|
%I #15 Sep 08 2022 08:45:01
%S 0,0,0,0,6,2116,291966,23312156,1362515742,65691305652,2792020643502,
%T 108871903828732,3995501812110798,140371634250355508,
%U 4776934559777356158,158783001150185585628,5186356918189216064574,167203226479257200020084,5337930997910228958536334
%N Number of 5-antichain covers of a labeled n-set.
%D V. Jovovic and G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6)
%D V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.
%H G. C. Greubel, <a href="/A056048/b056048.txt">Table of n, a(n) for n = 0..670</a>
%H K. S. Brown, <a href="http://www.mathpages.com/home/kmath515.htm">Dedekind's problem</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cover.html">Antichain covers</a>
%F a(n) = (1/5!) * (31^n - 20*23^n + 60*19^n + 20*17^n + 10*16^n - 110*15^n - 120*14^n + 150*13^n + 120*12^n - 240*11^n + 20*10^n + 240*9^n + 40*8^n - 205*7^n + 60*6^n - 210*5^n + 210*4^n + 50*3^n - 100*2^n + 24).
%t Table[(1/5!)*(31^n - 20*23^n + 60*19^n + 20*17^n + 10*16^n - 110*15^n - 120*14^n + 150*13^n + 120*12^n - 240*11^n + 20*10^n + 240*9^n + 40*8^n - 205*7^n + 60*6^n - 210*5^n + 210*4^n + 50*3^n - 100*2^n + 24), {n,0,25}] (* _G. C. Greubel_, Oct 07 2017 *)
%o (PARI) for(n=0,25, print1((31^n - 20*23^n + 60*19^n + 20*17^n + 10*16^n - 110*15^n - 120*14^n + 150*13^n + 120*12^n - 240*11^n + 20*10^n + 240*9^n + 40*8^n - 205*7^n + 60*6^n - 210*5^n + 210*4^n + 50*3^n - 100*2^n + 24)/120, ", ")) \\ _G. C. Greubel_, Oct 07 2017
%o (Magma) [(31^n - 20*23^n + 60*19^n + 20*17^n + 10*16^n - 110*15^n - 120*14^n + 150*13^n + 120*12^n - 240*11^n + 20*10^n + 240*9^n + 40*8^n - 205*7^n + 60*6^n - 210*5^n + 210*4^n + 50*3^n - 100*2^n + 24)/120: n in [0..25]]; // _G. C. Greubel_, Oct 07 2017
%Y Cf. A051113.
%K nonn
%O 0,5
%A _Vladeta Jovovic_, Goran Kilibarda, Zoran Maksimovic, Jul 25 2000
|
