A344625 -id:A344625 - cp's OEIS frontend

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

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Fausto A. C. Cariboni, May 25 2021

nonn

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.

			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)

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

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

cp's OEIS Frontend

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

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