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 A080576 #52 Sep 22 2023 07:57:05
%S A080576 1,1,1,2,1,1,1,1,2,3,1,1,1,1,1,1,2,2,2,1,3,4,1,1,1,1,1,1,1,1,2,1,2,2,
%T A080576 1,1,3,2,3,1,4,5,1,1,1,1,1,1,1,1,1,1,2,1,1,2,2,2,2,2,1,1,1,3,1,2,3,3,
%U A080576 3,1,1,4,2,4,1,5,6,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,2,2,1,2,2,2
%N A080576 Triangle in which n-th row lists all partitions of n, in graded reflected lexicographic order.
%C A080576 The graded reflected lexicographic ordering of the partitions is used by Maple. - _Daniel Forgues_, Jan 19 2011
%C A080576 Each partition here is the conjugate of the corresponding partition in Abramowitz and Stegun order (A036036). The partitions are in the reverse of the order of the partitions in Mathematica order (A080577). - _Franklin T. Adams-Watters_, Oct 18 2006
%C A080576 Reversing all partitions gives A193073 (the non-reflected version). The version for reversed (weakly increasing) partitions is A211992. Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036. - _Gus Wiseman_, May 20 2020
%C A080576 Also reversed integer partitions in colexicographic order, cf. A228531. - _Gus Wiseman_, May 31 2020
%H A080576 Alois P. Heinz, <a href="/A080576/b080576.txt">Rows n = 1..20, flattened</a>
%H A080576 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. (uses Flash)
%H A080576 A. M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>
%H A080576 Wikiversity, <a href="https://en.wikiversity.org/wiki/Lexicographic_and_colexicographic_order">Lexicographic and colexicographic order</a>
%e A080576 First five rows are:
%e A080576 [[1]]
%e A080576 [[1, 1], [2]]
%e A080576 [[1, 1, 1], [1, 2], [3]]
%e A080576 [[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4]]
%e A080576 [[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [1, 1, 3], [2, 3], [1, 4], [5]]
%e A080576 From _Gus Wiseman_, May 20 2020: (Start)
%e A080576 The sequence of all reversed partitions begins:
%e A080576 () (122) (15) (25)
%e A080576 (1) (113) (6) (16)
%e A080576 (11) (23) (1111111) (7)
%e A080576 (2) (14) (111112) (11111111)
%e A080576 (111) (5) (11122) (1111112)
%e A080576 (12) (111111) (1222) (111122)
%e A080576 (3) (11112) (11113) (11222)
%e A080576 (1111) (1122) (1123) (2222)
%e A080576 (112) (222) (223) (111113)
%e A080576 (22) (1113) (133) (11123)
%e A080576 (13) (123) (1114) (1223)
%e A080576 (4) (33) (124) (1133)
%e A080576 (11111) (114) (34) (233)
%e A080576 (1112) (24) (115) (11114)
%e A080576 (End)
%p A080576 with(combinat); partition(6);
%t A080576 row[n_] := Flatten[Reverse /@ Reverse[SplitBy[Reverse /@ IntegerPartitions[n], Length]], 1]; Array[row, 7] // Flatten (* _Jean-François Alcover_, Dec 05 2016 *)
%t A080576 lexsort[f_,c_]:=OrderedQ[PadRight[{f,c}]];
%t A080576 Reverse/@Join@@Table[Sort[IntegerPartitions[n],lexsort],{n,0,8}] (* _Gus Wiseman_, May 20 2020 *)
%Y A080576 See A080577 for the Mathematica (graded reverse lexicographic) ordering.
%Y A080576 See A036036 for the Hindenburg (graded reflected colexicographic) ordering (listed in the Abramowitz and Stegun Handbook).
%Y A080576 See A036037 for the graded colexicographic ordering.
%Y A080576 See A193073 for the graded lexicographic ordering. - _M. F. Hasler_, Jul 16 2011
%Y A080576 See A228100 for the Fenner-Loizou (binary tree) ordering.
%Y A080576 Row n has A000041(n) partitions.
%Y A080576 Taking colexicographic instead of lexicographic gives A026791.
%Y A080576 Lengths of these partitions appear to be A049085.
%Y A080576 Reversing all partitions gives A193073 (the non-reflected version).
%Y A080576 The version for reversed (weakly increasing) partitions is A211992.
%Y A080576 The generalization to compositions is A228525.
%Y A080576 The Heinz numbers of these partitions are A334434.
%Y A080576 Cf. A026791, A036037, A112798, A129129, A185974, A228351, A228531, A334301, A334302, A334433, A334437.
%K A080576 nonn,tabf
%O A080576 1,4
%A A080576 _N. J. A. Sloane_, Mar 23 2003
%E A080576 Edited by _Daniel Forgues_, Jan 21 2011