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 A335479 Numbers k such that the k-th composition in standard order (A066099) matches the pattern (1,2,3). 12
 52, 104, 105, 108, 116, 180, 200, 208, 209, 210, 211, 212, 216, 217, 220, 232, 233, 236, 244, 308, 328, 360, 361, 364, 372, 400, 401, 404, 408, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 428, 432, 433, 434, 435, 436, 440, 441, 444, 456, 464, 465, 466 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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). LINKS Table of n, a(n) for n=1..52. Wikipedia, Permutation pattern Gus Wiseman, Sequences counting and ranking compositions by the patterns they match or avoid. Gus Wiseman, Statistics, classes, and transformations of standard compositions EXAMPLE The sequence of terms together with the corresponding compositions begins: 52: (1,2,3) 104: (1,2,4) 105: (1,2,3,1) 108: (1,2,1,3) 116: (1,1,2,3) 180: (2,1,2,3) 200: (1,3,4) 208: (1,2,5) 209: (1,2,4,1) 210: (1,2,3,2) 211: (1,2,3,1,1) 212: (1,2,2,3) 216: (1,2,1,4) 217: (1,2,1,3,1) 220: (1,2,1,1,3) MATHEMATICA stc[n_]:=Reverse[Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n, 2]], 1], 0]]]; Select[Range[0, 100], MatchQ[stc[#], {___, x_, ___, y_, ___, z_, ___}/; x

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Last modified July 12 14:24 EDT 2024. Contains 374251 sequences. (Running on oeis4.)