A344625 Number of knapsack partitions of n with largest part 9.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 11, 12, 1, 10, 7, 11, 10, 17, 12, 18, 16, 12, 15, 19, 13, 25, 20, 17, 22, 29, 6, 25, 20, 22, 20, 28, 16, 31, 21, 14, 23, 33, 15, 24, 22, 25, 28, 30, 8, 31, 20, 22, 22, 36, 16, 34, 26, 14, 23, 26, 22, 33, 25, 24

Offset

0,12

Comments

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

I computed terms a(n) for n = 0..50000 and the subsequence a(128)-a(2647) of length 2520 is repeated continuously.

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..3000

Example

The initial nonzero values count the following partitions:
   9: (9)
  10: (9,1)
  11: (9,1,1), (9,2)
  12: (9,1,1,1), (9,2,1), (9,3)

Crossrefs

Cf. A108917, A275972, A326017, A326034, A342684, A343321, A344310, A344340, A344412.

Sequence in context: A117851 A050679 A342684 * A158806 A184966 A018723

Adjacent sequences: A344622 A344623 A344624 * A344626 A344627 A344628

Keyword

nonn

Author

Fausto A. C. Cariboni, May 25 2021

Status

approved