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A119999
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Number of partitions of n into parts that occur in decimal representation as substrings of n.
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8
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 8, 6, 5, 5, 4, 4, 4, 4, 2, 12, 2, 5, 8, 4, 6, 3, 5, 3, 2, 12, 7, 2, 4, 4, 8, 3, 3, 6, 2, 12, 12, 5, 2, 4, 5, 3, 8, 3, 2, 12, 7, 5, 4, 2, 3, 3, 3, 3, 2, 12, 12, 12, 7, 4, 2, 3, 4, 5, 2, 12, 7, 5, 4, 4, 3, 2, 3, 3, 2, 12, 12, 5, 12, 4, 5, 3, 2, 3, 2, 12, 7, 12, 4, 4, 7, 3
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,11
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COMMENTS
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A120002 = first differences; A120003 = partial sums;
see A120000 and A120001 for records and where they occur: A120000(n)=a(A120001(n)).
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 0..1000
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EXAMPLE
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a(98) = #{98, 10x9+8, 2x9+10x8} = 3;
a(99) = #{99, 11x9} = 2;
a(100) = #{100, 10x10, 9x10+10x1, 8x10+20x1, 7x10+30x1,
6x10+40x1, 5x10+50x1, 4x10+60x1, 3x10+70x1, 2x10+80x1,
10+90x1, 100x1} = 12;
a(101) = #{101, 10x10+1, 9x10+11x1, 8x10+21x1, 7x10+31x1,
6x10+41x1, 5x10+51x1, 4x10+61x1, 3x10+71x1, 2x10+81x1,
10+91x1, 101x1} = 12;
a(102) = #{102, 10x10+2, 10x10+2x1, 9x10+6x2, ...} = 298.
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PROG
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(Haskell)
import Data.List (isInfixOf)
a119999 n = p (filter ((`isInfixOf` show n) . show) [1..n]) n where
p _ 0 = 1
p [] _ = 0
p ks'@(k:ks) m | m < k = 0
| otherwise = p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Aug 14 2011
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CROSSREFS
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Cf. A000041, A061827, A120004.
Sequence in context: A223041 A024558 A103238 * A061828 A086535 A067436
Adjacent sequences: A119996 A119997 A119998 * A120000 A120001 A120002
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller, Jun 13 2006
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STATUS
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approved
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