A344310 Number of knapsack partitions of n with largest part 4.

0, 0, 0, 0, 1, 1, 2, 3, 1, 2, 3, 3, 1, 3, 3, 3, 2, 3, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4

Offset: 0

Author

Fausto A. C. Cariboni, May 14 2021

Keywords

• nonn

Comments

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

I computed terms a(n) for n = 0..10000 and (3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4) is repeated continuously starting at a(18).

Examples

			The initial values count the following partitions:
   4: (4)
   5: (4,1)
   6: (4,1,1)
   6: (4,2)
   7: (4,1,1,1)
   7: (4,2,1)
   7: (4,3)
   8: (4,4)
		

Crossrefs

Cf. A108917, A275972, A326017, A326034, A343321.