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 A334440 Irregular triangle T(n,k) read by rows: row n lists numbers of distinct parts of the n-th integer partition in Abramowitz-Stegun (sum/length/lex) order. 15
 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 3, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 2, 1, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 3, 2, 2, 3, 3, 2, 2, 3, 3, 3, 3, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS The total number of parts, counting duplicates, is A036043. The version for reversed partitions is A103921. LINKS Robert Price, Table of n, a(n) for n = 0..9295 (25 rows). Wikiversity, Lexicographic and colexicographic order FORMULA a(n) = A001221(A334433(n)). EXAMPLE Triangle begins: 0 1 1 1 1 2 1 1 1 2 2 1 1 2 2 2 2 2 1 1 1 2 2 1 3 2 2 2 2 1 1 2 2 2 2 2 3 2 2 3 2 2 2 2 1 1 1 2 2 2 2 2 3 3 2 1 3 2 3 2 2 3 2 2 2 2 1 MATHEMATICA Join@@Table[Length/@Union/@Sort[IntegerPartitions[n]], {n, 0, 10}] CROSSREFS Row lengths are A000041. The number of not necessarily distinct parts is A036043. The version for reversed partitions is A103921. Ignoring length (sum/lex) gives A103921 (also). a(n) is the number of distinct elements in row n of A334301. The maximum part of the same partition is A334441. Lexicographically ordered reversed partitions are A026791. Reversed partitions in Abramowitz-Stegun (sum/length/lex) order are A036036. Partitions in increasing-length colex order (sum/length/colex) are A036037. Graded reverse-lexicographically ordered partitions are A080577. Partitions counted by sum and number of distinct parts are A116608. Graded lexicographically ordered partitions are A193073. Partitions in colexicographic order (sum/colex) are A211992. Partitions in dual Abramowitz-Stegun (sum/length/revlex) order are A334439. Cf. A001221, A049085, A124734, A185974, A296774, A299755, A334028, A334302, A334433, A334434, A334435, A334438. Sequence in context: A355241 A165190 A025890 * A316975 A043277 A265991 Adjacent sequences: A334437 A334438 A334439 * A334441 A334442 A334443 KEYWORD nonn,tabf AUTHOR Gus Wiseman, May 05 2020 STATUS approved

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