cp's OEIS Frontend

A211860 Number of partitions of n into parts <= 5 with the property that all parts have distinct multiplicities.

%I A211860 #8 Dec 27 2012 23:48:00
%S A211860 1,1,2,2,4,5,6,9,11,12,16,22,21,33,37,39,51,65,63,86,85,105,118,149,
%T A211860 148,185,198,238,251,304,304,381,388,454,478,565,576,679,704,819,842,
%U A211860 978,1013,1168,1195,1377,1415,1616,1668,1874,1937,2197,2246,2512,2625
%N A211860 Number of partitions of n into parts <= 5 with the property that all parts have distinct multiplicities.
%H A211860 Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/dmp.html">Using generatingfunctionology to enumerate distinct-multiplicity partitions</a>.
%e A211860 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 A211860 (Haskell)
%o A211860 a211860 n = p 0 [] [1..5] n where
%o A211860    p m ms _      0 = if m `elem` ms then 0 else 1
%o A211860    p _ _  []     _ = 0
%o A211860    p m ms ks'@(k:ks) x
%o A211860      | x < k       = 0
%o A211860      | m == 0      = p 1 ms ks' (x - k) + p 0 ms ks x
%o A211860      | m `elem` ms = p (m + 1) ms ks' (x - k)
%o A211860      | otherwise   = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x
%o A211860 -- _Reinhard Zumkeller_, Dec 27 2012
%Y A211860 Cf. A026811, A098859.
%Y A211860 Cf. A105637, A211858, A211859, A211861, A211862, A211863.
%K A211860 nonn
%O A211860 0,3
%A A211860 _Matthew C. Russell_, Apr 25 2012