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

Author

Reinhard Zumkeller, Oct 30 2011

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A003136, A198727.

Programs

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