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A226107 Number of strict partitions of n with Cookie Monster number 2. 0
0, 0, 1, 1, 2, 3, 3, 4, 4, 6, 5, 7, 6, 9, 7, 10, 8, 12, 9, 13, 10, 15, 11, 16, 12, 18, 13, 19, 14, 21, 15, 22, 16, 24, 17, 25, 18, 27, 19, 28, 20, 30, 21, 31, 22, 33, 23, 34, 24, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Given a set of integers representing the number of cookies in jars, The Cookie Monster number is the minimum number of moves Cookie Monster must use to empty the jars when in one move he may choose any subset of jars and take the same number of cookies from each of those jars.

Partitions have Cookie Monster number 2 if either they have two distinct values, or they have three distinct values, where the largest value is the sum of the other two. These are the partitions of n into distinct numbers with Cookie Monster number 2.

LINKS

Table of n, a(n) for n=1..50.

L. M. Braswell and T. Khovanova, Cookie Monster Devours Naccis arXiv:1305.4305 [math.HO]

EXAMPLE

If there are 7 cookies, the total number of partitions is 15. 5 partitions of 7 are strict: (7), (1,6), (2,5), (3,4), (1,2,4). One of these partitions, (7), corresponds to Cookie Monster number 1 (it has one value). One of these partitions, (1,2,4), has Cookie Monster number 3 (it has three values and the largest is not the sum of the other two). The remaining 3 partitions, (1,6), (2,5) and (3,4) have Cookie Monster number 2, so a(7)= 3.

MATHEMATICA

Table[Length[

  Select[Union[Map[Union, IntegerPartitions[n]]],

   Total[#] ==

      n && (Length[#] ==

        2 || (Length[#] == 3 && #[[3]] == #[[1]] + #[[2]])) &]], {n, 50}]

CROSSREFS

A000041, A226084, A000009

Sequence in context: A266475 A205402 A322007 * A318283 A105677 A230476

Adjacent sequences:  A226104 A226105 A226106 * A226108 A226109 A226110

KEYWORD

nonn

AUTHOR

Leigh Marie Braswell and Tanya Khovanova, May 26 2013

STATUS

approved

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Last modified February 19 22:38 EST 2019. Contains 320328 sequences. (Running on oeis4.)