A194020 - OEIS

%I #12 Jan 29 2014 04:03:03

%S 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 42,50,58,70,80,95,110,129,150,96,107,126,143,167,188,221,248,288,326,

%U 376,424,491,304,346,390,443,498,565,635,719,807,911,1022,1153

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

%H Reinhard Zumkeller, <a href="/A194020/b194020.txt">Table of n, a(n) for n = 0..250</a>

%e a(7) = #{7, 5+2, 4+3, 3+2+2} = 4;

%e a(8) = #{8, 6+2, 5+3, 4+4, 4+2+2, 3+3+2, 2+2+2+2} = 7;

%e a(9) = #{9, 6+3, 5+4, 3+3+3} = 4;

%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.

%t Table[Length[Select[IntegerPartitions[n], #[[-1]] >= Floor[Sqrt[n]] &]], {n, 60}] (* _Alonso del Arte_, Aug 12 2011 *)

%o (Haskell)

%o a194020 n = p (a000196 n) n where

%o    p _  0 = 1

%o    p k m | m < k     = 0

%o          | otherwise = p k (m - k) + p (k+1) m

%Y Cf. A097356, A000041, A000196.

%K nonn,look

%O 0,3

%A _Reinhard Zumkeller_, Aug 12 2011