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.
1, 5, 30, 229, 1938, 17530, 165852, 1621133, 16242474, 165923854, 1721675460, 18095802306, 192256162740, 2061367432212, 22276538889912, 242387718986301, 2653259550491034, 29198054511893638, 322835545567447092, 3584671507685675894, 39955514234936341980, 446897274497509974508
Offset: 1
Keywords
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.
Programs
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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 *) -
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
Formula
G.f.: (4-sqrt(1-12*x)-sqrt(5+24*x+4*sqrt(1-12*x)))/6.