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A211861
Number of partitions of n into parts <= 6 with the property that all parts have distinct multiplicities.
7
1, 1, 2, 2, 4, 5, 7, 9, 12, 13, 18, 23, 25, 36, 43, 45, 60, 75, 78, 102, 108, 126, 151, 184, 188, 237, 260, 305, 339, 408, 415, 521, 548, 627, 689, 815, 824, 997, 1050, 1202, 1287, 1497, 1537, 1831, 1903, 2166, 2288, 2658, 2721, 3156, 3274
OFFSET
0,3
EXAMPLE
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.
PROG
(Haskell)
a211861 n = p 0 [] [1..6] 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
-- Reinhard Zumkeller, Dec 27 2012
KEYWORD
nonn
AUTHOR
Matthew C. Russell, Apr 25 2012
STATUS
approved