A342684 Number of knapsack partitions of n with largest part 8.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 11, 1, 8, 6, 10, 7, 13, 9, 15, 6, 12, 10, 15, 8, 18, 10, 17, 6, 17, 12, 17, 9, 18, 13, 22, 7, 19, 10, 19, 13, 20, 14, 24, 4, 20, 12, 19, 13, 23, 15, 21, 4, 20, 13, 23, 11, 23, 15, 20, 7, 20, 12, 22, 15, 24, 12, 22

Offset

0,11

Comments

An integer partition is knapsack if every distinct submultiset has a different sum.

I computed terms a(n) for n = 0..40000 and the subsequence a(98)-a(937) of length 840 is repeated continuously.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..1000

Example

The initial nonzero values count the following partitions:
   8: (8)
   9: (8,1)
  10: (8,1,1), (8,2)
  11: (8,1,1,1), (8,2,1), (8,3)

Crossrefs

Cf. A108917, A275972, A326034, A343321, A344310, A344340, A344412.

Sequence in context: A362851 A117851 A050679 * A344625 A158806 A184966

Adjacent sequences: A342681 A342682 A342683 * A342685 A342686 A342687

Keyword

nonn

Author

Fausto A. C. Cariboni, May 18 2021

Status

approved