A056049 Number of 6-antichain covers of a labeled n-set.

1, 1375, 751192, 187216960, 29650991279, 3554308158345, 355235190457414, 31360944940860370, 2536696962910365277, 192628889065040142715, 13964833124133659520116, 978098391719401853480580

Offset: 4

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

• Vincenzo Librandi, Table of n, a(n) for n = 4..200
• K. S. Brown, Dedekind's problem
• Eric Weisstein's World of Mathematics, Antichain covers

Crossrefs

Cf. A051114.

Programs

Mathematica

Table[(1 / 6!) (63^n - 30*47^n + 120*39^n + 60*35^n + 60 *33^n - 12*32^n - 345*31^n-720*29^n + 810*27^n + 120*26^n + 480*25^n + 360*24^n - 480*23^n - 720*22^n -240*21^n - 540*20^n + 1380*19^n + 750*18^n + 60*17^n - 210*16^n - 1535*15^n - 1820*14^n + 2250*13^n + 1800*12^n - 2820*11^n + 300*10^n + 2040*9^n + 340*8^n - 1815*7^n + 510*6^n - 1350*5^n + 1350*4^n + 274*3^n -548*2^n + 120), {n, 4, 20}] (* Vincenzo Librandi, Jun 17 2013 *)

Formula

a(n)=(1/6!)*(63^n - 30*47^n + 120*39^n + 60*35^n + 60*33^n - 12*32^n - 345*31^n - 720*29^n + 810*27^n + 120*26^n + 480*25^n + 360*24^n - 480*23^n - 720*22^n - 240*21^n - 540*20^n + 1380*19^n + 750*18^n + 60*17^n - 210*16^n - 1535*15^n - 1820*14^n + 2250*13^n + 1800*12^n - 2820*11^n + 300*10^n + 2040*9^n + 340*8^n - 1815*7^n + 510*6^n - 1350*5^n + 1350*4^n + 274*3^n - 548*2^n + 120).