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%I #21 Sep 08 2022 08:45:11
%S 1,2,6,28,190,1692,16766,166028,1586430,14580412,129654526,1123451628,
%T 9544185470,79881877532,661135445886,5425962250828,44250287565310,
%U 359161631645052,2904756409742846,23429320590259628,188594431902253950
%N Number of 3-multiantichains of an n-set.
%H G. C. Greubel, <a href="/A084870/b084870.txt">Table of n, a(n) for n = 0..1000</a>
%H Goran Kilibarda and Vladeta Jovovic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL7/Kilibarda/kili2.html">Antichains of Multisets</a>, J. Integer Seqs., Vol. 7, 2004.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (28,-315,1820,-5684,9072,-5760).
%F a(n) = (1/3!)*(8^n - 6*6^n + 6*5^n + 9*4^n - 18*3^n + 14*2^n).
%F G.f.: ( 1-26*x+265*x^2-1330*x^3+3340*x^4-3432*x^5 ) / ( (6*x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(8*x-1)*(5*x-1) ). - _R. J. Mathar_, Jul 08 2011
%t Table[(8^n - 6*6^n + 6*5^n + 9*4^n - 18*3^n + 14*2^n)/6, {n, 0, 50}] (* _G. C. Greubel_, Oct 08 2017 *)
%o (PARI) for(n=0,50, print1((8^n - 6*6^n + 6*5^n + 9*4^n - 18*3^n + 14*2^n)/6, ", ")) \\ _G. C. Greubel_, Oct 08 2017
%o (Magma) [(8^n - 6*6^n + 6*5^n + 9*4^n - 18*3^n + 14*2^n)/6: n in [0..50]]; // _G. C. Greubel_, Oct 08 2017
%Y Cf. A016269, A047707, A051112-A051118, A084869-A084883.
%K nonn
%O 0,2
%A Goran Kilibarda, _Vladeta Jovovic_, Jun 10 2003