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A081008 a(n) = Fibonacci(4n+2) - 1, or Fibonacci(2n)*Lucas(2n+2).

%I A081008 #32 Jul 02 2025 16:02:01
%S A081008 0,7,54,376,2583,17710,121392,832039,5702886,39088168,267914295,
%T A081008 1836311902,12586269024,86267571271,591286729878,4052739537880,
%U A081008 27777890035287,190392490709134,1304969544928656,8944394323791463,61305790721611590,420196140727489672
%N A081008 a(n) = Fibonacci(4n+2) - 1, or Fibonacci(2n)*Lucas(2n+2).
%D A081008 Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
%H A081008 Nathaniel Johnston, <a href="/A081008/b081008.txt">Table of n, a(n) for n = 0..500</a>
%H A081008 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).
%F A081008 a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
%F A081008 G.f.: x*(7-2*x)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 24 2012
%p A081008 with(combinat) for n from 0 to 30 do printf(`%d,`,fibonacci(4*n+2)-1) od # _James Sellers_, Mar 03 2003
%t A081008 Fibonacci[4Range[25]-2]-1 (* or *)
%t A081008 LinearRecurrence[{8,-8,1},{0,7,54},25] (* _Paolo Xausa_, Jan 08 2024 *)
%o A081008 (Magma) [Fibonacci(4*n+2)-1: n in [0..30]]; // _Vincenzo Librandi_, Apr 15 2011
%o A081008 (PARI) vector(30, n, n--; fibonacci(4*n+2)-1) \\ _G. C. Greubel_, Jul 14 2019
%o A081008 (Sage) [fibonacci(4*n+2)-1 for n in (0..30)] # _G. C. Greubel_, Jul 14 2019
%o A081008 (GAP) List([0..30], n-> Fibonacci(4*n+2)-1); # _G. C. Greubel_, Jul 14 2019
%Y A081008 Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).
%K A081008 nonn,easy
%O A081008 0,2
%A A081008 _R. K. Guy_, Mar 01 2003
%E A081008 More terms from _James Sellers_, Mar 03 2003