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A190963
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a(n) = 3*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
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2
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0, 1, 3, 0, -27, -81, 0, 729, 2187, 0, -19683, -59049, 0, 531441, 1594323, 0, -14348907, -43046721, 0, 387420489, 1162261467, 0, -10460353203, -31381059609, 0, 282429536481, 847288609443, 0, -7625597484987, -22876792454961, 0, 205891132094649
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3, -9).
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FORMULA
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a(n) = (1/9*I)*sqrt(3)*((3/2-(3/2*I)*sqrt(3))^n - (3/2+(3/2*I)* sqrt(3))^n). - Paolo P. Lava, Jun 01 2011
G.f.: x/(1-3*x+9*x^2). - Philippe Deléham, Oct 11 2011
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MATHEMATICA
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LinearRecurrence[{3, -9}, {0, 1}, 50]
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PROG
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(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3*x+9*x^2))) \\ G. C. Greubel, Jan 25 2018
(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 3*Self(n-1) - 9*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018
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CROSSREFS
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Cf. A190958 (index to generalized Fibonacci sequences).
Sequence in context: A138543 A238104 A143769 * A296436 A215588 A215683
Adjacent sequences: A190960 A190961 A190962 * A190964 A190965 A190966
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KEYWORD
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sign
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AUTHOR
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Vladimir Joseph Stephan Orlovsky, May 24 2011
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STATUS
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approved
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