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A163062
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a(n) = ((3+sqrt(5))*(1+sqrt(5))^n + (3-sqrt(5))*(1-sqrt(5))^n)/2.
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3
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3, 8, 28, 88, 288, 928, 3008, 9728, 31488, 101888, 329728, 1067008, 3452928, 11173888, 36159488, 117014528, 378667008, 1225392128, 3965452288, 12832473088, 41526755328, 134383403008, 434873827328, 1407281266688
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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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a(n) = 2*a(n-1) + 4*a(n-2) for n > 1; a(0) = 3, a(1) = 8.
G.f.: (3+2*x)/(1-2*x-4*x^2).
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MATHEMATICA
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CoefficientList[Series[(3+2*x)/(1-2*x-4*x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 4}, {3, 8}, 30] (* G. C. Greubel, Dec 22 2017 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((3+r)*(1+r)^n+(3-r)*(1-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009
(Magma) I:=[3, 8]; [n le 2 select I[n] else 2*Self(n-1) + 4*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 22 2017
(PARI) x='x+O('x^30); Vec((3+2*x)/(1-2*x-4*x^2)) \\ G. C. Greubel, Dec 22 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
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EXTENSIONS
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STATUS
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approved
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