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

Author

Fausto A. C. Cariboni, May 25 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..50000 and the subsequence a(128)-a(2647) of length 2520 is repeated continuously.

Examples

			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)
		

Links

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

Crossrefs

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