A343321 Number of knapsack partitions of n with largest part 5.

0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 1, 4, 3, 5, 5, 4, 4, 6, 5, 7, 2, 6, 5, 8, 5, 4, 6, 7, 6, 8, 2, 8, 6, 7, 7, 5, 5, 8, 7, 8, 2, 8, 6, 9, 6, 3, 7, 9, 5, 8, 3, 8, 6, 8, 6, 5, 6, 7, 7, 9, 1, 8, 7, 8, 6, 4, 6, 9, 6, 7, 3, 9, 5, 8, 7, 4, 6, 8, 6, 9, 2, 7, 7, 9, 5, 4, 7

Offset

0,8

Comments

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

I computed terms a(n) for n = 0..10000 and (6,7,7,5,5,8,7,8,2,8,6,9,6,3,7,9,5,8,3,8,6,8,6,5,6,7,7,9,1,8,7,8,6,4,6,9,6,7,3,9,5,8,7,4,6,8,6,9,2,7,7,9,5,4,7,8,6,8,2,9) is repeated continuously starting at a(32).

Links

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

Example

The initial values count the following partitions:
   5: (5)
   6: (5,1)
   7: (5,1,1)
   7: (5,2)
   8: (5,1,1,1)
   8: (5,2,1)
   8: (5,3)

Crossrefs

Cf. A108917, A275972, A326017, A326034, A344310.

Sequence in context: A318308 A003324 A110630 * A238883 A363126 A363130

Adjacent sequences: A343318 A343319 A343320 * A343322 A343323 A343324

Keyword

nonn

Author

Fausto A. C. Cariboni, May 14 2021

Status

approved