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%I #9 Jul 13 2013 12:04:23
%S 1,1,2,3,5,7,4,4,7,4,5,6,5,5,7,5,6,7,6,6,8,6,7,8,7,7,9,7,8,9,8,8,10,8,
%T 9,10,9,9,11,9,10,11,10,10,12,10,11,12,11,11,13,11,12,13,12,12,14,12,
%U 13,14,13,13,15,13,14,15,14,14,16,14,15,16,15,15
%N Number of partitions of n into parts not less than max(1,n/3).
%H Reinhard Zumkeller, <a href="/A209037/b209037.txt">Table of n, a(n) for n = 0..1000</a>
%e a(10) = #{10, 7+3, 6+4, 5+5, 4+3+3} = 5;
%e a(11) = #{11, 8+3, 7+4, 6+5, 5+3+3, 4+4+3} = 6;
%e a(12) = #{12, 8+4, 7+5, 6+6, 4+4+4} = 5;
%e a(13) = #{13, 9+4, 8+5, 7+6, 5+4+4} = 5;
%e a(14) = #{14, 10+4, 9+5, 8+6, 7+7, 6+4+4, 5+5+4} = 7;
%e a(15) = #{15, 10+5, 9+6, 8+7, 5+5+5} = 5;
%e a(16) = #{16, 11+5, 10+6, 9+7, 8+8, 6+5+5} = 6;
%e a(17) = #{17, 12+5, 11+6, 10+7, 9+8, 7+5+5, 6+6+5} = 7;
%e a(18) = #{18, 12+6, 11+7, 10+8, 9+9, 6+6+6} = 6;
%e a(19) = #{19, 13+6, 12+7, 11+8, 10+9, 7+6+6} = 6;
%e a(20) = #{20, 14+6, 13+7, 12+8, 11+9, 10+10, 8+6+6, 7+7+6} = 8.
%o (Haskell)
%o a209037 n = p (max 1 (n `div` 3)) n where
%o p _ 0 = 1
%o p k m = if m < k then 0 else p k (m - k) + p (k + 1) m
%Y Cf. A209038, A209039.
%K nonn
%O 0,3
%A _Reinhard Zumkeller_, Mar 04 2012
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