A198727 Number of partitions of n into distinct positive Loeschian numbers (cf. A003136).

1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 2, 2, 3, 4, 3, 2, 6, 6, 1, 5, 9, 6, 5, 9, 9, 9, 11, 8, 13, 17, 11, 12, 22, 19, 13, 23, 25, 22, 26, 28, 30, 37, 34, 31, 47, 45, 35, 50, 61, 52, 56, 69, 68, 76, 74, 72, 95, 100, 82, 100, 130, 112, 113, 139, 144, 149, 154, 156, 183

Offset

0,5

Links

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

Example

a(20) = #{19+1, 16+4, 16+3+1, 13+7, 13+4+3, 12+7+1, 12+4+3+1, 9+7+4, 9+7+3+1} = 9;
a(21) = #{21, 16+4+1, 13+7+1, 13+4+3+1, 12+9, 9+7+4+1} = 6;
a(22) = #{21+1, 19+3, 13+9, 12+9+1, 12+7+3} = 5.

Prog

(Haskell)
import Data.MemoCombinators (memo2, list, integral)
a198727 n = a198727_list !! n
a198727_list = f 0 [] $ tail a003136_list where
   f u vs ws'@(w:ws) | u < w = (p' vs u) : f (u + 1) vs ws'
                     | otherwise = f u (vs ++ [w]) ws
   p' = memo2 (list integral) integral p
   p _  0 = 1
   p [] _ = 0
   p (k:ks) m = if m < k then 0 else p' ks (m - k) + p' ks m
-- Reinhard Zumkeller, Nov 16 2015, Oct 30 2011

Crossrefs

Cf. A003136, A198726.

Sequence in context: A229893 A317683 A366371 * A294508 A035152 A035204

Adjacent sequences: A198724 A198725 A198726 * A198728 A198729 A198730

Keyword

nonn

Author

Reinhard Zumkeller, Oct 30 2011

Status

approved