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A016177
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a(n) = 8^n - 7^n.
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14
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0, 1, 15, 169, 1695, 15961, 144495, 1273609, 11012415, 93864121, 791266575, 6612607849, 54878189535, 452866803481, 3719823438255, 30436810578889, 248242046141055, 2019169299698041, 16385984911571535, 132716292890482729, 1073129238309234975, 8664826172771491801
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OFFSET
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0,3
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COMMENTS
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Number of ways to assign truth values to n ternary conjunctions connected by disjunctions such that the proposition is true. For example, a(2) = 15, since for the proposition '(a & b & c) v (d & e & f)' there are 15 assignments that make the proposition true. - Ori Milstein, Dec 22 2022
Equivalently, the number of length-n words over the alphabet {0,1,...,7} with at least one letter = 7. - Joerg Arndt, Jan 01 2023
a(n) is also the number of n-digit numbers whose smallest decimal digit is 2. - Stefano Spezia, Nov 15 2023
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LINKS
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FORMULA
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G.f.: x/((1-7x)*(1-8x)).
a(n) = numerator(f(n-1)) where f(n) = Integral_{x=0..1/4} (1-x/2)^n dx. And denominator(f(n)) = 4*(n+1)*8^n. - Al Hakanson (hawkuu(AT)excite.com), Feb 22 2004 [corrected by Michel Marcus, Dec 23 2022]
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MATHEMATICA
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PROG
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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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STATUS
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approved
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