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A056074
Number of 3-element ordered antichain covers of an unlabeled n-element set.
4
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
OFFSET
3,1
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
K. S. Brown, Dedekind's problem
Eric Weisstein's World of Mathematics, Antichain covers
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). - Harvey P. Dale, Jul 12 2011
G.f.: (-2-3*x+6*x^2-2*x^3)/(x-1)^7. - Harvey P. Dale, Jul 12 2011
a(n) = n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720. - Charles R Greathouse IV, Feb 19 2017
MAPLE
A056074:=n->n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720: seq(A056074(n), n=3..60); # Wesley Ivan Hurt, Oct 06 2017
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}] (* Harvey P. Dale, Jul 12 2011 *)
PROG
(PARI) a(n)=n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720 \\ Charles R Greathouse IV, Feb 19 2017
(Magma) [n*(n^5 + 21*n^4 - 5*n^3 - 345*n^2 + 724*n - 396)/720: n in [3..25]]; // G. C. Greubel, Oct 06 2017
CROSSREFS
Cf. A056046 for 3-antichain (unordered) covers of a labeled n-set, A047707. See also A056090, A056093.
Sequence in context: A107815 A042803 A182876 * A320685 A268784 A338088
KEYWORD
nonn,nice,easy
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Jul 26 2000
STATUS
approved