%I #11 Jun 24 2024 22:27:47
%S 1,1,2,3,5,7,11,15,7,8,12,14,9,10,13,17,11,12,16,18,13,15,18,21,16,17,
%T 21,24,18,20,24,27,21,23,27,30,24,26,30,34,27,29,34,37,30,33,37,41,34,
%U 36,41,45,37,40,45,49,41,44,49,53,45,48,53,58,49,52,58
%N Number of partitions of n into parts not less than max(1,n/4).
%H Reinhard Zumkeller, <a href="/A209038/b209038.txt">Table of n, a(n) for n = 0..1000</a>
%e a(12) = #{12, 9+3, 8+4, 7+5, 6+6, 6+3+3, 5+4+3, 4+4+4, 3+3+3+3} = 9;
%e a(13) = #{13, 10+3, 9+4, 8+5, 7+6, 7+3+3, 6+4+3, 5+5+3, 5+4+4, 4+3+3+3} = 10;
%e a(14) = #{14, 11+3, 10+4, 9+5, 8+6, 8+3+3, 7+7, 7+4+3, 6+5+3, 6+4+4, 5+5+4, 5+3+3+3, 4+4+3+3} = 13;
%e a(15) = #{15, 12+3, 11+4, 10+5, 9+6, 9+3+3, 8+7, 8+4+3, 7+5+3, 7+4+4, 6+6+3, 6+5+4, 6+3+3+3, 5+5+5, 5+4+3+3, 4+4+4+3, 3+3+3+3+3} = 15;
%e a(16) = #{16, 12+4, 11+5, 10+6, 9+7, 8+8, 8+4+4, 7+5+4, 6+6+4, 6+5+5, 4+4+4+4} = 11.
%o (Haskell)
%o a209038 n = p (max 1 (n `div` 4)) 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. A209037, A209039.
%K nonn
%O 0,3
%A _Reinhard Zumkeller_, Mar 04 2012