A211861 Number of partitions of n into parts <= 6 with the property that all parts have distinct multiplicities.

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

Links

Table of n, a(n) for n=0..50.

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

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

Crossrefs

Cf. A026812, A098859.

Cf. A105637, A211858, A211859, A211860, A211862, A211863.

Sequence in context: A283106 A030769 A030739 * A027597 A258318 A027592

Adjacent sequences: A211858 A211859 A211860 * A211862 A211863 A211864

Keyword

nonn

Author

Matthew C. Russell, Apr 25 2012

Status

approved