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Search: id:A122934
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| A122934 |
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Triangle T(n,k) = number of partitions of n into k parts, with each part size divisible by the next. |
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6
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| 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 3, 2, 4, 2, 2, 1, 1, 1, 2, 4, 2, 4, 2, 2, 1, 1, 1, 3, 4, 5, 3, 4, 2, 2, 1, 1, 1, 1, 3, 4, 5, 3, 4, 2, 2, 1, 1, 1, 5, 4, 6, 5, 6, 3, 4, 2, 2, 1, 1, 1, 1, 5, 4, 6, 5, 6, 3, 4, 2, 2, 1, 1, 1, 3, 4, 7, 6, 7, 6, 6, 3, 4, 2, 2, 1, 1
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OFFSET
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1,8
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FORMULA
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T(n,1) = 1. T(n,k+1) = Sum_{d|n, d<n} T(n/d-1,k) = Sum_{d|n, d>1} T(d-1,k).
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EXAMPLE
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Table starts 1; 1,1; 1,1,1; 1,2,1,1; 1,1,2,1,1; 1,3,2,2,1,1; ...
T(6,3) = 2 because of the 3 partitions of 6 into 3 parts, [4,1,1] and [2,2,2] meet the definition; [3,2,1] fails because 2 does not divide 3.
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CROSSREFS
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Columns: A057427, A032741, A049822, A121895; row sums A003238.
Sequence in context: A078470 A151683 A133912 this_sequence A072170 A056624 A093997
Adjacent sequences: A122931 A122932 A122933 this_sequence A122935 A122936 A122937
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 20 2006
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