A211861 - OEIS

%I #7 Dec 27 2012 23:47:37

%S 1,1,2,2,4,5,7,9,12,13,18,23,25,36,43,45,60,75,78,102,108,126,151,184,

%T 188,237,260,305,339,408,415,521,548,627,689,815,824,997,1050,1202,

%U 1287,1497,1537,1831,1903,2166,2288,2658,2721,3156,3274

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

%H Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/dmp.html">Using generatingfunctionology to enumerate distinct-multiplicity partitions</a>.

%e 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.

%o (Haskell)

%o a211861 n = p 0 [] [1..6] n where

%o    p m ms _      0 = if m `elem` ms then 0 else 1

%o    p _ _  []     _ = 0

%o    p m ms ks'@(k:ks) x

%o      | x < k       = 0

%o      | m == 0      = p 1 ms ks' (x - k) + p 0 ms ks x

%o      | m `elem` ms = p (m + 1) ms ks' (x - k)

%o      | otherwise   = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x

%o -- _Reinhard Zumkeller_, Dec 27 2012

%Y Cf. A026812, A098859.

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

%K nonn

%O 0,3

%A _Matthew C. Russell_, Apr 25 2012