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A211862
Number of partitions of n into parts <= 7 with the property that all parts have distinct multiplicities.
7
1, 1, 2, 2, 4, 5, 7, 10, 12, 14, 19, 25, 26, 39, 46, 51, 65, 84, 87, 116, 123, 147, 171, 216, 220, 281, 306, 364, 402, 496, 511, 636, 678, 793, 861, 1032, 1062, 1273, 1360, 1569, 1683, 1978, 2054, 2428, 2566, 2953, 3118, 3627, 3812, 4378, 4631
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)
a211862 n = p 0 [] [1..7] 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