A209037 Number of partitions of n into parts not less than max(1,n/3).

1, 1, 2, 3, 5, 7, 4, 4, 7, 4, 5, 6, 5, 5, 7, 5, 6, 7, 6, 6, 8, 6, 7, 8, 7, 7, 9, 7, 8, 9, 8, 8, 10, 8, 9, 10, 9, 9, 11, 9, 10, 11, 10, 10, 12, 10, 11, 12, 11, 11, 13, 11, 12, 13, 12, 12, 14, 12, 13, 14, 13, 13, 15, 13, 14, 15, 14, 14, 16, 14, 15, 16, 15, 15

Offset

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Example

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;
a(12) = #{12, 8+4, 7+5, 6+6, 4+4+4} = 5;
a(13) = #{13, 9+4, 8+5, 7+6, 5+4+4} = 5;
a(14) = #{14, 10+4, 9+5, 8+6, 7+7, 6+4+4, 5+5+4} = 7;
a(15) = #{15, 10+5, 9+6, 8+7, 5+5+5} = 5;
a(16) = #{16, 11+5, 10+6, 9+7, 8+8, 6+5+5} = 6;
a(17) = #{17, 12+5, 11+6, 10+7, 9+8, 7+5+5, 6+6+5} = 7;
a(18) = #{18, 12+6, 11+7, 10+8, 9+9, 6+6+6} = 6;
a(19) = #{19, 13+6, 12+7, 11+8, 10+9, 7+6+6} = 6;
a(20) = #{20, 14+6, 13+7, 12+8, 11+9, 10+10, 8+6+6, 7+7+6} = 8.

Prog

(Haskell)
a209037 n = p (max 1 (n `div` 3)) n where
   p _ 0 = 1
   p k m = if m < k then 0 else p k (m - k) + p (k + 1) m

Crossrefs

Cf. A209038, A209039.

Sequence in context: A156294 A126607 A124322 * A334455 A075241 A239694

Adjacent sequences: A209034 A209035 A209036 * A209038 A209039 A209040

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2012

Status

approved