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A194020 Number of partitions of n into parts not less than the integer part of the square root of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A053269 A163873 A309563

Adjacent sequences:  A194017 A194018 A194019 * A194021 A194022 A194023

KEYWORD

nonn,look

AUTHOR

Reinhard Zumkeller, Aug 12 2011

STATUS

approved

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Last modified September 26 20:36 EDT 2020. Contains 337374 sequences. (Running on oeis4.)