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Search: id:A109950
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| A109950 |
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Number of partitions of n into parts having in decimal representation mutually no common digits. |
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+0
4
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| 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 11, 14, 16, 18, 23, 25, 29, 32, 39, 41, 49, 51, 57, 66, 71, 74, 82, 92, 92, 106, 105, 117, 123, 129, 132, 145, 153, 157, 173, 173, 187, 204, 214, 218, 250, 257, 266, 298, 301, 329, 359, 368, 370, 412, 433, 433, 478, 475, 508, 538, 526
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OFFSET
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1,3
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COMMENT
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A109968(n) <= a(n) <= A000009(n);
A109951(n) = a(n+1) - a(n);
all partitions have not more than 9 parts.
a(n) <= A000009(n), a(n) < A000009(n) for n>10.
a(9876543210) = 1 and a(n) = 0 for n > 9876543210; problem: what is the smallest n such that a(n) = 0?. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 11 2006
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EXAMPLE
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n=20: there are A000009(20)=64 partitions into distinct
parts,
the following 23 partitions contain parts with common digits:
19+1, 17+2+1, 16+3+1, 15+5, 15+4+1, 14+5+1, 14+4+2, 14+3+2+1,
13+6+1, 13+4+3, 13+4+2+1, 12+7+1, 12+6+2, 12+5+2+1, 12+4+3+1,
11+8+1, 11+6+2+1, 11+5+3+1, 10+9+1, 10+7+2+1, 10+6+3+1,
10+5+4+1 and 10+4+3+2+1, therefore a(20) = 64 - 23 = 41.
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CROSSREFS
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Sequence in context: A027196 A100928 A034140 this_sequence A008674 A067596 A114098
Adjacent sequences: A109947 A109948 A109949 this_sequence A109951 A109952 A109953
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KEYWORD
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nonn,base
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 06 2005
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