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A320385 Number of partitions of n into distinct parts such that the successive differences of consecutive parts are decreasing, and first difference < first part. 7
1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 2, 3, 4, 3, 3, 5, 3, 5, 6, 4, 5, 7, 5, 7, 8, 6, 7, 10, 8, 9, 11, 8, 11, 13, 9, 13, 15, 12, 14, 17, 13, 16, 20, 15, 18, 22, 18, 21, 25, 20, 23, 27, 23, 28, 30, 26, 30, 34, 30, 33, 38, 31, 38, 43, 36, 42, 46, 42, 47, 50, 45, 50, 58, 51, 55 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..2000 (terms 0..300 from Seiichi Manyama)

EXAMPLE

There are a(29) = 10 such partitions of 29:

01: [29]

02: [10, 19]

03: [11, 18]

04: [12, 17]

05: [13, 16]

06: [14, 15]

07: [6, 10, 13]

08: [6, 11, 12]

09: [7, 10, 12]

10: [8, 10, 11]

There are a(30) = 8 such partitions of 30:

01: [30]

02: [11, 19]

03: [12, 18]

04: [13, 17]

05: [14, 16]

06: [6, 11, 13]

07: [7, 11, 12]

08: [4, 7, 9, 10]

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|

    ary << 0

    ary0 = (1..ary.size - 1).map{|i| ary[i - 1] - ary[i]}

    cnt += 1 if ary0.sort == ary0 && ary0.uniq == ary0

  }

  cnt

end

def A320385(n)

  (0..n).map{|i| f(i)}

end

p A320385(50)

CROSSREFS

Cf. A007294, A179254, A179255, A179269, A320382, A320387.

Sequence in context: A053280 A289122 A025832 * A112222 A112220 A185278

Adjacent sequences:  A320382 A320383 A320384 * A320386 A320387 A320388

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Oct 12 2018

STATUS

approved

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Last modified April 23 07:37 EDT 2021. Contains 343201 sequences. (Running on oeis4.)