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

0,3

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A097356, A000041, A000196.

Sequence in context: A002307 A287707 A029247 * A372053 A053269 A163873

Adjacent sequences: A194017 A194018 A194019 * A194021 A194022 A194023

Keyword

nonn,look

Author

Reinhard Zumkeller, Aug 12 2011

Status

approved