A344310 Number of knapsack partitions of n with largest part 4.

0, 0, 0, 0, 1, 1, 2, 3, 1, 2, 3, 3, 1, 3, 3, 3, 2, 3, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4, 3, 4, 2, 3, 4, 4, 1, 4, 4

Offset

0,7

Comments

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

I computed terms a(n) for n = 0..10000 and (3, 4, 2, 3, 4, 4, 1, 4, 4, 3, 2, 4) is repeated continuously starting at a(18).

Links

Table of n, a(n) for n=0..86.

Example

The initial values count the following partitions:
   4: (4)
   5: (4,1)
   6: (4,1,1)
   6: (4,2)
   7: (4,1,1,1)
   7: (4,2,1)
   7: (4,3)
   8: (4,4)

Crossrefs

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

Sequence in context: A130830 A131989 A305390 * A362068 A255890 A194300

Adjacent sequences: A344307 A344308 A344309 * A344311 A344312 A344313

Keyword

nonn

Author

Fausto A. C. Cariboni, May 14 2021

Status

approved