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Number of ordered 4-multiantichains on an n-set.
4

%I #11 Sep 08 2022 08:45:13

%S 1,2,18,206,3690,91742,2493738,63266366,1449722250,30406367582,

%T 595643428458,11087927110526,198731319099210,3462982712427422,

%U 59088178966503978,992435464713354686,16472174763523362570,270964491631927159262,4427273424527020664298

%N Number of ordered 4-multiantichains on an n-set.

%H G. C. Greubel, <a href="/A092882/b092882.txt">Table of n, a(n) for n = 0..825</a>

%F a(n) = 16^n - 12*12^n + 24*10^n + 4*9^n - 12*8^n + 6*7^n - 72*6^n + 72*5^n + 36*4^n - 72*3^n + 26*2^n.

%F G.f.: -(1159418880*x^10 -1168935552*x^9 +583922688*x^8 -190907480*x^7 +43558356*x^6 -6961978*x^5 +771571*x^4 -58030*x^3 +2824*x^2 -80*x +1) / ((2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(12*x -1)*(16*x -1)). - _Colin Barker_, Jul 11 2013

%t Table[16^n - 12*12^n + 24*10^n + 4*9^n - 12*8^n + 6*7^n - 72*6^n + 72*5^n + 36*4^n - 72*3^n + 26*2^n, {n, 0, 50}] (* _G. C. Greubel_, Oct 06 2017 *)

%o (PARI) for(n=0,50, print1(16^n - 12*12^n + 24*10^n + 4*9^n - 12*8^n + 6*7^n - 72*6^n + 72*5^n + 36*4^n - 72*3^n + 26*2^n, ", ")) \\ _G. C. Greubel_, Oct 06 2017

%o (Magma) [16^n - 12*12^n + 24*10^n + 4*9^n - 12*8^n + 6*7^n - 72*6^n + 72*5^n + 36*4^n - 72*3^n + 26*2^n: n in [0..50]]; // _G. C. Greubel_, Oct 06 2017

%Y Cf. A092880, A092881, A092883, A092884.

%K nonn,easy

%O 0,2

%A Goran Kilibarda, _Vladeta Jovovic_, Mar 10 2004

%E More terms from _Colin Barker_, Jul 11 2013