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A198727 Number of partitions of n into distinct positive Loeschian numbers (cf. A003136).

%I A198727 #12 Nov 16 2015 23:27:53
%S A198727 1,1,0,1,2,1,0,2,2,1,2,2,3,4,3,2,6,6,1,5,9,6,5,9,9,9,11,8,13,17,11,12,
%T A198727 22,19,13,23,25,22,26,28,30,37,34,31,47,45,35,50,61,52,56,69,68,76,74,
%U A198727 72,95,100,82,100,130,112,113,139,144,149,154,156,183
%N A198727 Number of partitions of n into distinct positive Loeschian numbers (cf. A003136).
%H A198727 Reinhard Zumkeller, <a href="/A198727/b198727.txt">Table of n, a(n) for n = 0..1000</a>
%e A198727 a(20) = #{19+1, 16+4, 16+3+1, 13+7, 13+4+3, 12+7+1, 12+4+3+1, 9+7+4, 9+7+3+1} = 9;
%e A198727 a(21) = #{21, 16+4+1, 13+7+1, 13+4+3+1, 12+9, 9+7+4+1} = 6;
%e A198727 a(22) = #{21+1, 19+3, 13+9, 12+9+1, 12+7+3} = 5.
%o A198727 (Haskell)
%o A198727 import Data.MemoCombinators (memo2, list, integral)
%o A198727 a198727 n = a198727_list !! n
%o A198727 a198727_list = f 0 [] $ tail a003136_list where
%o A198727    f u vs ws'@(w:ws) | u < w = (p' vs u) : f (u + 1) vs ws'
%o A198727                      | otherwise = f u (vs ++ [w]) ws
%o A198727    p' = memo2 (list integral) integral p
%o A198727    p _  0 = 1
%o A198727    p [] _ = 0
%o A198727    p (k:ks) m = if m < k then 0 else p' ks (m - k) + p' ks m
%o A198727 -- _Reinhard Zumkeller_, Nov 16 2015, Oct 30 2011
%Y A198727 Cf. A003136, A198726.
%K A198727 nonn
%O A198727 0,5
%A A198727 _Reinhard Zumkeller_, Oct 30 2011