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A083313
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a(0)=1; a(n) = 3^n - 2^(n-1) for n >= 1.
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11
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1, 2, 7, 23, 73, 227, 697, 2123, 6433, 19427, 58537, 176123, 529393, 1590227, 4774777, 14332523, 43013953, 129074627, 387289417, 1161999323, 3486260113, 10459304627, 31378962457, 94138984523, 282421147873, 847271832227, 2541832273897, 7625530376123
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OFFSET
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0,2
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COMMENTS
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Number of skinny Boolean functions f(x_1,...,x_n) that are also Horn functions. - Hugo Pfoertner, Mar 04 2019
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REFERENCES
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Donald E. Knuth, The Art of Computer Programming, Vol. 4, fascicle 1, section 7.1.4, pp. 134, 138, 139, 219, answer to exercise 172, Addison-Wesley, 2009.
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LINKS
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FORMULA
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a(n) = (2*3^n - (2^n - 0^n))/2.
a(0) = 1, a(n) = 3^n - 2^(n-1) for n >= 1.
G.f.: ((1-x) + (1-2*x)*(1-3*x))/(2*(1-2*x)*(1-3*x)).
E.g.f.: (2*exp(3*x) - exp(2*x) + exp(0))/2.
Let b(n) = 2*(3/2)^n - 1. Then A003063(n) = -b(1-n)*3^(n-1) for n > 0. a(n) = A064686(n) = b(n)*2^(n-1) for n > 0. - Michael Somos, Aug 06 2006
a(n) mod 100 = 23 for n = 4*k-1, k >= 1.
a(n) mod 100 = 27 for n = 4*k+1, k >= 1.
(End)
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MAPLE
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if n = 0 then
1;
else
3^n-2^(n-1) ;
end if;
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MATHEMATICA
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CoefficientList[Series[((1 - x) + (1 - 2 x) (1 - 3 x)) / (2 (1 - 2 x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 01 2015 *)
LinearRecurrence[{5, -6}, {1, 2, 7}, 30] (* Harvey P. Dale, Sep 04 2017 *)
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PROG
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(PARI) Vec(((1-x)+(1-2*x)*(1-3*x))/(2*(1-2*x)*(1-3*x)) + O(x^30)) \\ Michel Marcus, Jan 31 2015
(PARI) print1(1, ", ", s=2, ", " ); for(k=2, 27, s=2^(k-2)+3*s; print1(s, ", ")) \\ Hugo Pfoertner, Mar 04 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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