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 A331581 Maximum part of the n-th integer partition in graded reverse-lexicographic order (A080577); a(1) = 0. 11
 0, 1, 2, 1, 3, 2, 1, 4, 3, 2, 2, 1, 5, 4, 3, 3, 2, 2, 1, 6, 5, 4, 4, 3, 3, 3, 2, 2, 2, 1, 7, 6, 5, 5, 4, 4, 4, 3, 3, 3, 3, 2, 2, 2, 1, 8, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1, 9, 8, 7, 7, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The first partition ranked by A080577 is (); there is no zeroth partition. LINKS OEIS Wiki, Orderings of partitions Wikiversity, Lexicographic and colexicographic order FORMULA a(n) = A061395(A129129(n - 1)). EXAMPLE The sequence of all partitions in graded reverse-lexicographic order begins as follows. The terms are the initial parts.   ()         (3,2)        (2,1,1,1,1)    (2,2,1,1,1)   (1)        (3,1,1)      (1,1,1,1,1,1)  (2,1,1,1,1,1)   (2)        (2,2,1)      (7)            (1,1,1,1,1,1,1)   (1,1)      (2,1,1,1)    (6,1)          (8)   (3)        (1,1,1,1,1)  (5,2)          (7,1)   (2,1)      (6)          (5,1,1)        (6,2)   (1,1,1)    (5,1)        (4,3)          (6,1,1)   (4)        (4,2)        (4,2,1)        (5,3)   (3,1)      (4,1,1)      (4,1,1,1)      (5,2,1)   (2,2)      (3,3)        (3,3,1)        (5,1,1,1)   (2,1,1)    (3,2,1)      (3,2,2)        (4,4)   (1,1,1,1)  (3,1,1,1)    (3,2,1,1)      (4,3,1)   (5)        (2,2,2)      (3,1,1,1,1)    (4,2,2)   (4,1)      (2,2,1,1)    (2,2,2,1)      (4,2,1,1) Triangle begins:   0   1   2 1   3 2 1   4 3 2 2 1   5 4 3 3 2 2 1   6 5 4 4 3 3 3 2 2 2 1   7 6 5 5 4 4 4 3 3 3 3 2 2 2 1   8 7 6 6 5 5 5 4 4 4 4 4 3 3 3 3 3 2 2 2 2 1 MATHEMATICA revlexsort[f_, c_]:=OrderedQ[PadRight[{c, f}]]; Prepend[First/@Join@@Table[Sort[IntegerPartitions[n], revlexsort], {n, 8}], 0] CROSSREFS Row lengths are A000041. Lexicographically ordered reversed partitions are A026791. Reverse-colexicographically ordered partitions are A026792. Reversed partitions in Abramowitz-Stegun order (sum/length/lex) are A036036. The version for compositions is A065120 or A333766. Reverse-lexicographically ordered partitions are A080577. Distinct parts of these partitions are counted by A115623. Lexicographically ordered partitions are A193073. Colexicographically ordered partitions are A211992. Lengths of these partitions are A238966. Cf. A036037, A048793, A063008, A066099, A129129, A185974, A228100, A228531, A334301, A334434, A334436, A334438. Sequence in context: A211230 A049085 A193173 * A227355 A226080 A167287 Adjacent sequences:  A331578 A331579 A331580 * A331582 A331583 A331584 KEYWORD nonn,tabf AUTHOR Gus Wiseman, May 08 2020 STATUS approved

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Last modified September 24 23:13 EDT 2020. Contains 337325 sequences. (Running on oeis4.)