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

0,3

Links

Table of n, a(n) for n=0..49.

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)
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

Crossrefs

Cf. A026814, A098859.

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

Sequence in context: A026930 A211862 A286948 * A333190 A098859 A364345

Adjacent sequences: A211860 A211861 A211862 * A211864 A211865 A211866

Keyword

nonn

Author

Matthew C. Russell, Apr 25 2012

Status

approved