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A168583
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The number of ways of partitioning the multiset {1,1,2,3,...,n-1} into exactly three nonempty parts.
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5
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1, 4, 16, 58, 196, 634, 1996, 6178, 18916, 57514, 174076, 525298, 1582036, 4758394, 14299756, 42948418, 128943556, 387027274, 1161475036, 3485211538, 10457207476, 31374768154, 94130595916, 282404370658, 847238277796, 2541765165034, 7625396158396
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OFFSET
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3,2
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COMMENTS
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The number of ways of partitioning the multiset {1, 1, 2, 3, ..., n-1} into exactly two, four and five nonempty parts are given in A083329, A168584 and A168585, respectively.
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LINKS
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FORMULA
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For a>=3, a(n) = 3^(n-2) - 3*2^(n-3) + 1.
E.g.f.: 3*e^(3x) - 3*e^(2x) + e^x (shifted).
O.g.f.: x^3*(1-2x+3x^2)/((1-x)*(1-2x)*(1-3x)).
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EXAMPLE
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The partitions of {1,1,2,3} into exactly three nonempty parts are {{1},{1},{2,3}}, {{1},{2},{1,3}}, {{1},{3},{1,2}} and {{2},{3},{1,1}}.
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MAPLE
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MATHEMATICA
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f1[n_] := 3^(n - 2) - 3 2^(n - 3) + 1; Table[f1[n], {n, 3, 25}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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