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 A344089 #5 May 12 2021 06:43:57
%S A344089 1,2,3,1,2,4,1,3,5,2,3,1,4,6,2,4,1,5,1,2,3,7,3,4,2,5,1,6,1,2,4,8,3,5,
%T A344089 2,6,1,7,1,3,4,1,2,5,9,4,5,3,6,2,7,1,8,2,3,4,1,3,5,1,2,6,10,4,6,3,7,2,
%U A344089 8,1,9,2,3,5,1,4,5,1,3,6,1,2,7,1,2,3,4
%N A344089 Flattened tetrangle of reversed strict integer partitions, sorted first by length and then colexicographically.
%C A344089 First differs from the revlex (instead of colex) version for partitions of 12.
%C A344089 The zeroth row contains only the empty partition.
%C A344089 A tetrangle is a sequence of finite triangles.
%H A344089 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order"> Lexicographic and colexicographic order</a>
%e A344089 Tetrangle begins:
%e A344089 0: ()
%e A344089 1: (1)
%e A344089 2: (2)
%e A344089 3: (3)(12)
%e A344089 4: (4)(13)
%e A344089 5: (5)(23)(14)
%e A344089 6: (6)(24)(15)(123)
%e A344089 7: (7)(34)(25)(16)(124)
%e A344089 8: (8)(35)(26)(17)(134)(125)
%e A344089 9: (9)(45)(36)(27)(18)(234)(135)(126)
%t A344089 Table[Reverse/@Sort[Select[IntegerPartitions[n],UnsameQ@@#&]],{n,0,30}]
%Y A344089 Positions of first appearances are A015724 plus one.
%Y A344089 Taking lex instead of colex gives A026793 (non-reversed: A118457).
%Y A344089 Triangle sums are A066189.
%Y A344089 Reversing all partitions gives A344090.
%Y A344089 The non-strict version is A344091.
%Y A344089 A319247 sorts strict partitions by Heinz number.
%Y A344089 A329631 sorts reversed strict partitions by Heinz number.
%Y A344089 Cf. A005117, A014466, A209862, A325683, A325859.
%Y A344089 Partition/composition orderings: A026791, A026792, A036036, A036037, A048793, A066099, A080577, A112798, A124734, A162247, A193073, A211992, A228100, A228351, A228531, A246688, A272020, A299755, A296774, A304038, A334301, A334302, A334439, A334442, A335122, A339351, A344085, A344086, A344087, A344088, A344089.
%Y A344089 Partition/composition applications: A001793, A005183, A036043, A049085, A070939, A115623, A124736, A129129, A185974, A238966, A246867, A294648, A333483, A333484, A333485, A333486, A334433, A334434, A334435, A334436, A334437, A334438, A334440, A334441, A335123, A335124, A339195.
%K A344089 nonn,tabf
%O A344089 0,2
%A A344089 _Gus Wiseman_, May 12 2021