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Search: id:A114701
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| A114701 |
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Number of sets {p, p'}, where p is a partition of n and p' is conjugate partition of p such that p and p' have no common parts. |
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1
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| 0, 1, 1, 1, 1, 2, 2, 4, 5, 5, 7, 9, 9, 13, 15, 18, 22, 30, 32, 41, 48, 57, 65, 82, 88, 111, 124, 148, 169, 203, 225, 275, 310, 363, 408, 484, 537, 635, 709, 824, 918, 1075, 1191, 1379, 1540, 1767, 1971, 2269, 2517, 2889, 3208, 3656, 4068, 4629, 5120
(list; graph; listen)
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OFFSET
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1,6
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EXAMPLE
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a(6)=2 because the pairs of conjugate partitions of 6 are {[6], [1, 1, 1, 1, 1, 1]}, {[3, 3], [2, 2, 2]}, {[5, 1], [2, 1, 1, 1, 1]}, {[4, 2], [2, 2, 1, 1]}, {[3, 2, 1], [3, 2, 1]}, {[3, 1, 1, 1], [4, 1, 1]} and only in the first two pairs there are no common parts.
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MAPLE
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with(combinat): a:=proc(n) local P, ct, j: P:=partition(n): ct:=0: for j from 1 to numbpart(n) do if convert(P[j], set) intersect convert(conjpart(P[j]), set) = {} then ct:=ct+1 else fi: od: ct/2: end: seq(a(n), n=1..55); # for 55 terms execution takes hours - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 15 2006
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CROSSREFS
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Sequence in context: A118003 A159296 A035632 this_sequence A049269 A085085 A121600
Adjacent sequences: A114698 A114699 A114700 this_sequence A114702 A114703 A114704
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2006
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 15 2006
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