A056047 Number of 4-antichain covers of a labeled n-set.

0, 0, 0, 0, 25, 1895, 70370, 1868650, 41062035, 802349205, 14514339340, 249104207000, 4120588431245, 66392465654515, 1049608974433110, 16365222591176550, 252584307401055655, 3869412829938587825, 58950765174112191680, 894469325684769169300, 13531152125348360663265

Offset: 0

Author

Vladeta Jovovic, Goran Kilibarda, Jul 25 2000

Keywords

• nonn
• easy

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..845
• K. S. Brown, Dedekind's problem
• Eric Weisstein's World of Mathematics, Antichain covers

Crossrefs

Cf. A051112.

Programs

Magma

[(15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6)/24: n in [0..25]]; // G. C. Greubel, Oct 07 2017

Mathematica

Table[(1/4!)*(15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6), {n,0,25}] (* G. C. Greubel, Oct 07 2017 *)

PARI

for(n=0,25, print1((15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6)/24, ", ")) \\ G. C. Greubel, Oct 07 2017

Formula

a(n) = (1/4!)*(15^n - 12*11^n + 24*9^n + 4*8^n - 18*7^n + 6*6^n - 36*5^n + 36*4^n + 11*3^n - 22*2^n + 6).

G.f.: -5*x^4*(517752*x^6 -251184*x^5 +4757*x^4 +12696*x^3 -1810*x^2 +24*x +5) / ((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)*(11*x -1)*(15*x -1)). - Colin Barker, Jul 11 2013

Extensions

More terms from Colin Barker, Jul 11 2013