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A198726
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Number of partitions of n into positive Loeschian numbers (cf. A003136).
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3
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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