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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 (list; graph; refs; listen; history; text; internal format)
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

G. C. Greubel, Table of n, a(n) for n = 3..1000

K. S. Brown, Dedekind's problem

Eric Weisstein's World of Mathematics, Antichain covers

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

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

Adjacent sequences:  A056071 A056072 A056073 * A056075 A056076 A056077

KEYWORD

nonn,nice,easy

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Jul 26 2000

STATUS

approved

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Last modified September 25 13:37 EDT 2021. Contains 347654 sequences. (Running on oeis4.)