A056048 Number of 5-antichain covers of a labeled n-set.

0, 0, 0, 0, 6, 2116, 291966, 23312156, 1362515742, 65691305652, 2792020643502, 108871903828732, 3995501812110798, 140371634250355508, 4776934559777356158, 158783001150185585628, 5186356918189216064574, 167203226479257200020084, 5337930997910228958536334

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 25 2000

Keywords

• nonn

References

• 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)
• V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..670
• K. S. Brown, Dedekind's problem
• Eric Weisstein's World of Mathematics, Antichain covers

Crossrefs

Cf. A051113.

Programs

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

Mathematica

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 *)

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

Formula

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).