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A084869
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Number of 2-multiantichains of an n-set.
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16
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1, 2, 5, 17, 71, 317, 1415, 6197, 26591, 112157, 466775, 1923077, 7863311, 31972397, 129459335, 522571157, 2104535231, 8460991037, 33972711095, 136277478437, 546270602351, 2188566048077, 8764718254055, 35090241492917
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OFFSET
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0,2
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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) = 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 but for which x is not a subset of y and y is not a subset of x, or 2) x = y. - Ross La Haye, Jan 11 2008
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LINKS
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FORMULA
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a(n) = (1/2!)*(4^n - 2*3^n + 3*2^n).
a(n) = 3*StirlingS2(n+1,4) + StirlingS2(n+1,3) + StirlingS2(n+1,2) + 1. - Ross La Haye, Jan 11 2008
G.f.: -(13*x^2-7*x+1) / ((2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Nov 27 2012
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MATHEMATICA
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Table[2^(2*n-1) - 3^n + 3*2^(n-1), {n, 0, 20}] (* Vaclav Kotesovec, Oct 30 2015 *)
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PROG
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(PARI) a(n) = 2^(2*n-1)-3^n+3*2^(n-1); \\ Altug Alkan, Sep 12 2017
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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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