A198726 Number of partitions of n into positive Loeschian numbers (cf. A003136).

1, 1, 1, 2, 3, 3, 4, 6, 7, 9, 11, 13, 17, 21, 24, 29, 37, 42, 49, 60, 70, 82, 96, 111, 129, 152, 173, 199, 234, 266, 302, 349, 399, 451, 515, 585, 661, 752, 847, 954, 1081, 1215, 1359, 1531, 1719, 1917, 2147, 2400, 2675, 2985, 3322, 3690, 4110, 4563, 5048, 5603

Offset

0,4

Links

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

Example

a(10) = #{9+1, 7+3, 7+1+1+1, 4+4+1+1, 4+3+3, 4+3+1+1+1, 4+6x1, 3+3+3+1, 3+3+1+1+1+1, 3+7x1, 10x1} = 11;
a(11) = #{9+1+1, 7+4, 7+3+1, 7+1+1+1+1, 4+4+3, 4+4+1+1+1, 4+3+3+1, 4+3+4x1, 4+7x1, 3+3+3+1+1, 3+3+5x1, 3+8x1, 11x1} = 13;
a(12) = #{12, 9+3, 9+1+1+1, 7+4+1, 7+3+1+1, 7+5x1, 4+4+4, 4+4+3+1, 4+4+4x1, 4+3+3+1+1, 4+3+5x1, 4+8x1, 3+3+3+3, 3+3+3+1+1+1, 3+3+6x1, 3+9x1, 12x1} = 17.

Prog

(Haskell)
import Data.MemoCombinators (memo2, list, integral)
a198726 n = a198726_list !! n
a198726_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 ks'@(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, A198727.

Sequence in context: A123552 A071610 A358993 * A117275 A327725 A253926

Adjacent sequences: A198723 A198724 A198725 * A198727 A198728 A198729

Keyword

nonn

Author

Reinhard Zumkeller, Oct 30 2011

Status

approved