cp's OEIS Frontend

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

%I A211863 #7 Dec 27 2012 23:46:53
%S A211863 1,1,2,2,4,5,7,10,13,14,20,26,28,40,49,53,71,89,95,125,136,160,192,
%T A211863 235,248,313,348,409,458,558,592,729,785,921,1018,1205,1264,1511,1627,
%U A211863 1888,2037,2382,2521,2961,3143,3660,3884,4502,4782,5510
%N A211863 Number of partitions of n into parts <= 8 with the property that all parts have distinct multiplicities.
%H A211863 Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/dmp.html">Using generatingfunctionology to enumerate distinct-multiplicity partitions</a>.
%e A211863 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 A211863 (Haskell)
%o A211863 a211863 n = p 0 [] [1..8] n where
%o A211863    p m ms _      0 = if m `elem` ms then 0 else 1
%o A211863    p _ _  []     _ = 0
%o A211863    p m ms ks'@(k:ks) x
%o A211863      | x < k       = 0
%o A211863      | m == 0      = p 1 ms ks' (x - k) + p 0 ms ks x
%o A211863      | m `elem` ms = p (m + 1) ms ks' (x - k)
%o A211863      | otherwise   = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x
%o A211863 -- _Reinhard Zumkeller_, Dec 27 2012
%Y A211863 Cf. A026814, A098859.
%Y A211863 Cf. A105637, A211858, A211859, A211860, A211861, A211862.
%K A211863 nonn
%O A211863 0,3
%A A211863 _Matthew C. Russell_, Apr 25 2012