A209038 Number of partitions of n into parts not less than max(1,n/4).

1, 1, 2, 3, 5, 7, 11, 15, 7, 8, 12, 14, 9, 10, 13, 17, 11, 12, 16, 18, 13, 15, 18, 21, 16, 17, 21, 24, 18, 20, 24, 27, 21, 23, 27, 30, 24, 26, 30, 34, 27, 29, 34, 37, 30, 33, 37, 41, 34, 36, 41, 45, 37, 40, 45, 49, 41, 44, 49, 53, 45, 48, 53, 58, 49, 52, 58

Offset

0,3

Links

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

Example

a(12) = #{12, 9+3, 8+4, 7+5, 6+6, 6+3+3, 5+4+3, 4+4+4, 3+3+3+3} = 9;
a(13) = #{13, 10+3, 9+4, 8+5, 7+6, 7+3+3, 6+4+3, 5+5+3, 5+4+4, 4+3+3+3} = 10;
a(14) = #{14, 11+3, 10+4, 9+5, 8+6, 8+3+3, 7+7, 7+4+3, 6+5+3, 6+4+4, 5+5+4, 5+3+3+3, 4+4+3+3} = 13;
a(15) = #{15, 12+3, 11+4, 10+5, 9+6, 9+3+3, 8+7, 8+4+3, 7+5+3, 7+4+4, 6+6+3, 6+5+4, 6+3+3+3, 5+5+5, 5+4+3+3, 4+4+4+3, 3+3+3+3+3} = 15;
a(16) = #{16, 12+4, 11+5, 10+6, 9+7, 8+8, 8+4+4, 7+5+4, 6+6+4, 6+5+5, 4+4+4+4} = 11.

Prog

(Haskell)
a209038 n = p (max 1 (n `div` 4)) n where
   p _ 0 = 1
   p k m = if m < k then 0 else p k (m - k) + p (k + 1) m

Crossrefs

Cf. A209037, A209039.

Sequence in context: A184642 A350836 A094252 * A182803 A106532 A240556

Adjacent sequences: A209035 A209036 A209037 * A209039 A209040 A209041

Keyword

nonn

Author

Reinhard Zumkeller, Mar 04 2012

Status

approved