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%I #19 Sep 08 2022 08:44:59
%S 0,0,0,1,30,605,9030,110901,1200150,11932285,111885510,1006471301,
%T 8786447670,75039565965,630534185190,5234341175701,43059373189590,
%U 351805681631645,2859550165976070,23152657123816101,186907026783617910,1505512392025329325
%N Number of 3-element proper antichains of an n-element set.
%H G. C. Greubel, <a href="/A051303/b051303.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (29,-343,2135,-7504,14756,-14832,5760).
%F a(n) = (8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!.
%F 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
%F 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
%p A051303:=n->(8^n -9*6^n +15*5^n -4*4^n -9*3^n +8*2^n -2)/3!: seq(A051303(n), n=0..30); # _Wesley Ivan Hurt_, Oct 06 2017
%t 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 *)
%o (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
%o (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
%Y Cf. A032263, A036239, A051112.
%K nonn,easy
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda, Zoran Maksimovic
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