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A051113
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Number of monotone Boolean functions of n variables with 5 mincuts.
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11
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0, 0, 0, 0, 6, 2146, 304752, 25400564, 1557306954, 78817977462, 3513106214484, 143429796694888, 5501383287745422, 201652447559180618, 7148287976359243896, 247151326758617289372, 8386495692534098616210, 280574309728711561269214, 9286566498536162168164188
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OFFSET
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0,5
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REFERENCES
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J. L. Arocha, Antichains in ordered sets, (in Spanish) An. Inst. Mat. UNAM, vol. 27, 1987, 1-21.
V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean function, Belgrade, 1999, in preparation.
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LINKS
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FORMULA
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a(n) = 1/5! * (32^n-20 * 24^n+ 60 * 20^n+ 20 * 18^n+ 10 * 17^n-110 * 16^n-120 * 15^n+ 150 * 14^n+ 120 * 13^n-240 * 12^n+ 20 * 11^n+ 240 * 10^n+ 40 * 9^n-205 * 8^n+ 60 * 7^n-210 * 6^n+ 210 * 5^n+ 50 * 4^n-100 * 3^n+ 24 * 2^n).
G.f.: -2*x^4*(140561100029952000*x^15 -73258140662784000*x^14 -8396658614522880*x^13 +15284070825850368*x^12 -4918391338514880*x^11 +748203166795520*x^10 -45197506544400*x^9 -3280961201664*x^8 +887950976060*x^7 -80597007540*x^6 +3942400065*x^5 -98697251*x^4 +532770*x^3 +26970*x^2 -335*x -3) / ((2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)*(11*x -1)*(12*x -1)*(13*x -1)*(14*x -1)*(15*x -1)*(16*x -1)*(17*x -1)*(18*x -1)*(20*x -1)*(24*x -1)*(32*x -1)). - Colin Barker, Jul 14 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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