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

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, 42, 50, 58, 70, 80, 95, 110, 129, 150, 96, 107, 126, 143, 167, 188, 221, 248, 288, 326, 376, 424, 491, 304, 346, 390, 443, 498, 565, 635, 719, 807, 911, 1022, 1153

Offset: 0

Author

Reinhard Zumkeller, Aug 12 2011

Keywords

• nonn
• look

Examples

			a(7) = #{7, 5+2, 4+3, 3+2+2} = 4;
a(8) = #{8, 6+2, 5+3, 4+4, 4+2+2, 3+3+2, 2+2+2+2} = 7;
a(9) = #{9, 6+3, 5+4, 3+3+3} = 4;
a(10) = #{10, 7+3, 6+4, 5+5, 4+3+3} = 5;
a(11) = #{11, 8+3, 7+4, 6+5, 5+3+3, 4+4+3} = 6.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A097356, A000041, A000196.

Programs

Haskell

a194020 n = p (a000196 n) n where
   p _  0 = 1
   p k m | m < k     = 0
         | otherwise = p k (m - k) + p (k+1) m

Mathematica

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