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A194020 Number of partitions of n into parts not less than the integer part of the square root of n.

%I A194020 #12 Jan 29 2014 04:03:03
%S A194020 1,1,2,3,2,2,4,4,7,4,5,6,9,10,13,17,11,12,16,18,24,27,34,39,50,30,36,
%T A194020 42,50,58,70,80,95,110,129,150,96,107,126,143,167,188,221,248,288,326,
%U A194020 376,424,491,304,346,390,443,498,565,635,719,807,911,1022,1153
%N A194020 Number of partitions of n into parts not less than the integer part of the square root of n.
%H A194020 Reinhard Zumkeller, <a href="/A194020/b194020.txt">Table of n, a(n) for n = 0..250</a>
%e A194020 a(7) = #{7, 5+2, 4+3, 3+2+2} = 4;
%e A194020 a(8) = #{8, 6+2, 5+3, 4+4, 4+2+2, 3+3+2, 2+2+2+2} = 7;
%e A194020 a(9) = #{9, 6+3, 5+4, 3+3+3} = 4;
%e A194020 a(10) = #{10, 7+3, 6+4, 5+5, 4+3+3} = 5;
%e A194020 a(11) = #{11, 8+3, 7+4, 6+5, 5+3+3, 4+4+3} = 6.
%t A194020 Table[Length[Select[IntegerPartitions[n], #[[-1]] >= Floor[Sqrt[n]] &]], {n, 60}] (* _Alonso del Arte_, Aug 12 2011 *)
%o A194020 (Haskell)
%o A194020 a194020 n = p (a000196 n) n where
%o A194020    p _  0 = 1
%o A194020    p k m | m < k     = 0
%o A194020          | otherwise = p k (m - k) + p (k+1) m
%Y A194020 Cf. A097356, A000041, A000196.
%K A194020 nonn,look
%O A194020 0,3
%A A194020 _Reinhard Zumkeller_, Aug 12 2011