This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A335465 #13 Jun 29 2020 17:10:48 %S A335465 1,3,3,3,3,3,3,3,3,3,3,4,3,12,4,3,3,3,3,4,3,4,12,4,3,12,4,12,4,12,4,3, %T A335465 3,3,3,4,3,3,6,4,3,6,3,3,6,10,10,4,3,12,6,12,3,10,10,12,4,12,3,12,4, %U A335465 12,4,3,3,3,3,4,3,3,6 %N A335465 Number of minimal normal patterns avoided by the n-th composition in standard order (A066099). %C A335465 These patterns comprise the basis of the class of patterns generated by this composition. %C A335465 We define a (normal) 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). %C A335465 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. %H A335465 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation_pattern">Permutation pattern</a> %H A335465 Gus Wiseman, <a href="https://oeis.org/A102726/a102726.txt">Sequences counting and ranking compositions by the patterns they match or avoid.</a> %H A335465 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 A335465 The bases of classes generated by (), (1), (2,1,1), (3,1,2), (2,1,2,1), and (1,2,1), corresponding to n = 0, 1, 11, 38, 45, 13, are the respective columns below. %e A335465 (1) (1,1) (1,2) (1,1) (1,1,1) (1,1,1) %e A335465 (1,2) (1,1,1) (1,2,3) (1,1,2) (1,1,2) %e A335465 (2,1) (2,2,1) (1,3,2) (1,2,2) (1,2,2) %e A335465 (3,2,1) (2,1,3) (1,2,3) (1,2,3) %e A335465 (2,3,1) (1,3,2) (1,3,2) %e A335465 (3,2,1) (2,1,3) (2,1,1) %e A335465 (2,3,1) (2,1,2) %e A335465 (3,1,2) (2,1,3) %e A335465 (3,2,1) (2,2,1) %e A335465 (2,2,1,1) (2,3,1) %e A335465 (3,1,2) %e A335465 (3,2,1) %Y A335465 Patterns matched by standard compositions are counted by A335454. %Y A335465 Patterns matched by compositions of n are counted by A335456(n). %Y A335465 The version for Heinz numbers of partitions is A335550. %Y A335465 Patterns are counted by A000670 and ranked by A333217. %Y A335465 Knapsack compositions are counted by A325676 and ranked by A333223. %Y A335465 The n-th composition has A334299(n) distinct subsequences. %Y A335465 Cf. A056986, A124767, A124770, A124771, A269134, A333218, A333257, A335549. %K A335465 nonn,more %O A335465 0,2 %A A335465 _Gus Wiseman_, Jun 20 2020