A344340 Number of knapsack partitions of n with largest part 6.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 1, 4, 4, 6, 5, 7, 3, 7, 4, 8, 6, 10, 2, 7, 6, 9, 6, 9, 2, 9, 5, 9, 7, 9, 2, 8, 7, 10, 5, 9, 3, 10, 6, 8, 7, 10, 3, 9, 6, 10, 6, 10, 4, 9, 6, 9, 8, 11, 1, 9, 7, 11, 7, 8, 3, 10, 7, 10, 6, 10, 2, 10, 8, 9, 6, 9, 4, 11, 5, 9, 7

Offset: 0

Author

Fausto A. C. Cariboni, May 15 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 (6,10,6,10,4,9,6,9,8,11,1,9,7,11,7,8,3,10,7,10,6,10,2,10,8,9,6,9,4,11,5,9,7,11,3,8,7,10,7,10,2,10,6,10,8,9,2,9,8,11,5,9,3,11,7,8,7,10,3,10) is repeated continuously starting at a(50).

Examples

			The initial values count the following partitions:
   6: (6)
   7: (6,1)
   8: (6,1,1)
   8: (6,2)
   9: (6,1,1,1)
   9: (6,2,1)
   9: (6,3)
		

Links

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

Crossrefs

Cf. A108917, A275972, A326017, A326034, A343321, A344310.