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 A320382 Number of partitions of n into distinct parts such that the successive differences of consecutive parts are nonincreasing. 9
 1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 7, 8, 10, 10, 12, 16, 14, 16, 20, 20, 23, 27, 26, 29, 35, 34, 38, 44, 43, 48, 55, 53, 59, 68, 67, 74, 83, 79, 88, 100, 98, 106, 118, 117, 127, 142, 139, 149, 164, 165, 179, 192, 191, 206, 226, 224, 240, 260, 257, 277, 301, 299, 319, 344, 346 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Partitions into distinct parts (p(1), p(2), ..., p(m)) such that p(k-1) - p(k-2) >= p(k) - p(k-1) for all k >= 3. LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..1000 (terms 0..100 from Seiichi Manyama) EXAMPLE There are a(17) = 16 such partitions of 17: 01: [17] 02: [1, 16] 03: [2, 15] 04: [3, 14] 05: [4, 13] 06: [5, 12] 07: [6, 11] 08: [7, 10] 09: [1, 6, 10] 10: [8, 9] 11: [1, 7, 9] 12: [2, 6, 9] 13: [2, 7, 8] 14: [3, 6, 8] 15: [4, 6, 7] 16: [2, 4, 5, 6] There are a(18) = 20 such partitions of 18: 01: [18] 02: [1, 17] 03: [2, 16] 04: [3, 15] 05: [4, 14] 06: [5, 13] 07: [6, 12] 08: [7, 11] 09: [1, 6, 11] 10: [8, 10] 11: [1, 7, 10] 12: [2, 6, 10] 13: [1, 8, 9] 14: [2, 7, 9] 15: [3, 6, 9] 16: [3, 7, 8] 17: [4, 6, 8] 18: [5, 6, 7] 19: [1, 4, 6, 7] 20: [3, 4, 5, 6] PROG (Ruby) def partition(n, min, max)   return [[]] if n == 0   [max, n].min.downto(min).flat_map{|i| partition(n - i, min, i - 1).map{|rest| [i, *rest]}} end def f(n)   return 1 if n == 0   cnt = 0   partition(n, 1, n).each{|ary|     ary0 = (1..ary.size - 1).map{|i| ary[i - 1] - ary[i]}     cnt += 1 if ary0.sort == ary0   }   cnt end def A320382(n)   (0..n).map{|i| f(i)} end p A320382(50) CROSSREFS Cf. A179255, A320385. Sequence in context: A097920 A029042 A320470 * A259200 A153155 A225085 Adjacent sequences:  A320379 A320380 A320381 * A320383 A320384 A320385 KEYWORD nonn AUTHOR Seiichi Manyama, Oct 12 2018 STATUS approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)