of terms together with the corresponding compositions begins:
%e A335481    44: (2,1,3)
%e A335481    88: (2,1,4)
%e A335481    89: (2,1,3,1)
%e A335481    92: (2,1,1,3)
%e A335481   108: (1,2,1,3)
%e A335481   152: (3,1,4)
%e A335481   172: (2,2,1,3)
%e A335481   176: (2,1,5)
%e A335481   177: (2,1,4,1)
%e A335481   178: (2,1,3,2)
%e A335481   179: (2,1,3,1,1)
%e A335481   180: (2,1,2,3)
%e A335481   184: (2,1,1,4)
%e A335481   185: (2,1,1,3,1)
%e A335481   188: (2,1,1,1,3)
%t A335481 stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]];
%t A335481 Select[Range[0,100],MatchQ[stc[#],{___,x_,___,y_,___,z_,___}/;y<x<z]&]
%Y A335481 The version counting permutations is A056986.
%Y A335481 Patterns matching this pattern are counted by A335515 (by length).
%Y A335481 Permutations of prime indices matching this pattern are counted by A335520.
%Y A335481 These compositions are counted by A335514 (by sum).
%Y A335481 Constant patterns are counted by A000005 and ranked by A272919.
%Y A335481 Permutations are counted by A000142 and ranked by A333218.
%Y A335481 Patterns are counted by A000670 and ranked by A333217.
%Y A335481 Non-unimodal compositions are counted by A115981 and ranked by A335373.
%Y A335481 Permutations matching (1,3,2,4) are counted by A158009.
%Y A335481 Combinatory separations are counted by A269134.
%Y A335481 Patterns matched by standard compositions are counted by A335454.
%Y A335481 Minimal patterns avoided by a standard composition are counted by A335465.
%Y A335481 Other permutations:
%Y A335481 - A335479 (1,2,3)
%Y A335481 - A335480 (1,3,2)
%Y A335481 - A335481 (2,1,3)
%Y A335481 - A335482 (2,3,1)
%Y A335481 - A335483 (3,1,2)
%Y A335481 - A335484 (3,2,1)
%Y A335481 Cf. A034691, A056986, A108917, A114994, A158005, A238279, A333224, A333257, A334968, A335456, A335458.
%K A335481 nonn
%O A335481 1,1
%A A335481 _Gus Wiseman_, Jun 18 2020