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A049655
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a(n) = (F(8n+2)-1)/3, where F=A000045 (the Fibonacci sequence).
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2
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0, 18, 861, 40464, 1900962, 89304765, 4195423008, 197095576626, 9259296678429, 434989848309552, 20435263573870530, 960022398123605373, 45100617448235582016, 2118768997668948749394, 99537042272992355639517, 4676122217832971766307920
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 3*x*(-6+x) / ( (x-1)*(x^2-47*x+1) ). - R. J. Mathar, Oct 26 2015
a(n) = (-1+((47+21*sqrt(5))^(-n)*(-2^(1+n)*(9+4*sqrt(5))+(123+55*sqrt(5))*(2207+987*sqrt(5))^n))/(105+47*sqrt(5)))/3. - Colin Barker, Mar 06 2016
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MATHEMATICA
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(Fibonacci[8*Range[0, 20]+2]-1)/3 (* or *) LinearRecurrence[{48, -48, 1}, {0, 18, 861}, 20] (* Harvey P. Dale, Dec 02 2015 *)
RecurrenceTable[{a[0] == 0, a[1] == 18, a[n] == 47 a[n-1] - a[n-2] + 15}, a, {n, 30}] (* Vincenzo Librandi, Mar 06 2016 *)
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PROG
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(PARI) concat(0, Vec(3*x*(-6+x)/((x-1)*(x^2-47*x+1)) + O(x^25))) \\ Colin Barker, Mar 06 2016
(Magma) I:=[0, 18]; [n le 2 select I[n] else 47*Self(n-1)-Self(n-2)+15: n in [1..30]]; // Vincenzo Librandi, Mar 06 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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