A344412 Number of knapsack partitions of n with largest part 7.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 1, 6, 5, 8, 7, 10, 8, 8, 9, 11, 8, 13, 11, 13, 5, 14, 8, 13, 10, 17, 12, 8, 10, 14, 13, 14, 12, 18, 3, 15, 11, 15, 14, 17, 12, 8, 12, 15, 13, 20, 12, 14, 5, 17, 15, 17, 10, 18, 14, 9, 13, 18, 13, 15, 15, 18, 5, 18, 11

Offset: 0

Author

Fausto A. C. Cariboni, May 17 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..25000 and the subsequence a(72)-a(491) of length 420 is repeated continuously.

Examples

			The initial nonzero values count the following partitions:
   7: (7)
   8: (7,1)
   9: (7,1,1), (7,2)
  10: (7,1,1,1), (7,2,1), (7,3)
		

Links

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

Crossrefs

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