cp's OEIS Frontend

A211862 Number of partitions of n into parts <= 7 with the property that all parts have distinct multiplicities.

%I A211862 #7 Dec 27 2012 23:47:15
%S A211862 1,1,2,2,4,5,7,10,12,14,19,25,26,39,46,51,65,84,87,116,123,147,171,
%T A211862 216,220,281,306,364,402,496,511,636,678,793,861,1032,1062,1273,1360,
%U A211862 1569,1683,1978,2054,2428,2566,2953,3118,3627,3812,4378,4631
%N A211862 Number of partitions of n into parts <= 7 with the property that all parts have distinct multiplicities.
%H A211862 Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/dmp.html">Using generatingfunctionology to enumerate distinct-multiplicity partitions</a>.
%e A211862 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 A211862 (Haskell)
%o A211862 a211862 n = p 0 [] [1..7] n where
%o A211862    p m ms _      0 = if m `elem` ms then 0 else 1
%o A211862    p _ _  []     _ = 0
%o A211862    p m ms ks'@(k:ks) x
%o A211862      | x < k       = 0
%o A211862      | m == 0      = p 1 ms ks' (x - k) + p 0 ms ks x
%o A211862      | m `elem` ms = p (m + 1) ms ks' (x - k)
%o A211862      | otherwise   = p (m + 1) ms ks' (x - k) + p 0 (m : ms) ks x
%o A211862 -- _Reinhard Zumkeller_, Dec 27 2012
%Y A211862 Cf. A026813, A098859.
%Y A211862 Cf. A105637, A211858, A211859, A211860, A211861, A211863.
%K A211862 nonn
%O A211862 0,3
%A A211862 _Matthew C. Russell_, Apr 25 2012