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%I #29 Jan 07 2024 15:47:46
%S 0,18,141,984,6762,46365,317808,2178306,14930349,102334152,701408730,
%T 4807526973,32951280096,225851433714,1548008755917,10610209857720,
%U 72723460248138,498454011879261,3416454622906704,23416728348467682
%N Fibonacci(4n)-3, or Fibonacci(2n-2)*Lucas(2n+2).
%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
%F G.f.: 3*x^2*(-6+x) / ( (x-1)*(x^2-7*x+1) ). a(n) = A033888(n)-3. - _R. J. Mathar_, Sep 03 2010
%p with(combinat): for n from 1 to 40 do printf(`%d,`,fibonacci(4*n)-3) od: # _James A. Sellers_, Mar 05 2003
%t Fibonacci[4Range[25]]-3 (* or *)
%t LinearRecurrence[{8,-8,1},{0,18,141},25] (* _Paolo Xausa_, Jan 07 2024 *)
%o (Magma) [Fibonacci(4*n)-3: n in [1..50]]; // _Vincenzo Librandi_, Apr 20 2011
%Y Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%K nonn,easy
%O 1,2
%A _R. K. Guy_, Mar 04 2003
%E More terms from _James A. Sellers_, Mar 05 2003