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 A036043 Irregular triangle read by rows: row n (n >= 0) gives number of parts in all partitions of n (in Abramowitz and Stegun order). 48
 0, 1, 1, 2, 1, 2, 3, 1, 2, 2, 3, 4, 1, 2, 2, 3, 3, 4, 5, 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 7, 8, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The sequence of row lengths of this array is p(n) = A000041(n) (partition numbers). The sequence of row sums is A006128(n). The number of times k appears in row n is A008284(n,k). - Franklin T. Adams-Watters, Jan 12 2006 The next level (row) gets created from each node by adding one or two more nodes. If a single node is added, its value is one more than the value of its parent. If two nodes are added, the first is equal in value to the parent and the value of the second is one more than the value of the parent. See A128628. - Alford Arnold, Mar 27 2007 The 1's in the (flattened) sequence mark the start of a new row, the value that precedes the 1 equals the row number minus one. (I.e., the 1 preceded by a 0 is the start of row 1, the 1 preceded by a 6 is the start of row 7, etc.) - M. F. Hasler, Jun 06 2018 Also the maximum part in the n-th partition in graded lexicographic order (sum/lex, A193073). - Gus Wiseman, May 24 2020 REFERENCES Abramowitz and Stegun, Handbook, p. 831, column labeled "m". LINKS M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy], p. 831. Kevin Brown, Generalized Birthday Problem (N Items in M Bins), 1994-2010. Wolfdieter Lang, Rows n = 1 ..20. OEIS Wiki, Orderings of partitions Wikiversity, Lexicographic and colexicographic order FORMULA a(n) = A001222(A334433(n)). - Gus Wiseman, May 22 2020 EXAMPLE 0; 1; 1, 2; 1, 2, 3; 1, 2, 2, 3, 4; 1, 2, 2, 3, 3, 4, 5; 1, 2, 2, 2, 3, 3, 3, 4, 4, 5, 6; 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7; MAPLE with(combinat): nmax:=9: for n from 1 to nmax do y(n):=numbpart(n): P(n):=sort(partition(n)): for k from 1 to y(n) do B(k) := P(n)[k] od: for k from 1 to y(n) do s:=0: j:=0: while s

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Last modified December 9 18:21 EST 2022. Contains 358703 sequences. (Running on oeis4.)