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A162852
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a(n) = 3*a(n-2) for n > 2; a(1) = 3, a(2) = -1.
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3
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3, -1, 9, -3, 27, -9, 81, -27, 243, -81, 729, -243, 2187, -729, 6561, -2187, 19683, -6561, 59049, -19683, 177147, -59049, 531441, -177147, 1594323, -531441, 4782969, -1594323, 14348907, -4782969, 43046721, -14348907, 129140163
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OFFSET
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1,1
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COMMENTS
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Third binomial transform is A162560.
Equivalently, 3^n followed by -3^(n-1), n > 0. - Muniru A Asiru, Oct 25 2018
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LINKS
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FORMULA
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a(n) = ((4-5*(-1)^n)*3^(1/4*(2*n-1+(-1)^n)))/3.
E.g.f.: (1 - cosh(sqrt(3)*x) + 3*sqrt(3)*sinh(sqrt(3)*x))/3. - G. C. Greubel, Oct 24 2018
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MAPLE
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MATHEMATICA
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Rest[CoefficientList[Series[x*(3-x)/(1-3*x^2), {x, 0, 40}], x]] (* or *) LinearRecurrence[{0, 3}, {3, -1}, 40] (* G. C. Greubel, Oct 24 2018 *)
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PROG
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(Magma) [ n le 2 select 7-4*n else 3*Self(n-2): n in [1..34] ];
(PARI) x='x+O('x^40); Vec(x*(3-x)/(1-3*x^2)) \\ G. C. Greubel, Oct 24 2018
(GAP) a:=[3, -1];; for n in [3..25] do a[n]:=3*a[n-2]; od; a; # Muniru A Asiru, Oct 25 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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