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A211860
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Number of partitions of n into parts <= 5 with the property that all parts have distinct multiplicities.
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7
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1, 1, 2, 2, 4, 5, 6, 9, 11, 12, 16, 22, 21, 33, 37, 39, 51, 65, 63, 86, 85, 105, 118, 149, 148, 185, 198, 238, 251, 304, 304, 381, 388, 454, 478, 565, 576, 679, 704, 819, 842, 978, 1013, 1168, 1195, 1377, 1415, 1616, 1668, 1874, 1937, 2197, 2246, 2512, 2625
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OFFSET
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0,3
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LINKS
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EXAMPLE
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For n=3 the a(3)=2 partitions are {3} and {1,1,1}. Note that {2,1} does not count, as 1 and 2 appear with the same nonzero multiplicity.
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PROG
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(Haskell)
a211860 n = p 0 [] [1..5] n where
p m ms _ 0 = if m `elem` ms then 0 else 1
p _ _ [] _ = 0
p m ms ks'@(k:ks) x
| x < k = 0
| m == 0 = p 1 ms ks' (x - k) + p 0 ms ks x
| m `elem` ms = p (m + 1) ms ks' (x - k)
| otherwise = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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