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A279791
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Number of twice-partitions of type (Q,R,Q) and weight n.
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13
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1, 1, 2, 2, 3, 6, 5, 8, 8, 16, 12, 23, 18, 36, 33, 50, 38, 84, 54, 106, 100, 155, 104, 244, 142, 301, 270, 436, 256, 684, 340, 788, 670, 1044, 585, 1868, 760, 1878, 1600, 2647
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OFFSET
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1,3
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LINKS
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EXAMPLE
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The a(8)=8 twice-partitions of type (Q,R,Q) are:
((8)), ((71)), ((62)), ((53)),
((521)), ((4)(31)), ((31)(4)), ((431)).
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MATHEMATICA
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nn=20;
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Total[Total[Factorial/@Length/@Select[sps[Sort[#]], SameQ@@Total/@#&]]&/@Select[IntegerPartitions[n], UnsameQ@@#&]], {n, nn}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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