A343321 - OEIS

A343321

Number of knapsack partitions of n with largest part 5.

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

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OFFSET

0,8

COMMENTS

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

I computed terms a(n) for n = 0..10000 and (6,7,7,5,5,8,7,8,2,8,6,9,6,3,7,9,5,8,3,8,6,8,6,5,6,7,7,9,1,8,7,8,6,4,6,9,6,7,3,9,5,8,7,4,6,8,6,9,2,7,7,9,5,4,7,8,6,8,2,9) is repeated continuously starting at a(32).

LINKS

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

EXAMPLE

The initial values count the following partitions:

5: (5)

6: (5,1)

7: (5,1,1)

7: (5,2)

8: (5,1,1,1)

8: (5,2,1)

8: (5,3)

CROSSREFS