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A342684
Number of knapsack partitions of n with largest part 8.
3
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 11, 1, 8, 6, 10, 7, 13, 9, 15, 6, 12, 10, 15, 8, 18, 10, 17, 6, 17, 12, 17, 9, 18, 13, 22, 7, 19, 10, 19, 13, 20, 14, 24, 4, 20, 12, 19, 13, 23, 15, 21, 4, 20, 13, 23, 11, 23, 15, 20, 7, 20, 12, 22, 15, 24, 12, 22
OFFSET
0,11
COMMENTS
An integer partition is knapsack if every distinct submultiset has a different sum.
I computed terms a(n) for n = 0..40000 and the subsequence a(98)-a(937) of length 840 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:
8: (8)
9: (8,1)
10: (8,1,1), (8,2)
11: (8,1,1,1), (8,2,1), (8,3)
KEYWORD
nonn
AUTHOR
STATUS
approved