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A051303
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Number of 3-element proper antichains of an n-element set.
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4
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0, 0, 0, 1, 30, 605, 9030, 110901, 1200150, 11932285, 111885510, 1006471301, 8786447670, 75039565965, 630534185190, 5234341175701, 43059373189590, 351805681631645, 2859550165976070, 23152657123816101, 186907026783617910, 1505512392025329325
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n) = (8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!.
G.f.: x^3*(360*x^3-78*x^2-x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(8*x-1)). - Colin Barker, Nov 27 2012
a(n) = 29*a(n-1) - 343*a(n-2) + 2135*a(n-3) - 7504*a(n-4) + 14756*a(n-5) - 14832*a(n-6) + 5760*a(n-7) for n > 6. - Wesley Ivan Hurt, Oct 06 2017
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MAPLE
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MATHEMATICA
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Table[(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!, {n, 0, 25}] (* G. C. Greubel, Oct 06 2017 *)
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PROG
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(PARI) for(n=0, 25, print1((8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2 )/3!, ", ")) \\ G. C. Greubel, Oct 06 2017
(Magma) [(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!: n in [0..25]]; // G. C. Greubel, Oct 06 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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