A344635 Number of knapsack partitions of n with largest part 10.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 11, 12, 17, 1, 13, 9, 16, 11, 20, 14, 24, 16, 25, 9, 27, 14, 29, 19, 32, 16, 34, 19, 37, 11, 32, 17, 38, 19, 32, 22, 41, 19, 40, 14, 38, 22, 41, 22, 39, 18, 44, 26, 46, 8, 46, 24, 38, 23, 40, 21, 48, 28, 42, 12

Offset

0,13

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(162)-a(2681) of length 2520 is repeated continuously.

Links

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

Example

The initial nonzero values count the following partitions:
  10: (10)
  11: (10,1)
  12: (10,1,1), (10,2)
  13: (10,1,1,1), (10,2,1), (10,3)

Crossrefs

Cf. A108917, A275972, A326017, A326034, A342684, A343321, A344310, A344340, A344412, A344625.

Sequence in context: A074177 A036470 A111243 * A203898 A108917 A237667

Adjacent sequences: A344632 A344633 A344634 * A344636 A344637 A344638

Keyword

nonn

Author

Fausto A. C. Cariboni, May 25 2021

Status

approved