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

0,10

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.

Links

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

Example

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)

Crossrefs

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

Sequence in context: A030209 A265399 A138588 * A143102 A013944 A123497

Adjacent sequences: A344409 A344410 A344411 * A344413 A344414 A344415

Keyword

nonn

Author

Fausto A. C. Cariboni, May 17 2021

Status

approved