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 A334439 Irregular triangle whose rows are all integer partitions sorted first by sum, then by length, and finally reverse-lexicographically. 43
 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 5, 4, 1, 3, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 1, 4, 2, 3, 3, 4, 1, 1, 3, 2, 1, 2, 2, 2, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 6, 1, 5, 2, 4, 3, 5, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First differs from A036037 for partitions of 9. Namely, this sequence has (5,2,2) before (4,4,1), while A036037 has (4,4,1) before (5,2,2). This is the Abramowitz-Stegun ordering of integer partitions (A334301) except that the finer order is reverse-lexicographic instead of lexicographic. The version for reversed partitions is A334302. LINKS Wikiversity, Lexicographic and colexicographic order EXAMPLE The sequence of all partitions begins: () (32) (21111) (22111) (4211) (63) (1) (311) (111111) (211111) (3311) (54) (2) (221) (7) (1111111) (3221) (711) (11) (2111) (61) (8) (2222) (621) (3) (11111) (52) (71) (41111) (531) (21) (6) (43) (62) (32111) (522) (111) (51) (511) (53) (22211) (441) (4) (42) (421) (44) (311111) (432) (31) (33) (331) (611) (221111) (333) (22) (411) (322) (521) (2111111) (6111) (211) (321) (4111) (431) (11111111) (5211) (1111) (222) (3211) (422) (9) (4311) (5) (3111) (2221) (332) (81) (4221) (41) (2211) (31111) (5111) (72) (3321) This sequence can also be interpreted as the following triangle, whose n-th row is itself a finite triangle with A000041(n) rows. 0 (1) (2)(11) (3)(21)(111) (4)(31)(22)(211)(1111) (5)(41)(32)(311)(221)(2111)(11111) Showing partitions as their Heinz numbers (see A334438) gives: 1 2 3 4 5 6 8 7 10 9 12 16 11 14 15 20 18 24 32 13 22 21 25 28 30 27 40 36 48 64 17 26 33 35 44 42 50 45 56 60 54 80 72 96 128 MATHEMATICA revlensort[f_, c_]:=If[Length[f]!=Length[c], Length[f]

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Last modified December 7 22:02 EST 2022. Contains 358671 sequences. (Running on oeis4.)