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%I #21 Sep 08 2022 08:44:58
%S 4,203,9552,448756,21081995,990405024,46527954148,2185823439947,
%T 102687173723376,4824111341558740,226630545879537419,
%U 10646811544996699968,500173512068965361092,23497508255696375271371,1103882714505660672393360,51858990073510355227216564
%N a(n) = (F(8n+7)-1)/3, where F=A000045 (the Fibonacci sequence).
%H Colin Barker, <a href="/A049656/b049656.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.: ( -4-11*x ) / ( (x-1)*(x^2-47*x+1) ). - _R. J. Mathar_, Oct 26 2015
%F a(n) = (-1+((94+42*sqrt(5))^(-n)*(4^n*(1+sqrt(5))+2*(47+21*sqrt(5))^(2*n)*(682+305*sqrt(5))))/(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[8Range[0,20]+7]-1)/3 (* _Harvey P. Dale_, Sep 21 2011 *)
%t RecurrenceTable[{a[0] == 4, a[1] == 203, a[n] == 47 a[n-1] - a[n-2] + 15}, a, {n, 30}] (* _Vincenzo Librandi_, Mar 06 2016 *)
%o (PARI) Vec((-4-11*x)/((x-1)*(x^2-47*x+1)) + O(x^25)) \\ _Colin Barker_, Mar 06 2016
%o (Magma) I:=[4,203]; [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. A049655, A049686.
%K nonn,easy
%O 0,1
%A _Clark Kimberling_
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