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 A345190 Number of rows with the value "true" in the Kleene truth tables of all bracketed formulae with n distinct propositions p1, ..., pn connected by the binary connective of implication. 2
 1, 5, 30, 229, 1938, 17530, 165852, 1621133, 16242474, 165923854, 1721675460, 18095802306, 192256162740, 2061367432212, 22276538889912, 242387718986301, 2653259550491034, 29198054511893638, 322835545567447092, 3584671507685675894, 39955514234936341980, 446897274497509974508 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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.: (4-sqrt(1-12*x)-sqrt(5+24*x+4*sqrt(1-12*x)))/6. a(n) = 2*A005159(n-1) - A345189(n). - G. C. Greubel, May 20 2022 MATHEMATICA CoefficientList[Series[(4 -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((4-sqrt(1-12*x)-sqrt(5+24*x+4*sqrt(1-12*x)))/6) (SageMath) def A345190_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( (4-sqrt(1-12*x)-sqrt(5+24*x+4*sqrt(1-12*x)))/6 ).list() a=A345190_list(40); a[1:] # G. C. Greubel, May 20 2022 CROSSREFS Cf. A005159 (unknown rows, shifted), A025226 (all rows), A345189 (false rows). Sequence in context: A318920 A363908 A167892 * A144498 A201368 A072213 Adjacent sequences: A345187 A345188 A345189 * A345191 A345192 A345193 KEYWORD nonn AUTHOR Michel Marcus, Jun 10 2021 STATUS approved

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Last modified August 15 19:07 EDT 2024. Contains 375173 sequences. (Running on oeis4.)