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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A320387 Number of partitions of n into distinct parts such that the successive differences of consecutive parts are nonincreasing, and first difference <= first part. 5
1, 1, 1, 2, 1, 2, 3, 2, 2, 4, 3, 4, 5, 3, 5, 7, 4, 7, 8, 6, 8, 11, 7, 9, 13, 9, 11, 16, 12, 15, 18, 13, 17, 20, 17, 21, 24, 19, 24, 30, 22, 28, 34, 26, 34, 38, 30, 37, 43, 37, 42, 48, 41, 50, 58, 48, 55, 64, 53, 64, 71, 59, 73, 81, 69, 79, 89, 79, 90, 101, 87, 100, 111 (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.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..300

EXAMPLE

There are a(29) = 15 such partitions of 29:

01: [29]

02: [10, 19]

03: [11, 18]

04: [12, 17]

05: [13, 16]

06: [14, 15]

07: [5, 10, 14]

08: [6, 10, 13]

09: [6, 11, 12]

10: [7, 10, 12]

11: [8, 10, 11]

12: [3, 6, 9, 11]

13: [5, 7, 8, 9]

14: [2, 4, 6, 8, 9]

15: [3, 5, 6, 7, 8]

There are a(30) = 18 such partitions of 30:

01: [30]

02: [10, 20]

03: [11, 19]

04: [12, 18]

05: [13, 17]

06: [14, 16]

07: [5, 10, 15]

08: [6, 10, 14]

09: [6, 11, 13]

10: [7, 10, 13]

11: [7, 11, 12]

12: [8, 10, 12]

13: [3, 6, 9, 12]

14: [9, 10, 11]

15: [4, 7, 9, 10]

16: [2, 4, 6, 8, 10]

17: [6, 7, 8, 9]

18: [4, 5, 6, 7, 8]

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

  }

  cnt

end

def A320387(n)

  (0..n).map{|i| f(i)}

end

p A320387(50)

CROSSREFS

Cf. A007294, A179254, A179255, A179269, A320382, A320385, A320388.

Sequence in context: A111725 A302257 A324748 * A304707 A112218 A172366

Adjacent sequences:  A320384 A320385 A320386 * A320388 A320389 A320390

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)