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

0,5

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

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A051112.

Sequence in context: A023113 A322247 A177837 * A281436 A197671 A051112

Adjacent sequences: A056044 A056045 A056046 * A056048 A056049 A056050

Keyword

nonn,easy

Author

Vladeta Jovovic, Goran Kilibarda, Jul 25 2000

Extensions

More terms from Colin Barker, Jul 11 2013

Status

approved