%I #21 Sep 08 2022 08:44:58
%S 0,18,861,40464,1900962,89304765,4195423008,197095576626,
%T 9259296678429,434989848309552,20435263573870530,960022398123605373,
%U 45100617448235582016,2118768997668948749394,99537042272992355639517,4676122217832971766307920
%N a(n) = (F(8n+2)-1)/3, where F=A000045 (the Fibonacci sequence).
%H Colin Barker, <a href="/A049655/b049655.txt">Table of n, a(n) for n = 0..500</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (48,-48,1).
%F G.f.: 3*x*(-6+x) / ( (x-1)*(x^2-47*x+1) ). - _R. J. Mathar_, Oct 26 2015
%F 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
%F a(n) = 47*a(n-1)-a(n-2)+15. - _Vincenzo Librandi_, Mar 06 2016
%t (Fibonacci[8*Range[0,20]+2]-1)/3 (* or *) LinearRecurrence[{48,-48,1},{0,18,861},20] (* _Harvey P. Dale_, Dec 02 2015 *)
%t 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 *)
%o (PARI) concat(0, Vec(3*x*(-6+x)/((x-1)*(x^2-47*x+1)) + O(x^25))) \\ _Colin Barker_, Mar 06 2016
%o (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
%Y Cf. A049656, A049686.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_