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A056074
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Number of 3-element ordered antichain covers of an unlabeled n-element set.
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3
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2, 17, 71, 212, 518, 1106, 2142, 3852, 6534, 10571, 16445, 24752, 36218, 51716, 72284, 99144, 133722, 177669, 232883, 301532, 386078, 489302, 614330, 764660, 944190, 1157247, 1408617, 1703576
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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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.
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LINKS
| K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers"
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FORMULA
| a(n)=C(n + 6, 6) - 6*C(n + 4, 4) + 6*C(n + 3, 3) + 3*C(n + 2, 2) - 6*C(n + 1, 1) + 2*C(n, 0).
a(0)=2, a(1)=17, a(2)=71, a(3)=212, a(4)=518, a(5)=1106, a(6)=2142, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)- 7*a(n-6)+ a(n-7) [From Harvey P. Dale, Jul 12 2011]
G.f.: (-2-3*x+6*x^2-2*x^3)/(x-1)^7 [From Harvey P. Dale, Jul 12 2011]
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MATHEMATICA
| LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {2, 17, 71, 212, 518, 1106, 2142}, 30] (* or *) Table[Binomial[n+6, 6]-6Binomial[n+4, 4]+6Binomial[n+3, 3]+ 3Binomial[n+2, 2]- 6Binomial[n+1, 1]+ 2Binomial[n, 0], {n, 3, 30}] (* From Harvey P. Dale, Jul 12 2011 *)
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CROSSREFS
| Cf. A056046 for 3-antichain (unordered) covers of a labeled n-set, A047707. See also A056090, A056093.
Sequence in context: A107815 A042803 A182876 * A155715 A054568 A183175
Adjacent sequences: A056071 A056072 A056073 * A056075 A056076 A056077
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Vladeta Jovovic, Goran Kilibarda (vladeta(AT)eunet.rs), Jul 26 2000
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