A211863 Number of partitions of n into parts <= 8 with the property that all parts have distinct multiplicities.

1, 1, 2, 2, 4, 5, 7, 10, 13, 14, 20, 26, 28, 40, 49, 53, 71, 89, 95, 125, 136, 160, 192, 235, 248, 313, 348, 409, 458, 558, 592, 729, 785, 921, 1018, 1205, 1264, 1511, 1627, 1888, 2037, 2382, 2521, 2961, 3143, 3660, 3884, 4502, 4782, 5510

Offset: 0

Author

Matthew C. Russell, Apr 25 2012

Keywords

• nonn

Examples

			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.
		

Links

• Doron Zeilberger, Using generatingfunctionology to enumerate distinct-multiplicity partitions.

Crossrefs

Cf. A026814, A098859.

Cf. A105637, A211858, A211859, A211860, A211861, A211862.

Programs

Haskell

a211863 n = p 0 [] [1..8] 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