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A214733
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a(n) = - a(n-1) - 3*a(n-2), with a(0) = 0 and a(1) = 1.
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1
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0, 1, -1, -2, 5, 1, -16, 13, 35, -74, -31, 253, -160, -599, 1079, 718, -3955, 1801, 10064, -15467, -14725, 61126, -16951, -166427, 217280, 282001, -933841, 87838, 2713685, -2977199, -5163856, 14095453, 1396115, -43682474, 39494129, 91553293, -210035680
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OFFSET
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0,4
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COMMENTS
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The sequence a(n) is conjugate with A110523 by the following alternative relations: either ((-1 + i*sqrt(11))/2)^n = A110523(n) + a(n)*(-1 + i*sqrt(11))/2, or ((-1 - i*sqrt(11))/2)^n = A110523(n) + a(n)*(-1 - i*sqrt(11))/2 (see also comments to A110523, where these relations and many other facts on a(n) is presented).
Apart from signs, the Lucas U(P=1,Q=3)-sequence. - R. J. Mathar, Oct 24 2012
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REFERENCES
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R. Witula, On Some Applications of Formulae for Unimodular Complex Numbers, Jacek Skalmierski's Press, Gliwice 2011.
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LINKS
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Table of n, a(n) for n=0..36.
Wikipedia, Lucas sequence
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FORMULA
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a(n+2) = - a(n+1) - 3a(n).
a(n) = (i*sqrt(11)/11)*(((-1 - i*sqrt(11))/2)^n - ((-1 + i*sqrt(11))/2)^n).
G.f.: x/(1 + x + 3*x^2).
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MATHEMATICA
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LinearRecurrence[{-1, -3}, {0, 1}, 40] (* T. D. Noe, Jul 30 2012 *)
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PROG
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(PARI) concat(0, Vec(1/(1+x+3*x^2)+O(x^99))) \\ Charles R Greathouse IV, Oct 01 2012
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CROSSREFS
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Cf. A106852, A110523.
Sequence in context: A186361 A197365 A121579 * A106852 A162975 A187244
Adjacent sequences: A214730 A214731 A214732 * A214734 A214735 A214736
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KEYWORD
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sign,easy
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AUTHOR
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Roman Witula, Jul 27 2012
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STATUS
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approved
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