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
Examples
There are 2 3-antichain covers of a labeled 3-set: {{1},{2},{3}}, {{1,2},{1,3},{2,3}}.
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).
Crossrefs
Cf. A047707.
Programs
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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 *) -
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
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