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A094033
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Number of connected 2-element antichains on a labeled n-set.
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16
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0, 0, 0, 3, 18, 75, 270, 903, 2898, 9075, 27990, 85503, 259578, 784875, 2366910, 7125303, 21425058, 64373475, 193317030, 580344303, 1741819338, 5227030875, 15684238350, 47059006503, 141189602418, 423593973075, 1270832250870
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OFFSET
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0,4
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COMMENTS
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Let P(A) be the power set of an n-element set A. Then a(n+1) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 1) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x. - Ross La Haye, Jan 10 2008
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LINKS
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FORMULA
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E.g.f.: (exp(3*x)-3*exp(2*x)+3*exp(x)-1)/2!.
a(n) = (3^n-3*2^n+3)/2.
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).
G.f.: 3*x^3/((1-x)*(1-2*x)*(1-3*x)). (End)
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MAPLE
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MATHEMATICA
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PROG
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(PARI) x='x+O('x^50); concat([0, 0, 0], Vec(serlaplace((exp(3*x)-3*exp(2*x)+3*exp(x)-1)/2!))) \\ G. C. Greubel, Oct 06 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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