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A198726 Number of partitions of n into positive Loeschian numbers (cf. A003136).

%I A198726 #13 Nov 16 2015 23:27:16
%S A198726 1,1,1,2,3,3,4,6,7,9,11,13,17,21,24,29,37,42,49,60,70,82,96,111,129,
%T A198726 152,173,199,234,266,302,349,399,451,515,585,661,752,847,954,1081,
%U A198726 1215,1359,1531,1719,1917,2147,2400,2675,2985,3322,3690,4110,4563,5048,5603
%N A198726 Number of partitions of n into positive Loeschian numbers (cf. A003136).
%H A198726 Reinhard Zumkeller, <a href="/A198726/b198726.txt">Table of n, a(n) for n = 0..1000</a>
%e A198726 a(10) = #{9+1, 7+3, 7+1+1+1, 4+4+1+1, 4+3+3, 4+3+1+1+1, 4+6x1, 3+3+3+1, 3+3+1+1+1+1, 3+7x1, 10x1} = 11;
%e A198726 a(11) = #{9+1+1, 7+4, 7+3+1, 7+1+1+1+1, 4+4+3, 4+4+1+1+1, 4+3+3+1, 4+3+4x1, 4+7x1, 3+3+3+1+1, 3+3+5x1, 3+8x1, 11x1} = 13;
%e A198726 a(12) = #{12, 9+3, 9+1+1+1, 7+4+1, 7+3+1+1, 7+5x1, 4+4+4, 4+4+3+1, 4+4+4x1, 4+3+3+1+1, 4+3+5x1, 4+8x1, 3+3+3+3, 3+3+3+1+1+1, 3+3+6x1, 3+9x1, 12x1} = 17.
%o A198726 (Haskell)
%o A198726 import Data.MemoCombinators (memo2, list, integral)
%o A198726 a198726 n = a198726_list !! n
%o A198726 a198726_list = f 0 [] $ tail a003136_list where
%o A198726    f u vs ws'@(w:ws) | u < w = (p' vs u) : f (u + 1) vs ws'
%o A198726                      | otherwise = f u (vs ++ [w]) ws
%o A198726    p' = memo2 (list integral) integral p
%o A198726    p _  0 = 1
%o A198726    p [] _ = 0
%o A198726    p ks'@(k:ks) m = if m < k then 0 else p' ks' (m - k) + p' ks m
%o A198726 -- _Reinhard Zumkeller_, Nov 16 2015, Oct 30 2011
%Y A198726 Cf. A003136, A198727.
%K A198726 nonn
%O A198726 0,4
%A A198726 _Reinhard Zumkeller_, Oct 30 2011