login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A179255 Number of partitions of n into distinct parts such that the successive differences of consecutive parts are nondecreasing. 10
1, 1, 1, 2, 2, 3, 4, 5, 5, 8, 9, 10, 13, 15, 16, 22, 24, 26, 33, 36, 39, 50, 54, 58, 70, 77, 83, 100, 109, 116, 137, 150, 159, 186, 202, 216, 249, 270, 288, 328, 355, 379, 428, 462, 491, 554, 597, 633, 707, 760, 807, 899, 964, 1020, 1127, 1211, 1282, 1412, 1512, 1596, 1750, 1873, 1976, 2160, 2305, 2434, 2652, 2826, 2978 (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

Joerg Arndt, Table of n, a(n) for n = 0..241

EXAMPLE

There are a(17) = 26 such partitions of 17:

01:  [ 1 2 3 4 7 ]

02:  [ 1 2 3 11 ]

03:  [ 1 2 4 10 ]  *

04:  [ 1 2 5 9 ]   *

05:  [ 1 2 14 ]   *

06:  [ 1 3 5 8 ]

07:  [ 1 3 13 ]   *

08:  [ 1 4 12 ]   *

09:  [ 1 5 11 ]   *

10:  [ 1 16 ]   *

11:  [ 2 3 4 8 ]

12:  [ 2 3 5 7 ]

13:  [ 2 3 12 ]   *

14:  [ 2 4 11 ]   *

15:  [ 2 5 10 ]   *

16:  [ 2 15 ]   *

17:  [ 3 4 10 ]   *

18:  [ 3 5 9 ]   *

19:  [ 3 14 ]   *

20:  [ 4 5 8 ]   *

21:  [ 4 13 ]   *

22:  [ 5 12 ]   *

23:  [ 6 11 ]   *

24:  [ 7 10 ]   *

25:  [ 8 9 ]   *

26:  [ 17 ]   *

The 21 partitions marked with * have strictly increasing differences, see the example for A179254.

- Joerg Arndt, Mar 31 2014

PROG

(Sage)

def A179255(n):

....has_nondecreasing_diffs = lambda x: min(differences(x, 2)) >= 0

....allowed = lambda x: len(x) < 3 or has_nondecreasing_diffs(x)

....return Partitions(n, max_slope=-1).filter(lambda x: allowed(x[::-1])).cardinality() # D. S. McNeil, Jan 06 2011

(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.reverse

  }

  cnt

end

def A179255(n)

  (0..n).map{|i| f(i)}

end

p A179255(50) # Seiichi Manyama, Oct 12 2018

CROSSREFS

Cf. A009994.

Cf. A179254 (strictly increasing differences), A179269, A007294.

Cf. A240026 (partitions with nondecreasing differences), A240027 (partitions with strictly increasing differences), A320382.

Sequence in context: A129306 A322077 A114094 * A324325 A318284 A241321

Adjacent sequences:  A179252 A179253 A179254 * A179256 A179257 A179258

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jan 05 2011

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 November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)