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A080042
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a(n) = 4*a(n-1)+3*a(n-2) for n>1, a(0)=2, a(1)=4.
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4
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2, 4, 22, 100, 466, 2164, 10054, 46708, 216994, 1008100, 4683382, 21757828, 101081458, 469599316, 2181641638, 10135364500, 47086382914, 218751625156, 1016265649366, 4721317472932, 21934066839826, 101900219778100
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OFFSET
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0,1
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COMMENTS
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This is the Lucas sequence V(4,-3). [Bruno Berselli, Jan 09 2013]
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LINKS
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Table of n, a(n) for n=0..21.
Wikipedia, Lucas sequence: Specific names.
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FORMULA
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G.f.: (2-4*x)/(1-4*x-3*x^2).
a(n) = (2+sqrt(7))^n+(2-sqrt(7))^n.
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MATHEMATICA
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CoefficientList[Series[(2 - 4 t)/(1 - 4 t - 3 t^2), {t, 0, 25}], t]
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PROG
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(Sage) [lucas_number2(n, 4, -3) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
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CROSSREFS
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Cf. A015530: Lucas sequence U(4,-3).
Sequence in context: A071298 A152104 A047035 * A165588 A110130 A019025
Adjacent sequences: A080039 A080040 A080041 * A080043 A080044 A080045
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KEYWORD
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nonn,easy
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003
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STATUS
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approved
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