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A056046
Number of 3-antichain covers of a labeled n-set.
8
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
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
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 25 2000
STATUS
approved