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 A334301 #13 May 31 2020 07:09:36
%S A334301 1,2,1,1,3,2,1,1,1,1,4,2,2,3,1,2,1,1,1,1,1,1,5,3,2,4,1,2,2,1,3,1,1,2,
%T A334301 1,1,1,1,1,1,1,1,6,3,3,4,2,5,1,2,2,2,3,2,1,4,1,1,2,2,1,1,3,1,1,1,2,1,
%U A334301 1,1,1,1,1,1,1,1,1,7,4,3,5,2,6,1,3,2,2
%N A334301 Irregular triangle read by rows where row k is the k-th integer partition, if partitions are sorted first by sum, then by length, and finally lexicographically.
%C A334301 This is the Abramowitz-Stegun ordering of integer partitions when they are read in the usual (weakly decreasing) order. The case of reversed (weakly increasing) partitions is A036036.
%H A334301 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e A334301 The sequence of all partitions in Abramowitz-Stegun order begins:
%e A334301 () (41) (21111) (31111) (3221)
%e A334301 (1) (221) (111111) (211111) (3311)
%e A334301 (2) (311) (7) (1111111) (4211)
%e A334301 (11) (2111) (43) (8) (5111)
%e A334301 (3) (11111) (52) (44) (22211)
%e A334301 (21) (6) (61) (53) (32111)
%e A334301 (111) (33) (322) (62) (41111)
%e A334301 (4) (42) (331) (71) (221111)
%e A334301 (22) (51) (421) (332) (311111)
%e A334301 (31) (222) (511) (422) (2111111)
%e A334301 (211) (321) (2221) (431) (11111111)
%e A334301 (1111) (411) (3211) (521) (9)
%e A334301 (5) (2211) (4111) (611) (54)
%e A334301 (32) (3111) (22111) (2222) (63)
%e A334301 This sequence can also be interpreted as the following triangle, whose n-th row is itself a finite triangle with A000041(n) rows.
%e A334301 0
%e A334301 (1)
%e A334301 (2) (1,1)
%e A334301 (3) (2,1) (1,1,1)
%e A334301 (4) (2,2) (3,1) (2,1,1) (1,1,1,1)
%e A334301 (5) (3,2) (4,1) (2,2,1) (3,1,1) (2,1,1,1) (1,1,1,1,1)
%e A334301 Showing partitions as their Heinz numbers (see A334433) gives:
%e A334301 1
%e A334301 2
%e A334301 3 4
%e A334301 5 6 8
%e A334301 7 9 10 12 16
%e A334301 11 15 14 18 20 24 32
%e A334301 13 25 21 22 27 30 28 36 40 48 64
%e A334301 17 35 33 26 45 50 42 44 54 60 56 72 80 96 128
%t A334301 Join@@Table[Sort[IntegerPartitions[n]],{n,0,8}]
%Y A334301 Lexicographically ordered reversed partitions are A026791.
%Y A334301 The version for reversed partitions (sum/length/lex) is A036036.
%Y A334301 Row lengths are A036043.
%Y A334301 Reverse-lexicographically ordered partitions are A080577.
%Y A334301 The version for compositions is A124734.
%Y A334301 Lexicographically ordered partitions are A193073.
%Y A334301 Sorting by Heinz number gives A296150, or A112798 for reversed partitions.
%Y A334301 Sorting first by sum, then by Heinz number gives A215366.
%Y A334301 Reversed partitions under the dual ordering (sum/length/revlex) are A334302.
%Y A334301 Taking Heinz numbers gives A334433.
%Y A334301 The reverse-lexicographic version is A334439 (not A036037).
%Y A334301 Cf. A000041, A048793, A066099, A162247, A211992, A228100, A228351, A228531.
%K A334301 nonn,tabf
%O A334301 0,2
%A A334301 _Gus Wiseman_, Apr 29 2020