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A056093
Number of 5-element ordered antichain covers of an unlabeled n-element set.
4
30, 2176, 54036, 709956, 6290051, 42606671, 237197942, 1135834242, 4823607212, 18563958502, 65783057592, 217240417628, 674884181813, 1987124979703, 5579019610088, 15010371955248, 38862554420034, 97163223921924, 235290234202584, 553296290481584
OFFSET
4,1
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
FORMULA
a(n)=C(n + 30, 30) - 20*C(n + 22, 22) + 60*C(n + 18, 18) + 20*C(n + 16, 16) + 10*C(n + 15, 15) - 110*C(n + 14, 14) - 120*C(n + 13, 13) + 150*C(n + 12, 12) + 120*C(n + 11, 11) - 240*C(n + 10, 10) + 20*C(n + 9, 9) + 240*C(n + 8, 8) + 40*C(n + 7, 7) - 205*C(n + 6, 6) + 60*C(n + 5, 5) - 210*C(n + 4, 4) + 210*C(n + 3, 3) + 50*C(n + 2, 2) - 100*C(n + 1, 1) + 24*C(n, 0).
MATHEMATICA
Table[Binomial[n+30, 30]-20 Binomial[n+22, 22]+60 Binomial[n+18, 18]+ 20 Binomial[n+16, 16]+ 10 Binomial[n+15, 15]-110 Binomial[n+14, 14]- 120 Binomial[n+13, 13]+ 150 Binomial[n+12, 12]+ 120 Binomial[n+11, 11]- 240 Binomial[n+10, 10]+ 20 Binomial[n+9, 9]+ 240 Binomial[n+8, 8]+ 40 Binomial[n+7, 7]- 205 Binomial[n+6, 6]+ 60 Binomial[n+5, 5]- 210 Binomial[n+4, 4]+ 210 Binomial[n+3, 3]+ 50 Binomial[n+2, 2]- 100 Binomial[n+1, 1]+ 24 Binomial[n, 0], {n, 4, 30}] (* Harvey P. Dale, Sep 06 2011 *)
CROSSREFS
Cf. A056048 for 5-antichain (unordered) covers of a labeled n-set, A051113. See also A056074, A056090.
Sequence in context: A255958 A092617 A295446 * A056070 A301377 A054647
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 27 2000
EXTENSIONS
More terms from Harvey P. Dale, Sep 06 2011
STATUS
approved