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A081006 a(n) = Fibonacci(4n) - 1, or Fibonacci(2n+1)*Lucas(2n-1). 1

%I

%S 2,20,143,986,6764,46367,317810,2178308,14930351,102334154,701408732,

%T 4807526975,32951280098,225851433716,1548008755919,10610209857722,

%U 72723460248140,498454011879263,3416454622906706,23416728348467684,160500643816367087

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

%C Apart from the offset, the same as A003481. - _R. J. Mathar_, Sep 18 2008

%D Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.

%H Nathaniel Johnston, <a href="/A081006/b081006.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-8,1).

%F a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).

%F a(n) = -1+(3/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(7/10)*sqrt(5)*{[(7/2)+(3 /2)*sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0. - _Paolo P. Lava_, Dec 01 2008

%F G.f.: x*(2+4*x-x^2)/((1-x)*(1-7*x+x^2)). - _Colin Barker_, Jun 24 2012

%p with(combinat) for n from 0 to 30 do printf(`%d,`,fibonacci(4*n)-1) od # _James A. Sellers_, Mar 03 2003

%t Fibonacci[4*Range[30]]-1 (* or *) LinearRecurrence[{8,-8,1}, {2,20,143}, 30] (* _Harvey P. Dale_, Mar 19 2018 *)

%o (MAGMA) [Fibonacci(4*n)-1: n in [1..30]]; // _Vincenzo Librandi_, Apr 15 2011

%o (PARI) vector(30, n, fibonacci(4*n)-1) \\ _G. C. Greubel_, Jul 15 2019

%o (Sage) [fibonacci(4*n)-1 for n in (1..30)] # _G. C. Greubel_, Jul 15 2019

%o (GAP) List([1..30], n-> Fibonacci(4*n)-1); # _G. C. Greubel_, Jul 15 2019

%Y Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers).

%K nonn,easy

%O 1,1

%A _R. K. Guy_, Mar 01 2003

%E More terms from _James A. Sellers_, Mar 03 2003

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)