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A344625
Number of knapsack partitions of n with largest part 9.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 7, 11, 12, 1, 10, 7, 11, 10, 17, 12, 18, 16, 12, 15, 19, 13, 25, 20, 17, 22, 29, 6, 25, 20, 22, 20, 28, 16, 31, 21, 14, 23, 33, 15, 24, 22, 25, 28, 30, 8, 31, 20, 22, 22, 36, 16, 34, 26, 14, 23, 26, 22, 33, 25, 24
OFFSET
0,12
COMMENTS
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(128)-a(2647) of length 2520 is repeated continuously.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..3000
EXAMPLE
The initial nonzero values count the following partitions:
9: (9)
10: (9,1)
11: (9,1,1), (9,2)
12: (9,1,1,1), (9,2,1), (9,3)
KEYWORD
nonn
AUTHOR
STATUS
approved