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A344412
Number of knapsack partitions of n with largest part 7.
4
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)
KEYWORD
nonn
AUTHOR
STATUS
approved