A056046 Number of 3-antichain covers of a labeled n-set.

0, 0, 0, 2, 56, 790, 8380, 76482, 638736, 5043950, 38390660, 285007162, 2079779416, 14995363110, 107204473740, 761823557042, 5390550296096, 38026057186270, 267656481977620, 1881017836414122, 13204444871932776, 92618543463601430, 649270263511862300

Offset

0,4

References

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..1000

K. S. Brown, Dedekind's problem

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.

Eric Weisstein's World of Mathematics, Antichain covers

Index entries for linear recurrences with constant coefficients, signature (22,-190,820,-1849,2038,-840).

Formula

a(n) = (1/6)*(7^n-6*5^n+6*4^n+3*3^n-6*2^n+2).

G.f.: -2*x^3*(31*x^2-6*x-1) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(7*x-1)). - Colin Barker, Nov 27 2012

Example

There are 2 3-antichain covers of a labeled 3-set: {{1},{2},{3}}, {{1,2},{1,3},{2,3}}.

Mathematica

Table[(1/6)*(7^n-6*5^n+6*4^n+3*3^n-6*2^n+2), {n, 0, 50}] (* G. C. Greubel, Oct 06 2017 *)
LinearRecurrence[{22, -190, 820, -1849, 2038, -840}, {0, 0, 0, 2, 56, 790}, 30] (* Harvey P. Dale, Dec 09 2017 *)

Prog

(PARI) for(n=0, 50, print1((1/6)*(7^n-6*5^n+6*4^n+3*3^n-6*2^n+2), ", ")) \\ G. C. Greubel, Oct 06 2017

Crossrefs

Cf. A047707.

Sequence in context: A287988 A193830 A196539 * A080313 A080268 A224297

Adjacent sequences: A056043 A056044 A056045 * A056047 A056048 A056049

Keyword

easy,nonn

Author

Vladeta Jovovic, Goran Kilibarda, Jul 25 2000

Status

approved