The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A320388 Number of partitions of n into distinct parts such that the successive differences of consecutive parts are decreasing. 4
 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 8, 7, 9, 11, 10, 12, 15, 14, 16, 19, 18, 21, 25, 23, 26, 31, 29, 33, 38, 36, 40, 46, 44, 49, 56, 53, 58, 66, 64, 70, 77, 76, 82, 92, 89, 96, 106, 104, 113, 123, 120, 130, 142, 141, 149, 162, 160, 172, 186, 184, 195, 211, 210, 223, 238 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Partitions are usually written with parts in descending order, but the conditions are easier to check "visually" if written in ascending order. 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..2000 (terms 0..100 from Seiichi Manyama) EXAMPLE There are a(17) = 15 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] There are a(18) = 14 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: [8, 10]   10: [1, 7, 10]   11: [1, 8, 9]   12: [2, 7, 9]   13: [3, 7, 8]   14: [1, 4, 6, 7] 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 && ary0.uniq == ary0   }   cnt end def A320388(n)   (0..n).map{|i| f(i)} end p A320388(50) CROSSREFS Cf. A007294, A179254, A179255, A179269, A320382, A320385, A320387. Cf. A081489. Sequence in context: A241951 A084630 A325393 * A264396 A007360 A029144 Adjacent sequences:  A320385 A320386 A320387 * A320389 A320390 A320391 KEYWORD nonn AUTHOR Seiichi Manyama, Oct 12 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 5 18:37 EDT 2021. Contains 343573 sequences. (Running on oeis4.)