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 A337460 #7 Feb 16 2025 08:34:00
%S A337460 22,38,44,70,76,88,134,140,148,152,176,262,268,276,280,296,304,352,
%T A337460 518,524,532,536,552,560,592,608,704,1030,1036,1044,1048,1064,1072,
%U A337460 1096,1104,1120,1184,1216,1408,2054,2060,2068,2072,2088,2096,2120,2128,2144,2192
%N A337460 Numbers k such that the k-th composition in standard order is a non-unimodal triple.
%C A337460 These are triples matching the pattern (2,1,2), (3,1,2), or (2,1,3).
%C A337460 A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence.
%C A337460 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 A337460 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnimodalSequence.html">Unimodal Sequence</a>
%H A337460 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vTCPiJVFUXN8IqfLlCXkgP15yrGWeRhFS4ozST5oA4Bl2PYS-XTA3sGsAEXvwW-B0ealpD8qnoxFqN3/pub">Statistics, classes, and transformations of standard compositions</a>
%F A337460 Intersection of A014311 and A335373.
%e A337460 The sequence together with the corresponding triples begins:
%e A337460 22: (2,1,2) 296: (3,2,4) 1048: (6,1,4)
%e A337460 38: (3,1,2) 304: (3,1,5) 1064: (5,2,4)
%e A337460 44: (2,1,3) 352: (2,1,6) 1072: (5,1,5)
%e A337460 70: (4,1,2) 518: (7,1,2) 1096: (4,3,4)
%e A337460 76: (3,1,3) 524: (6,1,3) 1104: (4,2,5)
%e A337460 88: (2,1,4) 532: (5,2,3) 1120: (4,1,6)
%e A337460 134: (5,1,2) 536: (5,1,4) 1184: (3,2,6)
%e A337460 140: (4,1,3) 552: (4,2,4) 1216: (3,1,7)
%e A337460 148: (3,2,3) 560: (4,1,5) 1408: (2,1,8)
%e A337460 152: (3,1,4) 592: (3,2,5) 2054: (9,1,2)
%e A337460 176: (2,1,5) 608: (3,1,6) 2060: (8,1,3)
%e A337460 262: (6,1,2) 704: (2,1,7) 2068: (7,2,3)
%e A337460 268: (5,1,3) 1030: (8,1,2) 2072: (7,1,4)
%e A337460 276: (4,2,3) 1036: (7,1,3) 2088: (6,2,4)
%e A337460 280: (4,1,4) 1044: (6,2,3) 2096: (6,1,5)
%t A337460 stc[n_]:=Differences[Prepend[Join@@Position[Reverse[IntegerDigits[n,2]],1],0]]//Reverse;
%t A337460 Select[Range[0,1000],Length[stc[#]]==3&&MatchQ[stc[#],{x_,y_,z_}/;x>y<z]&]
%Y A337460 A000212 counts unimodal triples.
%Y A337460 A000217(n - 2) counts 3-part compositions.
%Y A337460 A001399(n - 3) counts 3-part partitions.
%Y A337460 A001399(n - 6) counts 3-part strict partitions.
%Y A337460 A001399(n - 6)*2 counts non-unimodal 3-part strict compositions.
%Y A337460 A001399(n - 6)*4 counts unimodal 3-part strict compositions.
%Y A337460 A001399(n - 6)*6 counts 3-part strict compositions.
%Y A337460 A001523 counts unimodal compositions.
%Y A337460 A001840 counts non-unimodal triples.
%Y A337460 A059204 counts non-unimodal permutations.
%Y A337460 A115981 counts non-unimodal compositions.
%Y A337460 A328509 counts non-unimodal patterns.
%Y A337460 A337459 ranks unimodal triples.
%Y A337460 All of the following pertain to compositions in standard order (A066099):
%Y A337460 - Length is A000120.
%Y A337460 - Triples are A014311.
%Y A337460 - Sum is A070939.
%Y A337460 - Runs are counted by A124767.
%Y A337460 - Strict compositions are A233564.
%Y A337460 - Constant compositions are A272919.
%Y A337460 - Heinz number is A333219.
%Y A337460 - Non-unimodal compositions are A335373.
%Y A337460 - Non-co-unimodal compositions are A335374.
%Y A337460 - Strict triples are A337453.
%Y A337460 Cf. A007304, A014612, A069905, A072706, A156040, A211540, A227038, A332743, A337461, A337604.
%K A337460 nonn
%O A337460 1,1
%A A337460 _Gus Wiseman_, Sep 18 2020