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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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5
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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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LINKS
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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.
G.f.: G(0)/x -2/x, where G(k)= 1 + 1/(1 - x*(7*k-4)/(x*(7*k+3) - 2/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013
a(n) = [x^n] ( (1 + 4*x + sqrt(1 + 8*x + 28*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015
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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 range(0, 22)] # Zerinvary Lajos, May 14 2009
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CROSSREFS
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Cf. A015530: Lucas sequence U(4,-3).
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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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