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 A345189 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. 2
 1, 1, 6, 41, 330, 2882, 26604, 255313, 2521986, 25473638, 261898548, 2731724778, 28836047844, 307477681188, 3306988334808, 35833139582529, 390803960909106, 4286644113507902, 47258491871201508, 523372307883323566, 5819831138546794860, 64954314678710555612, 727371707764232349672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS G. C. Greubel, Table of n, a(n) for n = 1..925 Volkan Yildiz, Notes on algebraic structure of truth tables of bracketed formulae connected by implications, arXiv:2106.04728 [math.CO], 2021. FORMULA G.f.: (-2-sqrt(1-12*x)+sqrt(5+24*x+4*sqrt(1-12*x)))/6. a(n) = 2*A005159(n-1) - A345190(n). - G. C. Greubel, May 20 2022 MATHEMATICA 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 *) PROG (PARI) my(x='x+O('x^30)); Vec((-2-sqrt(1-12*x)+sqrt(5+24*x+4*sqrt(1-12*x)))/6) (SageMath) def A345189_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( (-2-sqrt(1-12*x)+sqrt(5+24*x+4*sqrt(1-12*x)))/6 ).list() a=A345189_list(40); a[1:] # G. C. Greubel, May 20 2022 CROSSREFS Cf. A005159 (unknown rows, shifted), A025226 (all rows), A345190 (true rows). Sequence in context: A199553 A225031 A307663 * A083430 A005011 A187814 Adjacent sequences: A345186 A345187 A345188 * A345190 A345191 A345192 KEYWORD nonn AUTHOR Michel Marcus, Jun 10 2021 STATUS approved

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Last modified August 14 22:14 EDT 2024. Contains 375167 sequences. (Running on oeis4.)