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A345189
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Number of rows with the value "false" in the Kleene truth tables of all bracketed formulae with n distinct propositions p1, ..., pn connected by the binary connective of implication.
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2
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1, 1, 6, 41, 330, 2882, 26604, 255313, 2521986, 25473638, 261898548, 2731724778, 28836047844, 307477681188, 3306988334808, 35833139582529, 390803960909106, 4286644113507902, 47258491871201508, 523372307883323566, 5819831138546794860, 64954314678710555612, 727371707764232349672
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: (-2-sqrt(1-12*x)+sqrt(5+24*x+4*sqrt(1-12*x)))/6.
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MATHEMATICA
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CoefficientList[Series[(-2 -Sqrt[1-12*x] +Sqrt[5 +24*x +4*Sqrt[1-12*x]])/6, {x, 0, 40}], x]//Rest (* G. C. Greubel, May 20 2022 *)
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PROG
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(PARI) my(x='x+O('x^30)); Vec((-2-sqrt(1-12*x)+sqrt(5+24*x+4*sqrt(1-12*x)))/6)
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (-2-sqrt(1-12*x)+sqrt(5+24*x+4*sqrt(1-12*x)))/6 ).list()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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